From 68f84be7e6557ee88bf2cc48166c4e5579518290 Mon Sep 17 00:00:00 2001
From: kevinsung <kevinsung@users.noreply.github.com>
Date: Thu, 19 Oct 2023 16:30:26 +0000
Subject: [PATCH] deploy: eba4655277fecb8ebbb55999423617ba0c369391

---
 .../api/generated/ffsim.hamiltonians.doctree  | Bin 70584 -> 70838 bytes
 .doctrees/environment.pickle                  | Bin 1566939 -> 1568358 bytes
 .../nbsphinx/tutorials/01-introduction.ipynb  |  24 +-
 .../tutorials/02-orbital-rotation.ipynb       |  32 +-
 .../tutorials/03-double-factorized.ipynb      | 140 ++++----
 .doctrees/nbsphinx/tutorials/04-lucj.ipynb    |  64 ++--
 .../tutorials/05-fermion-operator.ipynb       | 130 +++----
 .../tutorials/03-double-factorized.doctree    | Bin 54325 -> 54734 bytes
 .doctrees/tutorials/04-lucj.doctree           | Bin 38069 -> 38069 bytes
 .../tutorials/05-fermion-operator.doctree     | Bin 41385 -> 41325 bytes
 .../double_factorized_hamiltonian.html        | 319 +++++++++---------
 .../tutorials/03-double-factorized.ipynb.txt  |   8 +-
 api/generated/ffsim.hamiltonians.html         |  99 +++---
 api/generated/ffsim.html                      |   2 +-
 genindex.html                                 |   4 +-
 objects.inv                                   | Bin 4189 -> 4203 bytes
 searchindex.js                                |   2 +-
 tutorials/01-introduction.ipynb               |  24 +-
 tutorials/02-orbital-rotation.ipynb           |  32 +-
 tutorials/03-double-factorized.html           |  60 ++--
 tutorials/03-double-factorized.ipynb          | 140 ++++----
 tutorials/04-lucj.html                        |  32 +-
 tutorials/04-lucj.ipynb                       |  64 ++--
 tutorials/05-fermion-operator.html            |  58 ++--
 tutorials/05-fermion-operator.ipynb           | 130 +++----
 25 files changed, 687 insertions(+), 677 deletions(-)

diff --git a/.doctrees/api/generated/ffsim.hamiltonians.doctree b/.doctrees/api/generated/ffsim.hamiltonians.doctree
index 2e92229677a931b6c34f8ed81cfc3df539c1e35e..dfbf3127e0292a6e5dd1655517a51b0a977caee2 100644
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diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
index ee0cba34d5996e10ec08d26935b1314a88104ea0..5a38fd6ef515a61c671b920822f9d2de77cdd9cf 100644
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diff --git a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
index b46f68b04..9ba68d884 100644
--- a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
+++ b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:55.333137Z",
-     "iopub.status.busy": "2023-10-19T14:39:55.332800Z",
-     "iopub.status.idle": "2023-10-19T14:39:55.620635Z",
-     "shell.execute_reply": "2023-10-19T14:39:55.620092Z"
+     "iopub.execute_input": "2023-10-19T16:27:36.509941Z",
+     "iopub.status.busy": "2023-10-19T16:27:36.509492Z",
+     "iopub.status.idle": "2023-10-19T16:27:36.878359Z",
+     "shell.execute_reply": "2023-10-19T16:27:36.877646Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:55.625193Z",
-     "iopub.status.busy": "2023-10-19T14:39:55.624119Z",
-     "iopub.status.idle": "2023-10-19T14:39:55.629183Z",
-     "shell.execute_reply": "2023-10-19T14:39:55.628710Z"
+     "iopub.execute_input": "2023-10-19T16:27:36.884089Z",
+     "iopub.status.busy": "2023-10-19T16:27:36.882169Z",
+     "iopub.status.idle": "2023-10-19T16:27:36.888779Z",
+     "shell.execute_reply": "2023-10-19T16:27:36.888221Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:55.633035Z",
-     "iopub.status.busy": "2023-10-19T14:39:55.632089Z",
-     "iopub.status.idle": "2023-10-19T14:39:55.636031Z",
-     "shell.execute_reply": "2023-10-19T14:39:55.635577Z"
+     "iopub.execute_input": "2023-10-19T16:27:36.893261Z",
+     "iopub.status.busy": "2023-10-19T16:27:36.892022Z",
+     "iopub.status.idle": "2023-10-19T16:27:36.896757Z",
+     "shell.execute_reply": "2023-10-19T16:27:36.896155Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index be6e21fe5..9a019f00c 100644
--- a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
+++ b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.127490Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.127250Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.415242Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.414684Z"
+     "iopub.execute_input": "2023-10-19T16:27:38.740446Z",
+     "iopub.status.busy": "2023-10-19T16:27:38.740199Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.133772Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.133089Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.419456Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.418437Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.443882Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.443356Z"
+     "iopub.execute_input": "2023-10-19T16:27:39.139249Z",
+     "iopub.status.busy": "2023-10-19T16:27:39.137973Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.170534Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.169918Z"
     }
    },
    "outputs": [],
@@ -160,10 +160,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.447969Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.447021Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.458057Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.457553Z"
+     "iopub.execute_input": "2023-10-19T16:27:39.175431Z",
+     "iopub.status.busy": "2023-10-19T16:27:39.174296Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.187414Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.186695Z"
     }
    },
    "outputs": [],
@@ -203,10 +203,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.462338Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.461004Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.467050Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.466562Z"
+     "iopub.execute_input": "2023-10-19T16:27:39.192482Z",
+     "iopub.status.busy": "2023-10-19T16:27:39.190867Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.197986Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.197420Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index 2cb8abca1..09532880c 100644
--- a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
+++ b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:58.908837Z",
-     "iopub.status.busy": "2023-10-19T14:39:58.908499Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.292292Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.291735Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.295062Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.294805Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.768940Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.768320Z"
     }
    },
    "outputs": [
@@ -78,14 +78,16 @@
     "mol_hamiltonian = mol_data.hamiltonian\n",
     "\n",
     "# Get the Hamiltonian in the double-factorized representation\n",
-    "df_hamiltonian = ffsim.double_factorized_hamiltonian(mol_hamiltonian)"
+    "df_hamiltonian = ffsim.DoubleFactorizedHamiltonian.from_molecular_hamiltonian(\n",
+    "    mol_hamiltonian\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The function `double_factorized_hamiltonian` returns an object of type `DoubleFactorizedHamiltonian` which is just a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations."
+    "Here, `mol_hamiltonian` is an instance of `MolecularHamiltonian`, a dataclass that stores the one- and two-body tensors, and `df_hamiltonian` is an instance of `DoubleFactorizedHamiltonian`, a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations."
    ]
   },
   {
@@ -93,10 +95,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.296046Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.295505Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.303680Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.303208Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.797788Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.796959Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.805806Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.805115Z"
     }
    },
    "outputs": [
@@ -111,44 +113,44 @@
       " [-3.07220771e-16 -6.77238770e-01]]\n",
       "\n",
       "Two-body tensor:\n",
-      "[[[[5.23173938e-01 1.94289029e-16]\n",
-      "   [1.94289029e-16 5.33545754e-01]]\n",
+      "[[[[5.23173938e-01 1.57437591e-16]\n",
+      "   [1.57437591e-16 5.33545754e-01]]\n",
       "\n",
-      "  [[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]]\n",
+      "  [[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]]\n",
       "\n",
       "\n",
-      " [[[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]\n",
+      " [[[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]\n",
       "\n",
-      "  [[5.33545754e-01 1.11022302e-16]\n",
-      "   [1.11022302e-16 5.53132024e-01]]]]\n",
+      "  [[5.33545754e-01 1.24884750e-16]\n",
+      "   [1.24884750e-16 5.53132024e-01]]]]\n",
       "\n",
       "Double-factorized representation\n",
       "--------------------------------\n",
       "One-body tensor:\n",
-      "[[-1.21318608e+00 -4.05183033e-16]\n",
-      " [-4.59876437e-16 -1.07792507e+00]]\n",
+      "[[-1.21318608e+00 -4.25870402e-16]\n",
+      " [-4.76015378e-16 -1.07792507e+00]]\n",
       "\n",
       "Diagonal Coulomb matrices:\n",
-      "[[[ 5.14653029e-001  5.33545754e-001]\n",
-      "  [ 5.33545754e-001  5.53132024e-001]]\n",
+      "[[[ 5.14653029e-01  5.33545754e-01]\n",
+      "  [ 5.33545754e-01  5.53132024e-01]]\n",
       "\n",
-      " [[ 2.48240570e-001 -2.48240570e-001]\n",
-      "  [-2.48240570e-001  2.48240570e-001]]\n",
+      " [[ 2.48240570e-01 -2.48240570e-01]\n",
+      "  [-2.48240570e-01  2.48240570e-01]]\n",
       "\n",
-      " [[ 5.96958401e-121 -7.13206008e-062]\n",
-      "  [-7.13206008e-062  8.52090881e-003]]]\n",
+      " [[ 1.50800163e-59 -3.58462611e-31]\n",
+      "  [-3.58462611e-31  8.52090881e-03]]]\n",
       "\n",
       "Orbital rotations:\n",
-      "[[[-1.00000000e+00  4.25128053e-15]\n",
-      "  [ 4.25128053e-15  1.00000000e+00]]\n",
+      "[[[-1.00000000e+00  8.24520980e-15]\n",
+      "  [ 8.24520980e-15  1.00000000e+00]]\n",
       "\n",
-      " [[ 7.07106781e-01 -7.07106781e-01]\n",
-      "  [-7.07106781e-01 -7.07106781e-01]]\n",
+      " [[-7.07106781e-01 -7.07106781e-01]\n",
+      "  [ 7.07106781e-01 -7.07106781e-01]]\n",
       "\n",
-      " [[ 2.89310728e-30 -1.00000000e+00]\n",
-      "  [-1.00000000e+00 -2.89310728e-30]]]\n"
+      " [[ 6.48603030e-15 -1.00000000e+00]\n",
+      "  [-1.00000000e+00 -6.48603030e-15]]]\n"
      ]
     }
    ],
@@ -227,10 +229,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.307553Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.306455Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.312345Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.311867Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.808878Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.808498Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.813796Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.813248Z"
     }
    },
    "outputs": [],
@@ -285,10 +287,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.315343Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.315133Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.319932Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.319386Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.816718Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.816364Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.820574Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.820031Z"
     }
    },
    "outputs": [],
@@ -325,10 +327,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.322653Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.322251Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.327160Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.326695Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.823525Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.823163Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.828409Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.827885Z"
     }
    },
    "outputs": [
@@ -336,7 +338,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.837796382593709\n"
+      "Hartree Fock energy: -0.8377963825937088\n"
      ]
     }
    ],
@@ -367,10 +369,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.329875Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.329325Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.339042Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.338412Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.831595Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.831104Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.842211Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.841656Z"
     }
    },
    "outputs": [
@@ -409,10 +411,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.341671Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.341479Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.349853Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.349232Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.845098Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.844747Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.853809Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.853262Z"
     }
    },
    "outputs": [
@@ -420,7 +422,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083491\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999027574408349\n"
      ]
     }
    ],
@@ -450,10 +452,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.353772Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.353568Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.390939Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.389931Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.856607Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.856244Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.899624Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.898940Z"
     }
    },
    "outputs": [
@@ -461,7 +463,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -493,10 +495,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.393689Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.393490Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.425221Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.424460Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.902790Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.902330Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.945843Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.945194Z"
     }
    },
    "outputs": [
@@ -504,7 +506,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -535,10 +537,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.427658Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.427469Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.443022Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.442331Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.949120Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.948837Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.967055Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.966238Z"
     }
    },
    "outputs": [
@@ -546,7 +548,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740059\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740057\n"
      ]
     }
    ],
diff --git a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
index 1d8185999..c1e1946d5 100644
--- a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
+++ b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:40:01.376785Z",
-     "iopub.status.busy": "2023-10-19T14:40:01.376450Z",
-     "iopub.status.idle": "2023-10-19T14:40:01.984780Z",
-     "shell.execute_reply": "2023-10-19T14:40:01.984205Z"
+     "iopub.execute_input": "2023-10-19T16:27:44.173731Z",
+     "iopub.status.busy": "2023-10-19T16:27:44.173460Z",
+     "iopub.status.idle": "2023-10-19T16:27:44.890778Z",
+     "shell.execute_reply": "2023-10-19T16:27:44.890166Z"
     }
    },
    "outputs": [
@@ -25,14 +25,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "converged SCF energy = -77.4456267643961\n"
+      "converged SCF energy = -77.4456267643962\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000\n"
+      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -109,10 +109,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:40:01.990201Z",
-     "iopub.status.busy": "2023-10-19T14:40:01.988624Z",
-     "iopub.status.idle": "2023-10-19T14:40:02.504800Z",
-     "shell.execute_reply": "2023-10-19T14:40:02.504249Z"
+     "iopub.execute_input": "2023-10-19T16:27:44.897251Z",
+     "iopub.status.busy": "2023-10-19T16:27:44.895577Z",
+     "iopub.status.idle": "2023-10-19T16:27:45.598357Z",
+     "shell.execute_reply": "2023-10-19T16:27:45.597692Z"
     }
    },
    "outputs": [
@@ -120,14 +120,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754462  E_corr = -0.04824536314851573\n"
+      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851328\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -77.46975600021692\n"
+      "Energy at initialialization: -77.46975600021656\n"
      ]
     }
    ],
@@ -177,10 +177,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:40:02.507719Z",
-     "iopub.status.busy": "2023-10-19T14:40:02.507477Z",
-     "iopub.status.idle": "2023-10-19T14:41:13.658634Z",
-     "shell.execute_reply": "2023-10-19T14:41:13.658109Z"
+     "iopub.execute_input": "2023-10-19T16:27:45.601966Z",
+     "iopub.status.busy": "2023-10-19T16:27:45.601316Z",
+     "iopub.status.idle": "2023-10-19T16:29:31.891294Z",
+     "shell.execute_reply": "2023-10-19T16:29:31.890594Z"
     }
    },
    "outputs": [
@@ -192,12 +192,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62873343946598\n",
-      "        x: [-2.541e-01 -8.978e-02 ...  2.239e-01 -5.438e-01]\n",
-      "      nit: 329\n",
-      "      jac: [ 6.537e-05  3.098e-04 ...  2.956e-04 -1.734e-04]\n",
-      "     nfev: 25696\n",
-      "     njev: 352\n",
+      "      fun: -77.62901334909452\n",
+      "        x: [-4.597e-01 -2.974e-01 ...  3.896e-01  1.161e+00]\n",
+      "      nit: 403\n",
+      "      jac: [ 9.521e-05  2.245e-04 ...  1.236e-04 -4.150e-04]\n",
+      "     nfev: 31682\n",
+      "     njev: 434\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -252,10 +252,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:41:13.662631Z",
-     "iopub.status.busy": "2023-10-19T14:41:13.661664Z",
-     "iopub.status.idle": "2023-10-19T14:42:35.356542Z",
-     "shell.execute_reply": "2023-10-19T14:42:35.356016Z"
+     "iopub.execute_input": "2023-10-19T16:29:31.895316Z",
+     "iopub.status.busy": "2023-10-19T16:29:31.894949Z",
+     "iopub.status.idle": "2023-10-19T16:30:19.776632Z",
+     "shell.execute_reply": "2023-10-19T16:30:19.776089Z"
     }
    },
    "outputs": [
@@ -267,12 +267,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62881470757267\n",
-      "        x: [-3.795e+00 -1.386e+00 ... -4.020e-01  1.230e-01]\n",
-      "      nit: 585\n",
-      "      jac: [ 4.434e-04 -1.933e-04 ...  4.007e-04 -1.450e-04]\n",
-      "     nfev: 29422\n",
-      "     njev: 626\n",
+      "      fun: -77.62873223663462\n",
+      "        x: [-1.942e+00  3.888e-01 ...  3.479e-01 -8.915e-02]\n",
+      "      nit: 285\n",
+      "      jac: [ 1.563e-05  3.695e-05 ... -1.279e-05 -1.776e-04]\n",
+      "     nfev: 14335\n",
+      "     njev: 305\n",
       " hess_inv: <46x46 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
diff --git a/.doctrees/nbsphinx/tutorials/05-fermion-operator.ipynb b/.doctrees/nbsphinx/tutorials/05-fermion-operator.ipynb
index fa09bcb38..e5cda2ddd 100644
--- a/.doctrees/nbsphinx/tutorials/05-fermion-operator.ipynb
+++ b/.doctrees/nbsphinx/tutorials/05-fermion-operator.ipynb
@@ -29,10 +29,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.077633Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.077306Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.362479Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.361769Z"
+     "iopub.execute_input": "2023-10-19T16:30:21.670393Z",
+     "iopub.status.busy": "2023-10-19T16:30:21.669989Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.023880Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.023224Z"
     }
    },
    "outputs": [
@@ -40,8 +40,8 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(0), des_a(3)): 0.5,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 1+1j,\n",
+       "    (cre_a(0), des_a(3)): 0.5,\n",
        "    (cre_a(3), des_a(0)): -0.25\n",
        "})"
       ]
@@ -76,17 +76,17 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.367296Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.366261Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.372138Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.371678Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.028811Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.027408Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.034307Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.033759Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j})'"
+       "'FermionOperator({((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j})'"
       ]
      },
      "execution_count": 2,
@@ -110,10 +110,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.375800Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.374921Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.381567Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.381116Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.037944Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.037568Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.044977Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.044445Z"
     }
    },
    "outputs": [
@@ -122,16 +122,16 @@
       "text/plain": [
        "FermionOperator({\n",
        "    (des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
-       "    (cre_a(3), des_a(0)): -0.5,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
-       "    (cre_a(0), des_a(3)): 1,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
+       "    (cre_a(0), des_a(3)): 1,\n",
        "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
-       "    (cre_b(2)): 0-0.25j\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
+       "    (cre_b(2)): 0-0.25j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_a(3), des_a(0)): -0.5\n",
        "})"
       ]
      },
@@ -169,10 +169,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.385304Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.384396Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.390385Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.389901Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.049374Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.048155Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.054897Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.054383Z"
     }
    },
    "outputs": [
@@ -181,16 +181,16 @@
       "text/plain": [
        "FermionOperator({\n",
        "    (des_a(3), des_b(3)): 0-1.25j,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_b(2)): -5\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
+       "    (cre_b(2)): -5,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_a(3), des_a(0)): 0+3j\n",
        "})"
       ]
      },
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.394709Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.393740Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.399514Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.399055Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.058256Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.057797Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.064878Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.064352Z"
     }
    },
    "outputs": [
@@ -230,16 +230,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\n",
-       "    (cre_b(2)): -5,\n",
-       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
-       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
-       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
-       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (des_b(3), des_a(3)): 0+1.25j,\n",
+       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
-       "    (cre_b(1), cre_a(4), des_b(5)): -12+12j\n",
+       "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
+       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,\n",
+       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
+       "    (cre_a(3), des_a(0)): 0+3j,\n",
+       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
+       "    (cre_b(2)): -5\n",
        "})"
       ]
      },
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.403183Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.402262Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.407487Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.407040Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.069240Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.068020Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.074090Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.073516Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.411097Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.410179Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.416471Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.416023Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.078346Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.077123Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.084444Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.083907Z"
     }
    },
    "outputs": [
@@ -340,21 +340,21 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.420049Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.419152Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.426669Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.426204Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.087872Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.087478Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.095690Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.095163Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.11889056-0.13114645j, 0.        +0.j        ,\n",
-       "       0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.        +0.j        ])"
+       "array([0.        +0.j       , 0.        +0.j       ,\n",
+       "       0.        +0.j       , 0.        +0.j       ,\n",
+       "       0.14601055-0.2517831j, 0.        +0.j       ,\n",
+       "       0.        +0.j       , 0.        +0.j       ,\n",
+       "       0.        +0.j       ])"
       ]
      },
      "execution_count": 8,
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.430250Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.429345Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.441262Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.440811Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.099160Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.098684Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.112817Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.112282Z"
     }
    },
    "outputs": [
diff --git a/.doctrees/tutorials/03-double-factorized.doctree b/.doctrees/tutorials/03-double-factorized.doctree
index f54f0264cc79b035a48c5c453c4b6dc657f84e03..cce62444806cee70729b7fd9b10a8798bdb51be5 100644
GIT binary patch
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diff --git a/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html b/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
index c59fc37e5..c585f5b4d 100644
--- a/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
+++ b/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
@@ -161,6 +161,166 @@ <h1>Source code for ffsim.hamiltonians.double_factorized_hamiltonian</h1><div cl
             <span class="n">constant</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">constant</span> <span class="o">-</span> <span class="n">constant_correction</span><span class="p">,</span>
             <span class="n">z_representation</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
         <span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="DoubleFactorizedHamiltonian.from_molecular_hamiltonian">
+<a class="viewcode-back" href="../../../api/generated/ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.from_molecular_hamiltonian">[docs]</a>
+    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">from_molecular_hamiltonian</span><span class="p">(</span>
+        <span class="n">hamiltonian</span><span class="p">:</span> <span class="n">MolecularHamiltonian</span><span class="p">,</span>
+        <span class="o">*</span><span class="p">,</span>
+        <span class="n">z_representation</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+        <span class="n">tol</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-8</span><span class="p">,</span>
+        <span class="n">max_vecs</span><span class="p">:</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">optimize</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+        <span class="n">method</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;L-BFGS-B&quot;</span><span class="p">,</span>
+        <span class="n">options</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">diag_coulomb_mask</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">cholesky</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">DoubleFactorizedHamiltonian</span><span class="p">:</span>
+<span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Double-factorized decomposition of a molecular Hamiltonian.</span>
+
+<span class="sd">        The double-factorized decomposition acts on a Hamiltonian of the form</span>
+
+<span class="sd">        .. math::</span>
+
+<span class="sd">            H = \sum_{pq, \sigma} h_{pq} a^\dagger_{p, \sigma} a_{q, \sigma}</span>
+<span class="sd">                + \frac12 \sum_{pqrs, \sigma \tau} h_{pqrs}</span>
+<span class="sd">                a^\dagger_{p, \sigma} a^\dagger_{r, \tau} a_{s, \tau} a_{q, \sigma}</span>
+<span class="sd">                + \text{constant}.</span>
+
+<span class="sd">        The Hamiltonian is decomposed into the double-factorized form</span>
+
+<span class="sd">        .. math::</span>
+
+<span class="sd">            H = \sum_{pq, \sigma} \kappa_{pq} a^\dagger_{p, \sigma} a_{q, \sigma}</span>
+<span class="sd">            + \frac12 \sum_t \sum_{ij, \sigma\tau}</span>
+<span class="sd">            Z^{(t)}_{ij} n^{(t)}_{i, \sigma} n^{(t)}_{j, \tau}</span>
+<span class="sd">            + \text{constant}&#39;.</span>
+
+<span class="sd">        where</span>
+
+<span class="sd">        .. math::</span>
+
+<span class="sd">            n^{(t)}_{i, \sigma} = \sum_{pq} U^{(t)}_{pi}</span>
+<span class="sd">            a^\dagger_{p, \sigma} a^\dagger_{q, \sigma} U^{(t)}_{qi}.</span>
+
+<span class="sd">        Here :math:`U^{(t)}_{ij}` and :math:`Z^{(t)}_{ij}` are tensors that are output</span>
+<span class="sd">        by the decomposition, and :math:`\kappa_{pq}` is an updated one-body tensor.</span>
+<span class="sd">        Each matrix :math:`U^{(t)}` is guaranteed to be unitary so that the</span>
+<span class="sd">        :math:`n^{(t)}_{i, \sigma}` are number operators in a rotated basis, and</span>
+<span class="sd">        each :math:`Z^{(t)}` is a real symmetric matrix.</span>
+<span class="sd">        The number of terms :math:`t` in the decomposition depends on the allowed</span>
+<span class="sd">        error threshold. A larger error threshold leads to a smaller number of terms.</span>
+<span class="sd">        Furthermore, the `max_rank` parameter specifies an optional upper bound</span>
+<span class="sd">        on :math:`t`.</span>
+
+<span class="sd">        The default behavior of this routine is to perform a straightforward</span>
+<span class="sd">        &quot;exact&quot; factorization of the two-body tensor based on a nested</span>
+<span class="sd">        eigenvalue decomposition. Additionally, one can choose to optimize the</span>
+<span class="sd">        coefficients stored in the tensor to achieve a &quot;compressed&quot; factorization.</span>
+<span class="sd">        This option is enabled by setting the `optimize` parameter to `True`.</span>
+<span class="sd">        The optimization attempts to minimize a least-squares objective function</span>
+<span class="sd">        quantifying the error in the low rank decomposition.</span>
+<span class="sd">        It uses `scipy.optimize.minimize`, passing both the objective function</span>
+<span class="sd">        and its gradient. The diagonal coulomb matrices returned by the optimization</span>
+<span class="sd">        can be optionally constrained to have only certain elements allowed to be</span>
+<span class="sd">        nonzero. This is achieved by passing the `diag_coulomb_mask` parameter, which is</span>
+<span class="sd">        an :math:`N \times N` matrix of boolean values where :math:`N` is the number</span>
+<span class="sd">        of orbitals. The nonzero elements of this matrix indicate where the diagonal</span>
+<span class="sd">        Coulomb matrices are allowed to be nonzero. Only the upper triangular part of</span>
+<span class="sd">        the matrix is used because the diagonal Coulomb matrices are symmetric.</span>
+
+<span class="sd">        **&quot;Z&quot; representation**</span>
+
+<span class="sd">        The &quot;Z&quot; representation of the double factorization is an alternative</span>
+<span class="sd">        representation that sometimes yields simpler quantum circuits.</span>
+
+<span class="sd">        Under the Jordan-Wigner transformation, the number operators take the form</span>
+
+<span class="sd">        .. math::</span>
+
+<span class="sd">            n^{(t)}_{i, \sigma} = \frac{(1 - z^{(t)}_{i, \sigma})}{2}</span>
+
+<span class="sd">        where :math:`z^{(t)}_{i, \sigma}` is the Pauli Z operator in the rotated basis.</span>
+<span class="sd">        The &quot;Z&quot; representation is obtained by rewriting the two-body part in terms</span>
+<span class="sd">        of these Pauli Z operators and updating the one-body term as appropriate:</span>
+
+<span class="sd">        .. math::</span>
+
+<span class="sd">            H = \sum_{pq, \sigma} \kappa&#39;_{pq} a^\dagger_{p, \sigma} a_{q, \sigma}</span>
+<span class="sd">            + \frac18 \sum_t \sum_{ij, \sigma\tau}^*</span>
+<span class="sd">            Z^{(t)}_{ij} z^{(t)}_{i, \sigma} z^{(t)}_{j, \tau}</span>
+<span class="sd">            + \text{constant}&#39;&#39;</span>
+
+<span class="sd">        where the asterisk denotes summation over indices :math:`ij, \sigma\tau`</span>
+<span class="sd">        where :math:`i \neq j` or :math:`\sigma \neq \tau`.</span>
+
+<span class="sd">        Note: Currently, only real-valued two-body tensors are supported.</span>
+
+<span class="sd">        Args:</span>
+<span class="sd">            one_body_tensor: The one-body tensor of the Hamiltonian.</span>
+<span class="sd">            two_body_tensor: The two-body tensor of the Hamiltonian.</span>
+<span class="sd">            z_representation: Whether to use the &quot;Z&quot; representation of the</span>
+<span class="sd">                low rank decomposition.</span>
+<span class="sd">            tol: Tolerance for error in the decomposition.</span>
+<span class="sd">                The error is defined as the maximum absolute difference between</span>
+<span class="sd">                an element of the original tensor and the corresponding element of</span>
+<span class="sd">                the reconstructed tensor.</span>
+<span class="sd">            max_vecs: An optional limit on the number of terms to keep in the</span>
+<span class="sd">                decomposition of the two-body tensor. This argument overrides ``tol``.</span>
+<span class="sd">            optimize: Whether to optimize the tensors returned by the decomposition.</span>
+<span class="sd">            method: The optimization method. See the documentation of</span>
+<span class="sd">                `scipy.optimize.minimize`_ for possible values.</span>
+<span class="sd">            callback: Callback function for the optimization. See the documentation of</span>
+<span class="sd">                `scipy.optimize.minimize`_ for usage.</span>
+<span class="sd">            options: Options for the optimization. See the documentation of</span>
+<span class="sd">                `scipy.optimize.minimize`_ for usage.</span>
+<span class="sd">            diag_coulomb_mask: Diagonal Coulomb matrix mask to use in the optimization.</span>
+<span class="sd">                This is a matrix of boolean values where the nonzero elements indicate</span>
+<span class="sd">                where the diagonal Coulomb matrices returned by optimization are allowed</span>
+<span class="sd">                to be nonzero. This parameter is only used if `optimize` is set to</span>
+<span class="sd">                True, and only the upper triangular part of the matrix is used.</span>
+<span class="sd">            cholesky: Whether to perform the factorization using a modified Cholesky</span>
+<span class="sd">                decomposition. If False, a full eigenvalue decomposition is used</span>
+<span class="sd">                instead, which can be much more expensive. This argument is ignored if</span>
+<span class="sd">                ``optimize`` is set to True.</span>
+
+<span class="sd">        Returns:</span>
+<span class="sd">            The double-factorized Hamiltonian.</span>
+
+<span class="sd">        References:</span>
+<span class="sd">            - `arXiv:1808.02625`_</span>
+<span class="sd">            - `arXiv:2104.08957`_</span>
+
+<span class="sd">        .. _arXiv:1808.02625: https://arxiv.org/abs/1808.02625</span>
+<span class="sd">        .. _arXiv:2104.08957: https://arxiv.org/abs/2104.08957</span>
+<span class="sd">        .. _scipy.optimize.minimize: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">one_body_tensor</span> <span class="o">=</span> <span class="n">hamiltonian</span><span class="o">.</span><span class="n">one_body_tensor</span> <span class="o">-</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span>
+            <span class="s2">&quot;prqr&quot;</span><span class="p">,</span> <span class="n">hamiltonian</span><span class="o">.</span><span class="n">two_body_tensor</span>
+        <span class="p">)</span>
+
+        <span class="n">diag_coulomb_mats</span><span class="p">,</span> <span class="n">orbital_rotations</span> <span class="o">=</span> <span class="n">double_factorized</span><span class="p">(</span>
+            <span class="n">hamiltonian</span><span class="o">.</span><span class="n">two_body_tensor</span><span class="p">,</span>
+            <span class="n">tol</span><span class="o">=</span><span class="n">tol</span><span class="p">,</span>
+            <span class="n">max_vecs</span><span class="o">=</span><span class="n">max_vecs</span><span class="p">,</span>
+            <span class="n">optimize</span><span class="o">=</span><span class="n">optimize</span><span class="p">,</span>
+            <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
+            <span class="n">options</span><span class="o">=</span><span class="n">options</span><span class="p">,</span>
+            <span class="n">diag_coulomb_mask</span><span class="o">=</span><span class="n">diag_coulomb_mask</span><span class="p">,</span>
+            <span class="n">cholesky</span><span class="o">=</span><span class="n">cholesky</span><span class="p">,</span>
+        <span class="p">)</span>
+        <span class="n">df_hamiltonian</span> <span class="o">=</span> <span class="n">DoubleFactorizedHamiltonian</span><span class="p">(</span>
+            <span class="n">one_body_tensor</span><span class="o">=</span><span class="n">one_body_tensor</span><span class="p">,</span>
+            <span class="n">diag_coulomb_mats</span><span class="o">=</span><span class="n">diag_coulomb_mats</span><span class="p">,</span>
+            <span class="n">orbital_rotations</span><span class="o">=</span><span class="n">orbital_rotations</span><span class="p">,</span>
+        <span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">z_representation</span><span class="p">:</span>
+            <span class="n">df_hamiltonian</span> <span class="o">=</span> <span class="n">df_hamiltonian</span><span class="o">.</span><span class="n">to_z_representation</span><span class="p">()</span>
+
+        <span class="k">return</span> <span class="n">df_hamiltonian</span></div>
 </div>
 
 
@@ -186,165 +346,6 @@ <h1>Source code for ffsim.hamiltonians.double_factorized_hamiltonian</h1><div cl
         <span class="n">diag_coulomb_mats</span>
     <span class="p">)</span>
     <span class="k">return</span> <span class="n">one_body_correction</span><span class="p">,</span> <span class="n">constant_correction</span>
-
-
-<div class="viewcode-block" id="double_factorized_hamiltonian">
-<a class="viewcode-back" href="../../../api/generated/ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian">[docs]</a>
-<span class="k">def</span> <span class="nf">double_factorized_hamiltonian</span><span class="p">(</span>
-    <span class="n">hamiltonian</span><span class="p">:</span> <span class="n">MolecularHamiltonian</span><span class="p">,</span>
-    <span class="o">*</span><span class="p">,</span>
-    <span class="n">z_representation</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
-    <span class="n">tol</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-8</span><span class="p">,</span>
-    <span class="n">max_vecs</span><span class="p">:</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-    <span class="n">optimize</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
-    <span class="n">method</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;L-BFGS-B&quot;</span><span class="p">,</span>
-    <span class="n">options</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-    <span class="n">diag_coulomb_mask</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-    <span class="n">cholesky</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
-<span class="p">)</span> <span class="o">-&gt;</span> <span class="n">DoubleFactorizedHamiltonian</span><span class="p">:</span>
-<span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Double-factorized decomposition of a molecular Hamiltonian.</span>
-
-<span class="sd">    The double-factorized decomposition acts on a Hamiltonian of the form</span>
-
-<span class="sd">    .. math::</span>
-
-<span class="sd">        H = \sum_{pq, \sigma} h_{pq} a^\dagger_{p, \sigma} a_{q, \sigma}</span>
-<span class="sd">            + \frac12 \sum_{pqrs, \sigma \tau} h_{pqrs}</span>
-<span class="sd">            a^\dagger_{p, \sigma} a^\dagger_{r, \tau} a_{s, \tau} a_{q, \sigma}</span>
-<span class="sd">            + \text{constant}.</span>
-
-<span class="sd">    The Hamiltonian is decomposed into the double-factorized form</span>
-
-<span class="sd">    .. math::</span>
-
-<span class="sd">        H = \sum_{pq, \sigma} \kappa_{pq} a^\dagger_{p, \sigma} a_{q, \sigma}</span>
-<span class="sd">        + \frac12 \sum_t \sum_{ij, \sigma\tau}</span>
-<span class="sd">        Z^{(t)}_{ij} n^{(t)}_{i, \sigma} n^{(t)}_{j, \tau}</span>
-<span class="sd">        + \text{constant}&#39;.</span>
-
-<span class="sd">    where</span>
-
-<span class="sd">    .. math::</span>
-
-<span class="sd">        n^{(t)}_{i, \sigma} = \sum_{pq} U^{(t)}_{pi}</span>
-<span class="sd">        a^\dagger_{p, \sigma} a^\dagger_{q, \sigma} U^{(t)}_{qi}.</span>
-
-<span class="sd">    Here :math:`U^{(t)}_{ij}` and :math:`Z^{(t)}_{ij}` are tensors that are output by</span>
-<span class="sd">    the decomposition, and :math:`\kappa_{pq}` is an updated one-body tensor.</span>
-<span class="sd">    Each matrix :math:`U^{(t)}` is guaranteed to be unitary so that the</span>
-<span class="sd">    :math:`n^{(t)}_{i, \sigma}` are number operators in a rotated basis, and</span>
-<span class="sd">    each :math:`Z^{(t)}` is a real symmetric matrix.</span>
-<span class="sd">    The number of terms :math:`t` in the decomposition depends on the allowed</span>
-<span class="sd">    error threshold. A larger error threshold leads to a smaller number of terms.</span>
-<span class="sd">    Furthermore, the `max_rank` parameter specifies an optional upper bound</span>
-<span class="sd">    on :math:`t`.</span>
-
-<span class="sd">    The default behavior of this routine is to perform a straightforward</span>
-<span class="sd">    &quot;exact&quot; factorization of the two-body tensor based on a nested</span>
-<span class="sd">    eigenvalue decomposition. Additionally, one can choose to optimize the</span>
-<span class="sd">    coefficients stored in the tensor to achieve a &quot;compressed&quot; factorization.</span>
-<span class="sd">    This option is enabled by setting the `optimize` parameter to `True`.</span>
-<span class="sd">    The optimization attempts to minimize a least-squares objective function</span>
-<span class="sd">    quantifying the error in the low rank decomposition.</span>
-<span class="sd">    It uses `scipy.optimize.minimize`, passing both the objective function</span>
-<span class="sd">    and its gradient. The core tensors returned by the optimization can be optionally</span>
-<span class="sd">    constrained to have only certain elements allowed to be nonzero. This is achieved by</span>
-<span class="sd">    passing the `diag_coulomb_mask` parameter, which is an :math:`N \times N` matrix of</span>
-<span class="sd">    boolean values where :math:`N` is the number of orbitals. The nonzero elements of</span>
-<span class="sd">    this matrix indicate where the core tensors are allowed to be nonzero. Only the</span>
-<span class="sd">    upper triangular part of the matrix is used because the core tensors are symmetric.</span>
-
-<span class="sd">    **&quot;Z&quot; representation**</span>
-
-<span class="sd">    The &quot;Z&quot; representation of the double factorization is an alternative</span>
-<span class="sd">    representation that sometimes yields simpler quantum circuits.</span>
-
-<span class="sd">    Under the Jordan-Wigner transformation, the number operators take the form</span>
-
-<span class="sd">    .. math::</span>
-
-<span class="sd">        n^{(t)}_{i, \sigma} = \frac{(1 - z^{(t)}_{i, \sigma})}{2}</span>
-
-<span class="sd">    where :math:`z^{(t)}_{i, \sigma}` is the Pauli Z operator in the rotated basis.</span>
-<span class="sd">    The &quot;Z&quot; representation is obtained by rewriting the two-body part in terms</span>
-<span class="sd">    of these Pauli Z operators and updating the one-body term as appropriate:</span>
-
-<span class="sd">    .. math::</span>
-
-<span class="sd">        H = \sum_{pq, \sigma} \kappa&#39;_{pq} a^\dagger_{p, \sigma} a_{q, \sigma}</span>
-<span class="sd">        + \frac18 \sum_t \sum_{ij, \sigma\tau}^*</span>
-<span class="sd">        Z^{(t)}_{ij} z^{(t)}_{i, \sigma} z^{(t)}_{j, \tau}</span>
-<span class="sd">        + \text{constant}&#39;&#39;</span>
-
-<span class="sd">    where the asterisk denotes summation over indices :math:`ij, \sigma\tau`</span>
-<span class="sd">    where :math:`i \neq j` or :math:`\sigma \neq \tau`.</span>
-
-<span class="sd">    Note: Currently, only real-valued two-body tensors are supported.</span>
-
-<span class="sd">    Args:</span>
-<span class="sd">        one_body_tensor: The one-body tensor of the Hamiltonian.</span>
-<span class="sd">        two_body_tensor: The two-body tensor of the Hamiltonian.</span>
-<span class="sd">        z_representation: Whether to use the &quot;Z&quot; representation of the</span>
-<span class="sd">            low rank decomposition.</span>
-<span class="sd">        tol: Tolerance for error in the decomposition.</span>
-<span class="sd">            The error is defined as the maximum absolute difference between</span>
-<span class="sd">            an element of the original tensor and the corresponding element of</span>
-<span class="sd">            the reconstructed tensor.</span>
-<span class="sd">        max_vecs: An optional limit on the number of terms to keep in the decomposition</span>
-<span class="sd">            of the two-body tensor. This argument overrides ``tol``.</span>
-<span class="sd">        optimize: Whether to optimize the tensors returned by the decomposition.</span>
-<span class="sd">        method: The optimization method. See the documentation of</span>
-<span class="sd">            `scipy.optimize.minimize`_ for possible values.</span>
-<span class="sd">        callback: Callback function for the optimization. See the documentation of</span>
-<span class="sd">            `scipy.optimize.minimize`_ for usage.</span>
-<span class="sd">        options: Options for the optimization. See the documentation of</span>
-<span class="sd">            `scipy.optimize.minimize`_ for usage.</span>
-<span class="sd">        diag_coulomb_mask: Diagonal Coulomb matrix mask to use in the optimization.</span>
-<span class="sd">            This is a matrix of boolean values where the nonzero elements indicate where</span>
-<span class="sd">            the diagonal coulomb matrices returned by optimization are allowed to be</span>
-<span class="sd">            nonzero. This parameter is only used if `optimize` is set to `True`, and</span>
-<span class="sd">            only the upper triangular part of the matrix is used.</span>
-<span class="sd">        cholesky: Whether to perform the factorization using a modified Cholesky</span>
-<span class="sd">            decomposition. If False, a full eigenvalue decomposition is used instead,</span>
-<span class="sd">            which can be much more expensive. This argument is ignored if ``optimize``</span>
-<span class="sd">            is set to True.</span>
-
-<span class="sd">    Returns:</span>
-<span class="sd">        The double-factorized Hamiltonian.</span>
-
-<span class="sd">    References:</span>
-<span class="sd">        - `arXiv:1808.02625`_</span>
-<span class="sd">        - `arXiv:2104.08957`_</span>
-
-<span class="sd">    .. _arXiv:1808.02625: https://arxiv.org/abs/1808.02625</span>
-<span class="sd">    .. _arXiv:2104.08957: https://arxiv.org/abs/2104.08957</span>
-<span class="sd">    .. _scipy.optimize.minimize: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html</span>
-<span class="sd">    &quot;&quot;&quot;</span>
-    <span class="n">one_body_tensor</span> <span class="o">=</span> <span class="n">hamiltonian</span><span class="o">.</span><span class="n">one_body_tensor</span> <span class="o">-</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span>
-        <span class="s2">&quot;prqr&quot;</span><span class="p">,</span> <span class="n">hamiltonian</span><span class="o">.</span><span class="n">two_body_tensor</span>
-    <span class="p">)</span>
-
-    <span class="n">diag_coulomb_mats</span><span class="p">,</span> <span class="n">orbital_rotations</span> <span class="o">=</span> <span class="n">double_factorized</span><span class="p">(</span>
-        <span class="n">hamiltonian</span><span class="o">.</span><span class="n">two_body_tensor</span><span class="p">,</span>
-        <span class="n">tol</span><span class="o">=</span><span class="n">tol</span><span class="p">,</span>
-        <span class="n">max_vecs</span><span class="o">=</span><span class="n">max_vecs</span><span class="p">,</span>
-        <span class="n">optimize</span><span class="o">=</span><span class="n">optimize</span><span class="p">,</span>
-        <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
-        <span class="n">options</span><span class="o">=</span><span class="n">options</span><span class="p">,</span>
-        <span class="n">diag_coulomb_mask</span><span class="o">=</span><span class="n">diag_coulomb_mask</span><span class="p">,</span>
-        <span class="n">cholesky</span><span class="o">=</span><span class="n">cholesky</span><span class="p">,</span>
-    <span class="p">)</span>
-    <span class="n">df_hamiltonian</span> <span class="o">=</span> <span class="n">DoubleFactorizedHamiltonian</span><span class="p">(</span>
-        <span class="n">one_body_tensor</span><span class="o">=</span><span class="n">one_body_tensor</span><span class="p">,</span>
-        <span class="n">diag_coulomb_mats</span><span class="o">=</span><span class="n">diag_coulomb_mats</span><span class="p">,</span>
-        <span class="n">orbital_rotations</span><span class="o">=</span><span class="n">orbital_rotations</span><span class="p">,</span>
-    <span class="p">)</span>
-
-    <span class="k">if</span> <span class="n">z_representation</span><span class="p">:</span>
-        <span class="n">df_hamiltonian</span> <span class="o">=</span> <span class="n">df_hamiltonian</span><span class="o">.</span><span class="n">to_z_representation</span><span class="p">()</span>
-
-    <span class="k">return</span> <span class="n">df_hamiltonian</span></div>
-
 </pre></div>
 
           </div>
diff --git a/_sources/tutorials/03-double-factorized.ipynb.txt b/_sources/tutorials/03-double-factorized.ipynb.txt
index 935060978..589df6c62 100644
--- a/_sources/tutorials/03-double-factorized.ipynb.txt
+++ b/_sources/tutorials/03-double-factorized.ipynb.txt
@@ -63,14 +63,16 @@
     "mol_hamiltonian = mol_data.hamiltonian\n",
     "\n",
     "# Get the Hamiltonian in the double-factorized representation\n",
-    "df_hamiltonian = ffsim.double_factorized_hamiltonian(mol_hamiltonian)"
+    "df_hamiltonian = ffsim.DoubleFactorizedHamiltonian.from_molecular_hamiltonian(\n",
+    "    mol_hamiltonian\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The function `double_factorized_hamiltonian` returns an object of type `DoubleFactorizedHamiltonian` which is just a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations."
+    "Here, `mol_hamiltonian` is an instance of `MolecularHamiltonian`, a dataclass that stores the one- and two-body tensors, and `df_hamiltonian` is an instance of `DoubleFactorizedHamiltonian`, a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations."
    ]
   },
   {
@@ -404,7 +406,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.11"
+   "version": "3.10.13"
   },
   "orig_nbformat": 4
  },
diff --git a/api/generated/ffsim.hamiltonians.html b/api/generated/ffsim.hamiltonians.html
index ad02c7c7f..ff84fc0fe 100644
--- a/api/generated/ffsim.hamiltonians.html
+++ b/api/generated/ffsim.hamiltonians.html
@@ -110,39 +110,9 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 than the “number” representation.</p>
 </dd></dl>
 
-<dl class="py property">
-<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">norb</span></span><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb" title="Link to this definition">¶</a></dt>
-<dd><p>The number of spatial orbitals.</p>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation">
-<span class="sig-name descname"><span class="pre">to_number_representation</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html#DoubleFactorizedHamiltonian.to_number_representation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation" title="Link to this definition">¶</a></dt>
-<dd><p>Return the Hamiltonian in the “number” representation.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian" title="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian"><code class="xref py py-class docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-
 <dl class="py method">
-<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation">
-<span class="sig-name descname"><span class="pre">to_z_representation</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html#DoubleFactorizedHamiltonian.to_z_representation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation" title="Link to this definition">¶</a></dt>
-<dd><p>Return the Hamiltonian in the “Z” representation.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian" title="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian"><code class="xref py py-class docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian">
-<span class="sig-prename descclassname"><span class="pre">ffsim.hamiltonians.double_factorized_hamiltonian.</span></span><span class="sig-name descname"><span class="pre">double_factorized_hamiltonian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">hamiltonian</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z_representation</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_vecs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">optimize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'L-BFGS-B'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">options</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diag_coulomb_mask</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cholesky</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html#double_factorized_hamiltonian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian" title="Link to this definition">¶</a></dt>
+<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.from_molecular_hamiltonian">
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_molecular_hamiltonian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">hamiltonian</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z_representation</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_vecs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">optimize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'L-BFGS-B'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">options</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diag_coulomb_mask</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cholesky</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html#DoubleFactorizedHamiltonian.from_molecular_hamiltonian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.from_molecular_hamiltonian" title="Link to this definition">¶</a></dt>
 <dd><p>Double-factorized decomposition of a molecular Hamiltonian.</p>
 <p>The double-factorized decomposition acts on a Hamiltonian of the form</p>
 <div class="math notranslate nohighlight">
@@ -160,8 +130,8 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 <div class="math notranslate nohighlight">
 \[n^{(t)}_{i, \sigma} = \sum_{pq} U^{(t)}_{pi}
 a^\dagger_{p, \sigma} a^\dagger_{q, \sigma} U^{(t)}_{qi}.\]</div>
-<p>Here <span class="math notranslate nohighlight">\(U^{(t)}_{ij}\)</span> and <span class="math notranslate nohighlight">\(Z^{(t)}_{ij}\)</span> are tensors that are output by
-the decomposition, and <span class="math notranslate nohighlight">\(\kappa_{pq}\)</span> is an updated one-body tensor.
+<p>Here <span class="math notranslate nohighlight">\(U^{(t)}_{ij}\)</span> and <span class="math notranslate nohighlight">\(Z^{(t)}_{ij}\)</span> are tensors that are output
+by the decomposition, and <span class="math notranslate nohighlight">\(\kappa_{pq}\)</span> is an updated one-body tensor.
 Each matrix <span class="math notranslate nohighlight">\(U^{(t)}\)</span> is guaranteed to be unitary so that the
 <span class="math notranslate nohighlight">\(n^{(t)}_{i, \sigma}\)</span> are number operators in a rotated basis, and
 each <span class="math notranslate nohighlight">\(Z^{(t)}\)</span> is a real symmetric matrix.
@@ -177,12 +147,13 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 The optimization attempts to minimize a least-squares objective function
 quantifying the error in the low rank decomposition.
 It uses <cite>scipy.optimize.minimize</cite>, passing both the objective function
-and its gradient. The core tensors returned by the optimization can be optionally
-constrained to have only certain elements allowed to be nonzero. This is achieved by
-passing the <cite>diag_coulomb_mask</cite> parameter, which is an <span class="math notranslate nohighlight">\(N \times N\)</span> matrix of
-boolean values where <span class="math notranslate nohighlight">\(N\)</span> is the number of orbitals. The nonzero elements of
-this matrix indicate where the core tensors are allowed to be nonzero. Only the
-upper triangular part of the matrix is used because the core tensors are symmetric.</p>
+and its gradient. The diagonal coulomb matrices returned by the optimization
+can be optionally constrained to have only certain elements allowed to be
+nonzero. This is achieved by passing the <cite>diag_coulomb_mask</cite> parameter, which is
+an <span class="math notranslate nohighlight">\(N \times N\)</span> matrix of boolean values where <span class="math notranslate nohighlight">\(N\)</span> is the number
+of orbitals. The nonzero elements of this matrix indicate where the diagonal
+Coulomb matrices are allowed to be nonzero. Only the upper triangular part of
+the matrix is used because the diagonal Coulomb matrices are symmetric.</p>
 <p><strong>“Z” representation</strong></p>
 <p>The “Z” representation of the double factorization is an alternative
 representation that sometimes yields simpler quantum circuits.</p>
@@ -211,8 +182,8 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 The error is defined as the maximum absolute difference between
 an element of the original tensor and the corresponding element of
 the reconstructed tensor.</p></li>
-<li><p><strong>max_vecs</strong> (<code class="xref py py-data docutils literal notranslate"><span class="pre">Optional</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>]) – An optional limit on the number of terms to keep in the decomposition
-of the two-body tensor. This argument overrides <code class="docutils literal notranslate"><span class="pre">tol</span></code>.</p></li>
+<li><p><strong>max_vecs</strong> (<code class="xref py py-data docutils literal notranslate"><span class="pre">Optional</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>]) – An optional limit on the number of terms to keep in the
+decomposition of the two-body tensor. This argument overrides <code class="docutils literal notranslate"><span class="pre">tol</span></code>.</p></li>
 <li><p><strong>optimize</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code>) – Whether to optimize the tensors returned by the decomposition.</p></li>
 <li><p><strong>method</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code>) – The optimization method. See the documentation of
 <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html">scipy.optimize.minimize</a> for possible values.</p></li>
@@ -221,14 +192,14 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 <li><p><strong>options</strong> (<code class="xref py py-data docutils literal notranslate"><span class="pre">Optional</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code>]) – Options for the optimization. See the documentation of
 <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html">scipy.optimize.minimize</a> for usage.</p></li>
 <li><p><strong>diag_coulomb_mask</strong> (<code class="xref py py-data docutils literal notranslate"><span class="pre">Optional</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>]) – Diagonal Coulomb matrix mask to use in the optimization.
-This is a matrix of boolean values where the nonzero elements indicate where
-the diagonal coulomb matrices returned by optimization are allowed to be
-nonzero. This parameter is only used if <cite>optimize</cite> is set to <cite>True</cite>, and
-only the upper triangular part of the matrix is used.</p></li>
+This is a matrix of boolean values where the nonzero elements indicate
+where the diagonal Coulomb matrices returned by optimization are allowed
+to be nonzero. This parameter is only used if <cite>optimize</cite> is set to
+True, and only the upper triangular part of the matrix is used.</p></li>
 <li><p><strong>cholesky</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code>) – Whether to perform the factorization using a modified Cholesky
-decomposition. If False, a full eigenvalue decomposition is used instead,
-which can be much more expensive. This argument is ignored if <code class="docutils literal notranslate"><span class="pre">optimize</span></code>
-is set to True.</p></li>
+decomposition. If False, a full eigenvalue decomposition is used
+instead, which can be much more expensive. This argument is ignored if
+<code class="docutils literal notranslate"><span class="pre">optimize</span></code> is set to True.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Return type<span class="colon">:</span></dt>
@@ -245,6 +216,36 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 </ul>
 </dd></dl>
 
+<dl class="py property">
+<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">norb</span></span><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb" title="Link to this definition">¶</a></dt>
+<dd><p>The number of spatial orbitals.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation">
+<span class="sig-name descname"><span class="pre">to_number_representation</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html#DoubleFactorizedHamiltonian.to_number_representation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation" title="Link to this definition">¶</a></dt>
+<dd><p>Return the Hamiltonian in the “number” representation.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian" title="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian"><code class="xref py py-class docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian</span></code></a></p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation">
+<span class="sig-name descname"><span class="pre">to_z_representation</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html#DoubleFactorizedHamiltonian.to_z_representation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation" title="Link to this definition">¶</a></dt>
+<dd><p>Return the Hamiltonian in the “Z” representation.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian" title="ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian"><code class="xref py py-class docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian</span></code></a></p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
 </section>
 <section id="module-ffsim.hamiltonians.molecular_hamiltonian">
 <span id="ffsim-hamiltonians-molecular-hamiltonian-module"></span><h2>ffsim.hamiltonians.molecular_hamiltonian module<a class="headerlink" href="#module-ffsim.hamiltonians.molecular_hamiltonian" title="Link to this heading">¶</a></h2>
diff --git a/api/generated/ffsim.html b/api/generated/ffsim.html
index e332543e2..e0148a0d6 100644
--- a/api/generated/ffsim.html
+++ b/api/generated/ffsim.html
@@ -102,12 +102,12 @@ <h2>Subpackages<a class="headerlink" href="#subpackages" title="Link to this hea
 <li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.orbital_rotations"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.orbital_rotations</span></code></a></li>
 <li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.constant"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.constant</span></code></a></li>
 <li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.z_representation</span></code></a></li>
+<li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.from_molecular_hamiltonian"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.from_molecular_hamiltonian()</span></code></a></li>
 <li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.norb</span></code></a></li>
 <li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.to_number_representation()</span></code></a></li>
 <li class="toctree-l4"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation"><code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian.to_z_representation()</span></code></a></li>
 </ul>
 </li>
-<li class="toctree-l3"><a class="reference internal" href="ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian"><code class="docutils literal notranslate"><span class="pre">double_factorized_hamiltonian()</span></code></a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="ffsim.hamiltonians.html#module-ffsim.hamiltonians.molecular_hamiltonian">ffsim.hamiltonians.molecular_hamiltonian module</a><ul>
diff --git a/genindex.html b/genindex.html
index 5006d9e5f..7814778e8 100644
--- a/genindex.html
+++ b/genindex.html
@@ -143,8 +143,6 @@ <h2 id="D">D</h2>
       <li><a href="api/generated/ffsim.html#ffsim.states.dims">dims() (in module ffsim.states)</a>
 </li>
       <li><a href="api/generated/ffsim.linalg.html#ffsim.linalg.double_factorized.double_factorized">double_factorized() (in module ffsim.linalg.double_factorized)</a>
-</li>
-      <li><a href="api/generated/ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian">double_factorized_hamiltonian() (in module ffsim.hamiltonians.double_factorized_hamiltonian)</a>
 </li>
       <li><a href="api/generated/ffsim.linalg.html#ffsim.linalg.double_factorized.double_factorized_t2">double_factorized_t2() (in module ffsim.linalg.double_factorized)</a>
 </li>
@@ -408,6 +406,8 @@ <h2 id="F">F</h2>
 </li>
       </ul></li>
       <li><a href="api/generated/ffsim.variational.html#ffsim.variational.lucj.UCJOperator.final_orbital_rotation">final_orbital_rotation (ffsim.variational.lucj.UCJOperator attribute)</a>
+</li>
+      <li><a href="api/generated/ffsim.hamiltonians.html#ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.from_molecular_hamiltonian">from_molecular_hamiltonian() (ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian static method)</a>
 </li>
       <li><a href="api/generated/ffsim.variational.html#ffsim.variational.lucj.UCJOperator.from_parameters">from_parameters() (ffsim.variational.lucj.UCJOperator static method)</a>
 </li>
diff --git a/objects.inv b/objects.inv
index 56ad4d828b3945cb2d448f208488f46e8d443996..fc16251cbaccf73a83ca266342d24e9864bc83c5 100644
GIT binary patch
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diff --git a/searchindex.js b/searchindex.js
index 70940076b..ffd6b101b 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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ffsim": [[11, "Introduction-to-ffsim"]], "Orbital rotations and quadratic Hamiltonians": [[12, "Orbital-rotations-and-quadratic-Hamiltonians"]], "Orbital rotations": [[12, "Orbital-rotations"]], "Time evolution by a quadratic Hamiltonian": [[12, "Time-evolution-by-a-quadratic-Hamiltonian"]], "Diagonal Coulomb operators and double-factorized Trotter simulation": [[13, "Diagonal-Coulomb-operators-and-double-factorized-Trotter-simulation"]], "Double-factorized representation of the molecular Hamiltonian": [[13, "Double-factorized-representation-of-the-molecular-Hamiltonian"]], "Trotter simulation of the double-factorized Hamiltonian": [[13, "Trotter-simulation-of-the-double-factorized-Hamiltonian"]], "Brief background on Trotter-Suzuki formulas": [[13, "Brief-background-on-Trotter-Suzuki-formulas"]], "Implementing Trotter simulation of the double-factorized Hamiltonian": [[13, "Implementing-Trotter-simulation-of-the-double-factorized-Hamiltonian"]], "The local unitary cluster Jastrow (LUCJ) ansatz": [[14, "The-local-unitary-cluster-Jastrow-(LUCJ)-ansatz"], [14, "id1"]], "The unitary cluster Jastrow (UCJ) ansatz": [[14, "The-unitary-cluster-Jastrow-(UCJ)-ansatz"]], "The FermionOperator class": [[15, "The-FermionOperator-class"]], "Tutorials": [[16, "tutorials"]]}, "indexentries": {"fermionaction (class in ffsim.fermion_action)": [[0, "ffsim.fermion_action.FermionAction"]], "moleculardata (class in ffsim.molecular_data)": [[0, "ffsim.molecular_data.MolecularData"]], "action (ffsim.fermion_action.fermionaction attribute)": [[0, "ffsim.fermion_action.FermionAction.action"]], "cre() (in module ffsim.fermion_action)": [[0, "ffsim.fermion_action.cre"]], "cre_a() (in module ffsim.fermion_action)": [[0, "ffsim.fermion_action.cre_a"]], "cre_b() (in module ffsim.fermion_action)": [[0, "ffsim.fermion_action.cre_b"]], "des() (in module ffsim.fermion_action)": [[0, "ffsim.fermion_action.des"]], "des_a() (in module ffsim.fermion_action)": [[0, "ffsim.fermion_action.des_a"]], 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(ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.diag_coulomb_mats"]], "double_factorized_hamiltonian() (in module ffsim.hamiltonians.double_factorized_hamiltonian)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian"]], "ffsim.hamiltonians": [[3, "module-ffsim.hamiltonians"]], "ffsim.hamiltonians.double_factorized_hamiltonian": [[3, "module-ffsim.hamiltonians.double_factorized_hamiltonian"]], "ffsim.hamiltonians.molecular_hamiltonian": [[3, "module-ffsim.hamiltonians.molecular_hamiltonian"]], "norb (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian property)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian property)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.norb"]], "one_body_tensor (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.one_body_tensor"]], "one_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.one_body_tensor"]], "orbital_rotations (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.orbital_rotations"]], "to_number_representation() (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation"]], "to_z_representation() (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation"]], "two_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation"]], "apply_matrix_to_slices() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[4, "module-ffsim.linalg"]], "ffsim.linalg.double_factorized": [[4, "module-ffsim.linalg.double_factorized"]], "ffsim.linalg.givens": [[4, "module-ffsim.linalg.givens"]], "ffsim.linalg.linalg": [[4, "module-ffsim.linalg.linalg"]], "ffsim.linalg.predicates": [[4, "module-ffsim.linalg.predicates"]], "givens_decomposition() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_unitary"]], "lup() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.modified_cholesky"]], "optimal_diag_coulomb_mats() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.optimal_diag_coulomb_mats"]], "zrotg() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.zrotg"]], "supportsapproximateequality (class in ffsim.protocols.approximate_equality)": [[5, "ffsim.protocols.approximate_equality.SupportsApproximateEquality"]], "supportslinearoperator (class in ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.SupportsLinearOperator"]], "supportstrace (class in ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.SupportsTrace"]], "approx_eq() (in module ffsim.protocols.approximate_equality)": [[5, "ffsim.protocols.approximate_equality.approx_eq"]], "ffsim.protocols": [[5, "module-ffsim.protocols"]], "ffsim.protocols.approximate_equality": [[5, "module-ffsim.protocols.approximate_equality"]], "ffsim.protocols.linear_operator": [[5, "module-ffsim.protocols.linear_operator"]], "ffsim.protocols.trace": [[5, "module-ffsim.protocols.trace"]], "linear_operator() (in module ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.linear_operator"]], "trace() (in module ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.trace"]], "expectation_squared_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.expectation_squared_diag_coulomb"]], "ffsim.trotter": [[6, "module-ffsim.trotter"]], "ffsim.trotter.qdrift": [[6, "module-ffsim.trotter.qdrift"]], "ffsim.trotter.trotter": [[6, "module-ffsim.trotter.trotter"]], "one_body_square_decomposition() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.one_body_square_decomposition"]], "qdrift_probabilities() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.qdrift_probabilities"]], "simulate_qdrift_double_factorized() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim.trotter.trotter)": [[6, "ffsim.trotter.trotter.simulate_trotter_double_factorized"]], "spectral_norm_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_diag_coulomb"]], "spectral_norm_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_one_body_tensor"]], "variance_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_diag_coulomb"]], "variance_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_one_body_tensor"]], "ucjoperator (class in ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.UCJOperator"]], "apply_ucj_operator() (in module ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.apply_ucj_operator"]], "diag_coulomb_mats_alpha_alpha (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_beta"]], "ffsim.variational": [[7, "module-ffsim.variational"]], "ffsim.variational.lucj": [[7, "module-ffsim.variational.lucj"]], "final_orbital_rotation (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.final_orbital_rotation"]], "from_parameters() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_t_amplitudes"]], "n_reps (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.n_reps"]], "norb (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.norb"]], "orbital_rotations (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.orbital_rotations"]], "to_parameters() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_t_amplitudes"]]}})
\ No newline at end of file
+Search.setIndex({"docnames": ["api/generated/ffsim", "api/generated/ffsim.contract", "api/generated/ffsim.gates", "api/generated/ffsim.hamiltonians", "api/generated/ffsim.linalg", "api/generated/ffsim.protocols", "api/generated/ffsim.trotter", "api/generated/ffsim.variational", "api/generated/modules", "api/index", "index", "tutorials/01-introduction", "tutorials/02-orbital-rotation", "tutorials/03-double-factorized", "tutorials/04-lucj", "tutorials/05-fermion-operator", "tutorials/index"], "filenames": ["api/generated/ffsim.rst", "api/generated/ffsim.contract.rst", "api/generated/ffsim.gates.rst", "api/generated/ffsim.hamiltonians.rst", "api/generated/ffsim.linalg.rst", "api/generated/ffsim.protocols.rst", "api/generated/ffsim.trotter.rst", "api/generated/ffsim.variational.rst", "api/generated/modules.rst", "api/index.rst", "index.rst", "tutorials/01-introduction.ipynb", "tutorials/02-orbital-rotation.ipynb", "tutorials/03-double-factorized.ipynb", "tutorials/04-lucj.ipynb", "tutorials/05-fermion-operator.ipynb", "tutorials/index.rst"], "titles": ["ffsim package", "ffsim.contract package", "ffsim.gates package", "ffsim.hamiltonians package", "ffsim.linalg package", "ffsim.protocols package", "ffsim.trotter package", "ffsim.variational package", "ffsim", "API reference", "ffsim documentation", "Introduction to ffsim", "Orbital rotations and quadratic Hamiltonians", "Diagonal Coulomb operators and double-factorized Trotter simulation", "The local unitary cluster Jastrow (LUCJ) ansatz", "The FermionOperator class", "Tutorials"], "terms": {"contract": [0, 8, 9, 12], "diag_coulomb": [0, 8], "contract_diag_coulomb": [0, 1], "diag_coulomb_linop": [0, 1], "hamiltonian": [0, 6, 8, 9, 14, 16], "hamiltonian_linop": [0, 1, 12], "hamiltonian_trac": [0, 1], "num_op_sum": [0, 8], "contract_num_op_sum": [0, 1], "num_op_sum_linop": [0, 1], "gate": [0, 8, 9, 14], "basic_g": [0, 8], "apply_fsim_g": [0, 2], "apply_givens_rot": [0, 2], "apply_hop_g": [0, 2], "apply_num_interact": [0, 2], "apply_num_num_interact": [0, 2], "apply_num_op_prod_interact": [0, 2], "apply_tunneling_interact": [0, 2], "apply_diag_coulomb_evolut": [0, 2, 13], "apply_num_op_sum_evolut": [0, 2, 12, 13], "orbital_rot": [0, 1, 3, 4, 6, 7, 8, 11, 12, 13], "apply_orbital_rot": [0, 2, 11, 12], "gen_orbital_rotation_index": [0, 2], "double_factorized_hamiltonian": [0, 8], "doublefactorizedhamiltonian": [0, 3, 6, 13], "one_body_tensor": [0, 1, 3, 6, 12, 13], "diag_coulomb_mat": [0, 3, 6, 13], "constant": [0, 1, 3, 13, 14], "z_represent": [0, 1, 2, 3, 6], "from_molecular_hamiltonian": [0, 3, 13], "norb": [0, 1, 2, 3, 5, 6, 7, 11, 12, 13, 14, 15], "to_number_represent": [0, 3], "to_z_represent": [0, 3], "molecular_hamiltonian": [0, 8], "molecularhamiltonian": [0, 3, 13], "two_body_tensor": [0, 1, 3, 4, 13], "linalg": [0, 8, 9, 12, 13, 15], "double_factor": [0, 8], "double_factorized_t2": [0, 4], "modified_choleski": [0, 4], "optimal_diag_coulomb_mat": [0, 4], "given": [0, 1, 2, 6, 8, 12, 13], "apply_matrix_to_slic": [0, 4], "givens_decomposit": [0, 4], "zrotg": [0, 4], "expm_multiply_taylor": [0, 4], "lup": [0, 4], "predic": [0, 8], "is_antihermitian": [0, 4], "is_hermitian": [0, 4], "is_orthogon": [0, 4], "is_real_symmetr": [0, 4], "is_special_orthogon": [0, 4], "is_unitari": [0, 4], "protocol": [0, 8, 9], "approximate_equ": [0, 8], "supportsapproximateequ": [0, 5], "approx_eq": [0, 5], "linear_oper": [0, 8, 13, 14, 15], "supportslinearoper": [0, 5], "trace": [0, 1, 8, 13], "supportstrac": [0, 5], "trotter": [0, 8, 9, 16], "qdrift": [0, 8], "expectation_squared_diag_coulomb": [0, 6], "one_body_square_decomposit": [0, 6], "qdrift_prob": [0, 6], "simulate_qdrift_double_factor": [0, 6], "spectral_norm_diag_coulomb": [0, 6], "spectral_norm_one_body_tensor": [0, 6], "variance_diag_coulomb": [0, 6], "variance_one_body_tensor": [0, 6], "simulate_trotter_double_factor": [0, 6, 13], "variat": [0, 8, 9, 14], "lucj": [0, 8, 16], "ucjoper": [0, 7, 14], "diag_coulomb_mats_alpha_alpha": [0, 7], "diag_coulomb_mats_alpha_beta": [0, 7], "final_orbital_rot": [0, 7], "from_paramet": [0, 7, 14], "from_t_amplitud": [0, 7, 14], "n_rep": [0, 7, 14], "to_paramet": [0, 7, 14], "to_t_amplitud": [0, 7], "apply_ucj_oper": [0, 7, 14], "The": [0, 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 16], "fermionact": [0, 8, 9], "namedtupl": 0, "construct": [0, 1, 13, 14, 15], "function": [0, 1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 15], "class": [0, 3, 5, 7, 11, 14, 16], "action": [0, 1, 8, 12, 15], "bool": [0, 1, 2, 3, 4, 5, 6, 7], "spin": [0, 1, 2, 7, 8, 11, 12, 14, 15], "orb": [0, 8, 15], "int": [0, 1, 2, 3, 4, 5, 6, 7, 13], "sourc": [0, 1, 2, 3, 4, 5, 6, 7], "base": [0, 3, 4, 5, 7, 14], "A": [0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15], "fermion": [0, 2, 10, 11, 12, 14, 15], "creat": [0, 2, 11, 12, 13, 14, 15], "new": [0, 12, 15], "instanc": [0, 12, 13], "alia": 0, "field": 0, "number": [0, 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15], "0": [0, 1, 2, 3, 6, 12, 13, 14, 15], "2": [0, 1, 2, 3, 4, 11, 12, 13, 14, 15], "1": [0, 2, 3, 4, 6, 7, 11, 12, 13, 14, 15], "cre": [0, 8, 9], "paramet": [0, 1, 2, 3, 4, 5, 6, 7, 14], "orbit": [0, 1, 2, 3, 4, 5, 6, 7, 11, 13, 14, 15, 16], "fals": [0, 1, 2, 3, 4, 5, 6, 7, 15], "alpha": [0, 1, 2, 5, 6, 7, 11, 14, 15], "true": [0, 2, 3, 4, 5, 6, 7, 11, 14, 15], "beta": [0, 1, 2, 5, 6, 7, 11, 14, 15], "index": [0, 2, 10, 11, 14, 15], "act": [0, 3, 15], "return": [0, 1, 2, 3, 4, 5, 6, 7, 13, 14, 15], "type": [0, 1, 2, 3, 4, 5, 6, 7], "cre_a": [0, 8, 9, 15], "cre_b": [0, 8, 9, 15], "de": [0, 8, 9], "destroi": [0, 15], "des_a": [0, 8, 9, 15], "des_b": [0, 8, 9, 15], "moleculardata": [0, 8, 9, 13, 14], "nelec": [0, 1, 2, 5, 6, 7, 11, 12, 13, 14, 15], "core_energi": 0, "dipole_integr": 0, "none": [0, 1, 2, 3, 4, 6, 7], "orbital_symmetri": 0, "object": [0, 3, 4, 5, 7, 14, 15], "random_antihermitian": [0, 8, 9], "dim": [0, 6, 8, 9, 11, 15], "seed": [0, 6, 11, 12], "dtype": [0, 14], "complex": [0, 4], "anti": [0, 4], "hermitian": [0, 4, 12], "matrix": [0, 1, 2, 3, 4, 6, 11, 12, 13, 14, 15], "width": 0, "height": 0, "rank": [0, 3, 4], "If": [0, 1, 2, 3, 4, 6, 7, 15], "maximum": [0, 3, 4], "i": [0, 1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 15], "us": [0, 1, 2, 3, 4, 6, 11, 12, 13, 14, 15], "initi": [0, 6, 7, 13, 14], "pseudorandom": [0, 6], "gener": [0, 2, 6, 11, 12, 13, 14], "should": [0, 6, 12, 13], "valid": [0, 6], "input": [0, 1, 6, 14], "np": [0, 2, 5, 6, 12, 13, 14], "default_rng": [0, 6], "dype": 0, "data": [0, 2, 6, 7, 13, 14, 15], "result": [0, 1, 4, 7, 12, 13, 14], "ndarrai": [0, 1, 2, 3, 4, 6, 7, 13], "sampl": [0, 6], "random_hermitian": [0, 8, 9, 12], "random_orthogon": [0, 8, 9], "float": [0, 1, 2, 3, 4, 5, 6, 13], "orthogon": [0, 4], "distribut": 0, "haar": 0, "measur": 0, "an": [0, 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15], "els": [0, 6], "refer": [0, 3, 4, 10, 14], "arxiv": [0, 3, 4], "math": 0, "ph": 0, "0609050": 0, "random_real_symmetric_matrix": [0, 8, 9], "real": [0, 1, 2, 3, 4, 7, 12, 13, 14], "symmetr": [0, 1, 2, 3, 4, 6, 13, 14], "option": [0, 1, 2, 3, 4, 6, 7, 14], "random_special_orthogon": [0, 8, 9], "special": [0, 4, 11], "random_statevector": [0, 8, 9, 15], "vector": [0, 1, 2, 4, 6, 7, 11, 12, 14, 15], "from": [0, 7, 11, 12, 14, 15], "uniform": [0, 6], "dimens": [0, 6, 11], "random_t2_amplitud": [0, 8, 9], "nocc": [0, 2, 7], "t2": [0, 4, 7, 14], "amplitud": [0, 4, 7, 14], "tensor": [0, 1, 3, 4, 6, 13, 14], "ar": [0, 1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 15], "occupi": [0, 1, 2, 13], "electron": [0, 1, 2, 5, 6, 7, 11, 13], "random_two_body_tensor_r": [0, 8, 9], "two": [0, 1, 2, 3, 4, 5, 6, 7, 13, 14], "bodi": [0, 1, 3, 4, 6, 13, 14], "valu": [0, 3, 4, 6, 7, 13, 14], "shape": [0, 4, 6, 11, 14], "default": [0, 3, 4], "behavior": [0, 3, 4], "which": [0, 2, 3, 4, 11, 12, 13, 14, 15], "random_unitari": [0, 8, 9, 11, 12], "unitari": [0, 1, 2, 3, 4, 7, 12, 13, 16], "get": [0, 1, 12, 13, 14], "fci": [0, 1, 11, 14], "space": [0, 14], "spatial": [0, 1, 2, 3, 5, 7, 11, 13, 14, 15], "tupl": [0, 1, 2, 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"ffsim.random.random_statevector"]], "random_t2_amplitudes() (in module ffsim.random)": [[0, "ffsim.random.random_t2_amplitudes"]], "random_two_body_tensor_real() (in module ffsim.random)": [[0, "ffsim.random.random_two_body_tensor_real"]], "random_unitary() (in module ffsim.random)": [[0, "ffsim.random.random_unitary"]], "slater_determinant() (in module ffsim.states)": [[0, "ffsim.states.slater_determinant"]], "slater_determinant_one_rdm() (in module ffsim.states)": [[0, "ffsim.states.slater_determinant_one_rdm"]], "spin (ffsim.fermion_action.fermionaction attribute)": [[0, "ffsim.fermion_action.FermionAction.spin"]], "contract_diag_coulomb() (in module ffsim.contract.diag_coulomb)": [[1, "ffsim.contract.diag_coulomb.contract_diag_coulomb"]], "contract_num_op_sum() (in module ffsim.contract.num_op_sum)": [[1, "ffsim.contract.num_op_sum.contract_num_op_sum"]], "diag_coulomb_linop() (in module ffsim.contract.diag_coulomb)": [[1, "ffsim.contract.diag_coulomb.diag_coulomb_linop"]], "ffsim.contract": [[1, "module-ffsim.contract"]], "ffsim.contract.diag_coulomb": [[1, "module-ffsim.contract.diag_coulomb"]], "ffsim.contract.hamiltonian": [[1, "module-ffsim.contract.hamiltonian"]], "ffsim.contract.num_op_sum": [[1, "module-ffsim.contract.num_op_sum"]], "hamiltonian_linop() (in module ffsim.contract.hamiltonian)": [[1, "ffsim.contract.hamiltonian.hamiltonian_linop"]], "hamiltonian_trace() (in module ffsim.contract.hamiltonian)": [[1, "ffsim.contract.hamiltonian.hamiltonian_trace"]], "num_op_sum_linop() (in module ffsim.contract.num_op_sum)": [[1, "ffsim.contract.num_op_sum.num_op_sum_linop"]], "apply_diag_coulomb_evolution() (in module ffsim.gates.diag_coulomb)": [[2, "ffsim.gates.diag_coulomb.apply_diag_coulomb_evolution"]], "apply_fsim_gate() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_fsim_gate"]], "apply_givens_rotation() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_givens_rotation"]], "apply_hop_gate() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_hop_gate"]], "apply_num_interaction() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_num_interaction"]], "apply_num_num_interaction() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_num_num_interaction"]], "apply_num_op_prod_interaction() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_num_op_prod_interaction"]], "apply_num_op_sum_evolution() (in module ffsim.gates.num_op_sum)": [[2, "ffsim.gates.num_op_sum.apply_num_op_sum_evolution"]], "apply_orbital_rotation() (in module ffsim.gates.orbital_rotation)": [[2, "ffsim.gates.orbital_rotation.apply_orbital_rotation"]], "apply_tunneling_interaction() (in module ffsim.gates.basic_gates)": [[2, "ffsim.gates.basic_gates.apply_tunneling_interaction"]], "ffsim.gates": [[2, "module-ffsim.gates"]], "ffsim.gates.basic_gates": [[2, "module-ffsim.gates.basic_gates"]], "ffsim.gates.diag_coulomb": [[2, "module-ffsim.gates.diag_coulomb"]], "ffsim.gates.num_op_sum": [[2, "module-ffsim.gates.num_op_sum"]], "ffsim.gates.orbital_rotation": [[2, "module-ffsim.gates.orbital_rotation"]], "gen_orbital_rotation_index() (in module ffsim.gates.orbital_rotation)": [[2, "ffsim.gates.orbital_rotation.gen_orbital_rotation_index"]], "doublefactorizedhamiltonian (class in ffsim.hamiltonians.double_factorized_hamiltonian)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian"]], "molecularhamiltonian (class in ffsim.hamiltonians.molecular_hamiltonian)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian"]], "constant (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.constant"]], "constant (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.constant"]], "diag_coulomb_mats (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.diag_coulomb_mats"]], "ffsim.hamiltonians": [[3, "module-ffsim.hamiltonians"]], "ffsim.hamiltonians.double_factorized_hamiltonian": [[3, "module-ffsim.hamiltonians.double_factorized_hamiltonian"]], "ffsim.hamiltonians.molecular_hamiltonian": [[3, "module-ffsim.hamiltonians.molecular_hamiltonian"]], "from_molecular_hamiltonian() (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian static method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.from_molecular_hamiltonian"]], "norb (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian property)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian property)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.norb"]], "one_body_tensor (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.one_body_tensor"]], "one_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.one_body_tensor"]], "orbital_rotations (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.orbital_rotations"]], "to_number_representation() (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_number_representation"]], "to_z_representation() (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation"]], "two_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation"]], "apply_matrix_to_slices() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[4, "module-ffsim.linalg"]], "ffsim.linalg.double_factorized": [[4, "module-ffsim.linalg.double_factorized"]], "ffsim.linalg.givens": [[4, "module-ffsim.linalg.givens"]], "ffsim.linalg.linalg": [[4, "module-ffsim.linalg.linalg"]], "ffsim.linalg.predicates": [[4, "module-ffsim.linalg.predicates"]], "givens_decomposition() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_unitary"]], "lup() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.modified_cholesky"]], "optimal_diag_coulomb_mats() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.optimal_diag_coulomb_mats"]], "zrotg() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.zrotg"]], "supportsapproximateequality (class in ffsim.protocols.approximate_equality)": [[5, "ffsim.protocols.approximate_equality.SupportsApproximateEquality"]], "supportslinearoperator (class in ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.SupportsLinearOperator"]], "supportstrace (class in ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.SupportsTrace"]], "approx_eq() (in module ffsim.protocols.approximate_equality)": [[5, "ffsim.protocols.approximate_equality.approx_eq"]], "ffsim.protocols": [[5, "module-ffsim.protocols"]], "ffsim.protocols.approximate_equality": [[5, "module-ffsim.protocols.approximate_equality"]], "ffsim.protocols.linear_operator": [[5, "module-ffsim.protocols.linear_operator"]], "ffsim.protocols.trace": [[5, "module-ffsim.protocols.trace"]], "linear_operator() (in module ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.linear_operator"]], "trace() (in module ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.trace"]], "expectation_squared_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.expectation_squared_diag_coulomb"]], "ffsim.trotter": [[6, "module-ffsim.trotter"]], "ffsim.trotter.qdrift": [[6, "module-ffsim.trotter.qdrift"]], "ffsim.trotter.trotter": [[6, "module-ffsim.trotter.trotter"]], "one_body_square_decomposition() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.one_body_square_decomposition"]], "qdrift_probabilities() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.qdrift_probabilities"]], "simulate_qdrift_double_factorized() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim.trotter.trotter)": [[6, "ffsim.trotter.trotter.simulate_trotter_double_factorized"]], "spectral_norm_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_diag_coulomb"]], "spectral_norm_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_one_body_tensor"]], "variance_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_diag_coulomb"]], "variance_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_one_body_tensor"]], "ucjoperator (class in ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.UCJOperator"]], "apply_ucj_operator() (in module ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.apply_ucj_operator"]], "diag_coulomb_mats_alpha_alpha (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_beta"]], "ffsim.variational": [[7, "module-ffsim.variational"]], "ffsim.variational.lucj": [[7, "module-ffsim.variational.lucj"]], "final_orbital_rotation (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.final_orbital_rotation"]], "from_parameters() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_t_amplitudes"]], "n_reps (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.n_reps"]], "norb (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.norb"]], "orbital_rotations (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.orbital_rotations"]], "to_parameters() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_t_amplitudes"]]}})
\ No newline at end of file
diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb
index b46f68b04..9ba68d884 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:55.333137Z",
-     "iopub.status.busy": "2023-10-19T14:39:55.332800Z",
-     "iopub.status.idle": "2023-10-19T14:39:55.620635Z",
-     "shell.execute_reply": "2023-10-19T14:39:55.620092Z"
+     "iopub.execute_input": "2023-10-19T16:27:36.509941Z",
+     "iopub.status.busy": "2023-10-19T16:27:36.509492Z",
+     "iopub.status.idle": "2023-10-19T16:27:36.878359Z",
+     "shell.execute_reply": "2023-10-19T16:27:36.877646Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:55.625193Z",
-     "iopub.status.busy": "2023-10-19T14:39:55.624119Z",
-     "iopub.status.idle": "2023-10-19T14:39:55.629183Z",
-     "shell.execute_reply": "2023-10-19T14:39:55.628710Z"
+     "iopub.execute_input": "2023-10-19T16:27:36.884089Z",
+     "iopub.status.busy": "2023-10-19T16:27:36.882169Z",
+     "iopub.status.idle": "2023-10-19T16:27:36.888779Z",
+     "shell.execute_reply": "2023-10-19T16:27:36.888221Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:55.633035Z",
-     "iopub.status.busy": "2023-10-19T14:39:55.632089Z",
-     "iopub.status.idle": "2023-10-19T14:39:55.636031Z",
-     "shell.execute_reply": "2023-10-19T14:39:55.635577Z"
+     "iopub.execute_input": "2023-10-19T16:27:36.893261Z",
+     "iopub.status.busy": "2023-10-19T16:27:36.892022Z",
+     "iopub.status.idle": "2023-10-19T16:27:36.896757Z",
+     "shell.execute_reply": "2023-10-19T16:27:36.896155Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index be6e21fe5..9a019f00c 100644
--- a/tutorials/02-orbital-rotation.ipynb
+++ b/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.127490Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.127250Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.415242Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.414684Z"
+     "iopub.execute_input": "2023-10-19T16:27:38.740446Z",
+     "iopub.status.busy": "2023-10-19T16:27:38.740199Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.133772Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.133089Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.419456Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.418437Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.443882Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.443356Z"
+     "iopub.execute_input": "2023-10-19T16:27:39.139249Z",
+     "iopub.status.busy": "2023-10-19T16:27:39.137973Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.170534Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.169918Z"
     }
    },
    "outputs": [],
@@ -160,10 +160,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.447969Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.447021Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.458057Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.457553Z"
+     "iopub.execute_input": "2023-10-19T16:27:39.175431Z",
+     "iopub.status.busy": "2023-10-19T16:27:39.174296Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.187414Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.186695Z"
     }
    },
    "outputs": [],
@@ -203,10 +203,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:57.462338Z",
-     "iopub.status.busy": "2023-10-19T14:39:57.461004Z",
-     "iopub.status.idle": "2023-10-19T14:39:57.467050Z",
-     "shell.execute_reply": "2023-10-19T14:39:57.466562Z"
+     "iopub.execute_input": "2023-10-19T16:27:39.192482Z",
+     "iopub.status.busy": "2023-10-19T16:27:39.190867Z",
+     "iopub.status.idle": "2023-10-19T16:27:39.197986Z",
+     "shell.execute_reply": "2023-10-19T16:27:39.197420Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.html b/tutorials/03-double-factorized.html
index 270204248..1cd1a40c2 100644
--- a/tutorials/03-double-factorized.html
+++ b/tutorials/03-double-factorized.html
@@ -84,7 +84,9 @@ <h2>Double-factorized representation of the molecular Hamiltonian<a class="heade
 <span class="n">mol_hamiltonian</span> <span class="o">=</span> <span class="n">mol_data</span><span class="o">.</span><span class="n">hamiltonian</span>
 
 <span class="c1"># Get the Hamiltonian in the double-factorized representation</span>
-<span class="n">df_hamiltonian</span> <span class="o">=</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">double_factorized_hamiltonian</span><span class="p">(</span><span class="n">mol_hamiltonian</span><span class="p">)</span>
+<span class="n">df_hamiltonian</span> <span class="o">=</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">DoubleFactorizedHamiltonian</span><span class="o">.</span><span class="n">from_molecular_hamiltonian</span><span class="p">(</span>
+    <span class="n">mol_hamiltonian</span>
+<span class="p">)</span>
 </pre></div>
 </div>
 </div>
@@ -96,7 +98,7 @@ <h2>Double-factorized representation of the molecular Hamiltonian<a class="heade
 converged SCF energy = -0.837796382593709
 </pre></div></div>
 </div>
-<p>The function <code class="docutils literal notranslate"><span class="pre">double_factorized_hamiltonian</span></code> returns an object of type <code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian</span></code> which is just a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations.</p>
+<p>Here, <code class="docutils literal notranslate"><span class="pre">mol_hamiltonian</span></code> is an instance of <code class="docutils literal notranslate"><span class="pre">MolecularHamiltonian</span></code>, a dataclass that stores the one- and two-body tensors, and <code class="docutils literal notranslate"><span class="pre">df_hamiltonian</span></code> is an instance of <code class="docutils literal notranslate"><span class="pre">DoubleFactorizedHamiltonian</span></code>, a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations.</p>
 <div class="nbinput docutils container">
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[2]:
 </pre></div>
@@ -136,44 +138,44 @@ <h2>Double-factorized representation of the molecular Hamiltonian<a class="heade
  [-3.07220771e-16 -6.77238770e-01]]
 
 Two-body tensor:
-[[[[5.23173938e-01 1.94289029e-16]
-   [1.94289029e-16 5.33545754e-01]]
+[[[[5.23173938e-01 1.57437591e-16]
+   [1.57437591e-16 5.33545754e-01]]
 
-  [[1.94289029e-16 2.48240570e-01]
-   [2.48240570e-01 8.32667268e-17]]]
+  [[2.12704463e-16 2.48240570e-01]
+   [2.48240570e-01 1.61492903e-16]]]
 
 
- [[[1.94289029e-16 2.48240570e-01]
-   [2.48240570e-01 8.32667268e-17]]
+ [[[2.12704463e-16 2.48240570e-01]
+   [2.48240570e-01 1.61492903e-16]]
 
-  [[5.33545754e-01 1.11022302e-16]
-   [1.11022302e-16 5.53132024e-01]]]]
+  [[5.33545754e-01 1.24884750e-16]
+   [1.24884750e-16 5.53132024e-01]]]]
 
 Double-factorized representation
 --------------------------------
 One-body tensor:
-[[-1.21318608e+00 -4.05183033e-16]
- [-4.59876437e-16 -1.07792507e+00]]
+[[-1.21318608e+00 -4.25870402e-16]
+ [-4.76015378e-16 -1.07792507e+00]]
 
 Diagonal Coulomb matrices:
-[[[ 5.14653029e-001  5.33545754e-001]
-  [ 5.33545754e-001  5.53132024e-001]]
+[[[ 5.14653029e-01  5.33545754e-01]
+  [ 5.33545754e-01  5.53132024e-01]]
 
- [[ 2.48240570e-001 -2.48240570e-001]
-  [-2.48240570e-001  2.48240570e-001]]
+ [[ 2.48240570e-01 -2.48240570e-01]
+  [-2.48240570e-01  2.48240570e-01]]
 
- [[ 5.96958401e-121 -7.13206008e-062]
-  [-7.13206008e-062  8.52090881e-003]]]
+ [[ 1.50800163e-59 -3.58462611e-31]
+  [-3.58462611e-31  8.52090881e-03]]]
 
 Orbital rotations:
-[[[-1.00000000e+00  4.25128053e-15]
-  [ 4.25128053e-15  1.00000000e+00]]
+[[[-1.00000000e+00  8.24520980e-15]
+  [ 8.24520980e-15  1.00000000e+00]]
 
- [[ 7.07106781e-01 -7.07106781e-01]
-  [-7.07106781e-01 -7.07106781e-01]]
+ [[-7.07106781e-01 -7.07106781e-01]
+  [ 7.07106781e-01 -7.07106781e-01]]
 
- [[ 2.89310728e-30 -1.00000000e+00]
-  [-1.00000000e+00 -2.89310728e-30]]]
+ [[ 6.48603030e-15 -1.00000000e+00]
+  [-1.00000000e+00 -6.48603030e-15]]]
 </pre></div></div>
 </div>
 </section>
@@ -297,7 +299,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Hartree Fock energy: -0.837796382593709
+Hartree Fock energy: -0.8377963825937088
 </pre></div></div>
 </div>
 <p>Now, we set the evolution time and calculate the exact result of time evolution by directly exponentiating the Hamiltonian using SciPy. Later, we will compare the result of our approximate time evolution with this exact result.</p>
@@ -352,7 +354,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9990275744083491
+Fidelity of Trotter-evolved state with exact state: 0.999027574408349
 </pre></div></div>
 </div>
 <p>The fidelity of the final result can be improved by increasing the number of Trotter steps.</p>
@@ -379,7 +381,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9999906233109653
+Fidelity of Trotter-evolved state with exact state: 0.9999906233109657
 </pre></div></div>
 </div>
 <p>As mentioned above, ffsim already includes functionality for Trotter simulation of double-factorized Hamiltonians. The implementation in ffsim includes higher-order Trotter-Suzuki formulas. The first-order asymmetric formula that we just implemented corresponds to <code class="docutils literal notranslate"><span class="pre">order=0</span></code> in ffsim’s implementation. <code class="docutils literal notranslate"><span class="pre">order=1</span></code> corresponds to the first-order symmetric (commonly known as the second-order) formula, <code class="docutils literal notranslate"><span class="pre">order=2</span></code> corresponds to the second-order symmetric (fourth-order) formula, and so on.</p>
@@ -408,7 +410,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9999906233109653
+Fidelity of Trotter-evolved state with exact state: 0.9999906233109657
 </pre></div></div>
 </div>
 <p>A higher order formula achieves a higher fidelity with fewer Trotter steps:</p>
@@ -436,7 +438,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9999999336740059
+Fidelity of Trotter-evolved state with exact state: 0.9999999336740057
 </pre></div></div>
 </div>
 </section>
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index 2cb8abca1..09532880c 100644
--- a/tutorials/03-double-factorized.ipynb
+++ b/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:58.908837Z",
-     "iopub.status.busy": "2023-10-19T14:39:58.908499Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.292292Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.291735Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.295062Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.294805Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.768940Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.768320Z"
     }
    },
    "outputs": [
@@ -78,14 +78,16 @@
     "mol_hamiltonian = mol_data.hamiltonian\n",
     "\n",
     "# Get the Hamiltonian in the double-factorized representation\n",
-    "df_hamiltonian = ffsim.double_factorized_hamiltonian(mol_hamiltonian)"
+    "df_hamiltonian = ffsim.DoubleFactorizedHamiltonian.from_molecular_hamiltonian(\n",
+    "    mol_hamiltonian\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The function `double_factorized_hamiltonian` returns an object of type `DoubleFactorizedHamiltonian` which is just a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations."
+    "Here, `mol_hamiltonian` is an instance of `MolecularHamiltonian`, a dataclass that stores the one- and two-body tensors, and `df_hamiltonian` is an instance of `DoubleFactorizedHamiltonian`, a dataclass that stores the updated one-body-tensor, diagonal Coulomb matrices, and orbital rotations. In the cell below, we print out the tensors describing the original and double-factorized representations."
    ]
   },
   {
@@ -93,10 +95,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.296046Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.295505Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.303680Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.303208Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.797788Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.796959Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.805806Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.805115Z"
     }
    },
    "outputs": [
@@ -111,44 +113,44 @@
       " [-3.07220771e-16 -6.77238770e-01]]\n",
       "\n",
       "Two-body tensor:\n",
-      "[[[[5.23173938e-01 1.94289029e-16]\n",
-      "   [1.94289029e-16 5.33545754e-01]]\n",
+      "[[[[5.23173938e-01 1.57437591e-16]\n",
+      "   [1.57437591e-16 5.33545754e-01]]\n",
       "\n",
-      "  [[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]]\n",
+      "  [[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]]\n",
       "\n",
       "\n",
-      " [[[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]\n",
+      " [[[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]\n",
       "\n",
-      "  [[5.33545754e-01 1.11022302e-16]\n",
-      "   [1.11022302e-16 5.53132024e-01]]]]\n",
+      "  [[5.33545754e-01 1.24884750e-16]\n",
+      "   [1.24884750e-16 5.53132024e-01]]]]\n",
       "\n",
       "Double-factorized representation\n",
       "--------------------------------\n",
       "One-body tensor:\n",
-      "[[-1.21318608e+00 -4.05183033e-16]\n",
-      " [-4.59876437e-16 -1.07792507e+00]]\n",
+      "[[-1.21318608e+00 -4.25870402e-16]\n",
+      " [-4.76015378e-16 -1.07792507e+00]]\n",
       "\n",
       "Diagonal Coulomb matrices:\n",
-      "[[[ 5.14653029e-001  5.33545754e-001]\n",
-      "  [ 5.33545754e-001  5.53132024e-001]]\n",
+      "[[[ 5.14653029e-01  5.33545754e-01]\n",
+      "  [ 5.33545754e-01  5.53132024e-01]]\n",
       "\n",
-      " [[ 2.48240570e-001 -2.48240570e-001]\n",
-      "  [-2.48240570e-001  2.48240570e-001]]\n",
+      " [[ 2.48240570e-01 -2.48240570e-01]\n",
+      "  [-2.48240570e-01  2.48240570e-01]]\n",
       "\n",
-      " [[ 5.96958401e-121 -7.13206008e-062]\n",
-      "  [-7.13206008e-062  8.52090881e-003]]]\n",
+      " [[ 1.50800163e-59 -3.58462611e-31]\n",
+      "  [-3.58462611e-31  8.52090881e-03]]]\n",
       "\n",
       "Orbital rotations:\n",
-      "[[[-1.00000000e+00  4.25128053e-15]\n",
-      "  [ 4.25128053e-15  1.00000000e+00]]\n",
+      "[[[-1.00000000e+00  8.24520980e-15]\n",
+      "  [ 8.24520980e-15  1.00000000e+00]]\n",
       "\n",
-      " [[ 7.07106781e-01 -7.07106781e-01]\n",
-      "  [-7.07106781e-01 -7.07106781e-01]]\n",
+      " [[-7.07106781e-01 -7.07106781e-01]\n",
+      "  [ 7.07106781e-01 -7.07106781e-01]]\n",
       "\n",
-      " [[ 2.89310728e-30 -1.00000000e+00]\n",
-      "  [-1.00000000e+00 -2.89310728e-30]]]\n"
+      " [[ 6.48603030e-15 -1.00000000e+00]\n",
+      "  [-1.00000000e+00 -6.48603030e-15]]]\n"
      ]
     }
    ],
@@ -227,10 +229,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.307553Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.306455Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.312345Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.311867Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.808878Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.808498Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.813796Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.813248Z"
     }
    },
    "outputs": [],
@@ -285,10 +287,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.315343Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.315133Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.319932Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.319386Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.816718Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.816364Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.820574Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.820031Z"
     }
    },
    "outputs": [],
@@ -325,10 +327,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.322653Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.322251Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.327160Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.326695Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.823525Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.823163Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.828409Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.827885Z"
     }
    },
    "outputs": [
@@ -336,7 +338,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.837796382593709\n"
+      "Hartree Fock energy: -0.8377963825937088\n"
      ]
     }
    ],
@@ -367,10 +369,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.329875Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.329325Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.339042Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.338412Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.831595Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.831104Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.842211Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.841656Z"
     }
    },
    "outputs": [
@@ -409,10 +411,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.341671Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.341479Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.349853Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.349232Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.845098Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.844747Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.853809Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.853262Z"
     }
    },
    "outputs": [
@@ -420,7 +422,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083491\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999027574408349\n"
      ]
     }
    ],
@@ -450,10 +452,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.353772Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.353568Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.390939Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.389931Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.856607Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.856244Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.899624Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.898940Z"
     }
    },
    "outputs": [
@@ -461,7 +463,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -493,10 +495,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.393689Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.393490Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.425221Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.424460Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.902790Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.902330Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.945843Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.945194Z"
     }
    },
    "outputs": [
@@ -504,7 +506,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -535,10 +537,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:39:59.427658Z",
-     "iopub.status.busy": "2023-10-19T14:39:59.427469Z",
-     "iopub.status.idle": "2023-10-19T14:39:59.443022Z",
-     "shell.execute_reply": "2023-10-19T14:39:59.442331Z"
+     "iopub.execute_input": "2023-10-19T16:27:41.949120Z",
+     "iopub.status.busy": "2023-10-19T16:27:41.948837Z",
+     "iopub.status.idle": "2023-10-19T16:27:41.967055Z",
+     "shell.execute_reply": "2023-10-19T16:27:41.966238Z"
     }
    },
    "outputs": [
@@ -546,7 +548,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740059\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740057\n"
      ]
     }
    ],
diff --git a/tutorials/04-lucj.html b/tutorials/04-lucj.html
index 4c09e8dcc..90fc1c8d4 100644
--- a/tutorials/04-lucj.html
+++ b/tutorials/04-lucj.html
@@ -94,8 +94,8 @@ <h1>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-converged SCF energy = -77.4456267643961
-CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000
+converged SCF energy = -77.4456267643962
+CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000
 </pre></div></div>
 </div>
 <section id="The-unitary-cluster-Jastrow-(UCJ)-ansatz">
@@ -151,8 +151,8 @@ <h2>The unitary cluster Jastrow (UCJ) ansatz<a class="headerlink" href="#The-uni
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-E(CCSD) = -77.49387212754462  E_corr = -0.04824536314851573
-Energy at initialialization: -77.46975600021692
+E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851328
+Energy at initialialization: -77.46975600021656
 </pre></div></div>
 </div>
 <p>To facilitate variational optimization of the ansatz, <code class="docutils literal notranslate"><span class="pre">UCJOperator</span></code> implements methods for conversion to and from a vector of real-valued parameters. The precise relation between a parameter vector and the matrices of the UCJ operator is somewhat complicated. In short, the parameter vector stores the entries of the UCJ matrices in a non-redundant way (for the orbital rotations, the parameter vector actually stores the entries of their generators.)</p>
@@ -193,12 +193,12 @@ <h2>The unitary cluster Jastrow (UCJ) ansatz<a class="headerlink" href="#The-uni
   message: CONVERGENCE: REL_REDUCTION_OF_F_&lt;=_FACTR*EPSMCH
   success: True
    status: 0
-      fun: -77.62873343946598
-        x: [-2.541e-01 -8.978e-02 ...  2.239e-01 -5.438e-01]
-      nit: 329
-      jac: [ 6.537e-05  3.098e-04 ...  2.956e-04 -1.734e-04]
-     nfev: 25696
-     njev: 352
+      fun: -77.62901334909452
+        x: [-4.597e-01 -2.974e-01 ...  3.896e-01  1.161e+00]
+      nit: 403
+      jac: [ 9.521e-05  2.245e-04 ...  1.236e-04 -4.150e-04]
+     nfev: 31682
+     njev: 434
  hess_inv: &lt;72x72 LbfgsInvHessProduct with dtype=float64&gt;
 </pre></div></div>
 </div>
@@ -259,12 +259,12 @@ <h2>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
   message: CONVERGENCE: REL_REDUCTION_OF_F_&lt;=_FACTR*EPSMCH
   success: True
    status: 0
-      fun: -77.62881470757267
-        x: [-3.795e+00 -1.386e+00 ... -4.020e-01  1.230e-01]
-      nit: 585
-      jac: [ 4.434e-04 -1.933e-04 ...  4.007e-04 -1.450e-04]
-     nfev: 29422
-     njev: 626
+      fun: -77.62873223663462
+        x: [-1.942e+00  3.888e-01 ...  3.479e-01 -8.915e-02]
+      nit: 285
+      jac: [ 1.563e-05  3.695e-05 ... -1.279e-05 -1.776e-04]
+     nfev: 14335
+     njev: 305
  hess_inv: &lt;46x46 LbfgsInvHessProduct with dtype=float64&gt;
 </pre></div></div>
 </div>
diff --git a/tutorials/04-lucj.ipynb b/tutorials/04-lucj.ipynb
index 1d8185999..c1e1946d5 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:40:01.376785Z",
-     "iopub.status.busy": "2023-10-19T14:40:01.376450Z",
-     "iopub.status.idle": "2023-10-19T14:40:01.984780Z",
-     "shell.execute_reply": "2023-10-19T14:40:01.984205Z"
+     "iopub.execute_input": "2023-10-19T16:27:44.173731Z",
+     "iopub.status.busy": "2023-10-19T16:27:44.173460Z",
+     "iopub.status.idle": "2023-10-19T16:27:44.890778Z",
+     "shell.execute_reply": "2023-10-19T16:27:44.890166Z"
     }
    },
    "outputs": [
@@ -25,14 +25,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "converged SCF energy = -77.4456267643961\n"
+      "converged SCF energy = -77.4456267643962\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000\n"
+      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -109,10 +109,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:40:01.990201Z",
-     "iopub.status.busy": "2023-10-19T14:40:01.988624Z",
-     "iopub.status.idle": "2023-10-19T14:40:02.504800Z",
-     "shell.execute_reply": "2023-10-19T14:40:02.504249Z"
+     "iopub.execute_input": "2023-10-19T16:27:44.897251Z",
+     "iopub.status.busy": "2023-10-19T16:27:44.895577Z",
+     "iopub.status.idle": "2023-10-19T16:27:45.598357Z",
+     "shell.execute_reply": "2023-10-19T16:27:45.597692Z"
     }
    },
    "outputs": [
@@ -120,14 +120,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754462  E_corr = -0.04824536314851573\n"
+      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851328\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -77.46975600021692\n"
+      "Energy at initialialization: -77.46975600021656\n"
      ]
     }
    ],
@@ -177,10 +177,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:40:02.507719Z",
-     "iopub.status.busy": "2023-10-19T14:40:02.507477Z",
-     "iopub.status.idle": "2023-10-19T14:41:13.658634Z",
-     "shell.execute_reply": "2023-10-19T14:41:13.658109Z"
+     "iopub.execute_input": "2023-10-19T16:27:45.601966Z",
+     "iopub.status.busy": "2023-10-19T16:27:45.601316Z",
+     "iopub.status.idle": "2023-10-19T16:29:31.891294Z",
+     "shell.execute_reply": "2023-10-19T16:29:31.890594Z"
     }
    },
    "outputs": [
@@ -192,12 +192,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62873343946598\n",
-      "        x: [-2.541e-01 -8.978e-02 ...  2.239e-01 -5.438e-01]\n",
-      "      nit: 329\n",
-      "      jac: [ 6.537e-05  3.098e-04 ...  2.956e-04 -1.734e-04]\n",
-      "     nfev: 25696\n",
-      "     njev: 352\n",
+      "      fun: -77.62901334909452\n",
+      "        x: [-4.597e-01 -2.974e-01 ...  3.896e-01  1.161e+00]\n",
+      "      nit: 403\n",
+      "      jac: [ 9.521e-05  2.245e-04 ...  1.236e-04 -4.150e-04]\n",
+      "     nfev: 31682\n",
+      "     njev: 434\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -252,10 +252,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:41:13.662631Z",
-     "iopub.status.busy": "2023-10-19T14:41:13.661664Z",
-     "iopub.status.idle": "2023-10-19T14:42:35.356542Z",
-     "shell.execute_reply": "2023-10-19T14:42:35.356016Z"
+     "iopub.execute_input": "2023-10-19T16:29:31.895316Z",
+     "iopub.status.busy": "2023-10-19T16:29:31.894949Z",
+     "iopub.status.idle": "2023-10-19T16:30:19.776632Z",
+     "shell.execute_reply": "2023-10-19T16:30:19.776089Z"
     }
    },
    "outputs": [
@@ -267,12 +267,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62881470757267\n",
-      "        x: [-3.795e+00 -1.386e+00 ... -4.020e-01  1.230e-01]\n",
-      "      nit: 585\n",
-      "      jac: [ 4.434e-04 -1.933e-04 ...  4.007e-04 -1.450e-04]\n",
-      "     nfev: 29422\n",
-      "     njev: 626\n",
+      "      fun: -77.62873223663462\n",
+      "        x: [-1.942e+00  3.888e-01 ...  3.479e-01 -8.915e-02]\n",
+      "      nit: 285\n",
+      "      jac: [ 1.563e-05  3.695e-05 ... -1.279e-05 -1.776e-04]\n",
+      "     nfev: 14335\n",
+      "     njev: 305\n",
       " hess_inv: <46x46 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
diff --git a/tutorials/05-fermion-operator.html b/tutorials/05-fermion-operator.html
index 95315f332..f8a4dd5b1 100644
--- a/tutorials/05-fermion-operator.html
+++ b/tutorials/05-fermion-operator.html
@@ -78,8 +78,8 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
-    (cre_a(0), des_a(3)): 0.5,
     (cre_b(1), des_b(5), cre_a(4)): 1+1j,
+    (cre_a(0), des_a(3)): 0.5,
     (cre_a(3), des_a(0)): -0.25
 })
 </pre></div></div>
@@ -99,7 +99,7 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-&#39;FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j})&#39;
+&#39;FermionOperator({((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j})&#39;
 </pre></div></div>
 </div>
 <p>FermionOperators support arithmetic operations. Note that when multiplying a FermionOperator by a scalar, the scalar must go on the left, i.e. <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">*</span> <span class="pre">op</span></code> and not <code class="docutils literal notranslate"><span class="pre">op</span> <span class="pre">*</span> <span class="pre">2</span></code>.</p>
@@ -128,16 +128,16 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="highlight"><pre>
 FermionOperator({
     (des_a(3), des_b(3)): 0.0625,
-    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
-    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
-    (cre_a(3), des_a(0)): -0.5,
     (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
-    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
-    (cre_a(0), des_a(3)): 1,
-    (cre_b(1), des_b(5), cre_a(4)): 2+2j,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
+    (cre_a(0), des_a(3)): 1,
     (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
-    (cre_b(2)): 0-0.25j
+    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
+    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
+    (cre_b(2)): 0-0.25j,
+    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
+    (cre_b(1), des_b(5), cre_a(4)): 2+2j,
+    (cre_a(3), des_a(0)): -0.5
 })
 </pre></div></div>
 </div>
@@ -163,16 +163,16 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="highlight"><pre>
 FermionOperator({
     (des_a(3), des_b(3)): 0-1.25j,
-    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
-    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
-    (cre_a(3), des_a(0)): 0+3j,
     (cre_a(0), des_a(3), cre_b(2)): 2,
-    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
-    (cre_a(0), des_a(3)): 0-6j,
-    (cre_b(1), des_b(5), cre_a(4)): 12-12j,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,
+    (cre_a(0), des_a(3)): 0-6j,
     (cre_a(3), des_a(0), cre_b(2)): -1,
-    (cre_b(2)): -5
+    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
+    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
+    (cre_b(2)): -5,
+    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
+    (cre_b(1), des_b(5), cre_a(4)): 12-12j,
+    (cre_a(3), des_a(0)): 0+3j
 })
 </pre></div></div>
 </div>
@@ -193,16 +193,16 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
-    (cre_a(3), des_a(0)): 0+3j,
-    (cre_b(2)): -5,
-    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,
-    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
-    (cre_a(0), des_a(3)): 0-6j,
-    (cre_b(2), cre_a(0), des_a(3)): 2,
-    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
     (des_b(3), des_a(3)): 0+1.25j,
+    (cre_b(2), cre_a(0), des_a(3)): 2,
+    (cre_a(0), des_a(3)): 0-6j,
     (cre_b(2), cre_a(3), des_a(0)): -1,
-    (cre_b(1), cre_a(4), des_b(5)): -12+12j
+    (cre_b(1), cre_a(4), des_b(5)): -12+12j,
+    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
+    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
+    (cre_a(3), des_a(0)): 0+3j,
+    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,
+    (cre_b(2)): -5
 })
 </pre></div></div>
 </div>
@@ -271,11 +271,11 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-array([0.        +0.j        , 0.        +0.j        ,
-       0.        +0.j        , 0.        +0.j        ,
-       0.11889056-0.13114645j, 0.        +0.j        ,
-       0.        +0.j        , 0.        +0.j        ,
-       0.        +0.j        ])
+array([0.        +0.j       , 0.        +0.j       ,
+       0.        +0.j       , 0.        +0.j       ,
+       0.14601055-0.2517831j, 0.        +0.j       ,
+       0.        +0.j       , 0.        +0.j       ,
+       0.        +0.j       ])
 </pre></div></div>
 </div>
 <p>It can also be passed into most linear algebra routines in <code class="docutils literal notranslate"><span class="pre">scipy.sparse.linalg</span></code>.</p>
diff --git a/tutorials/05-fermion-operator.ipynb b/tutorials/05-fermion-operator.ipynb
index fa09bcb38..e5cda2ddd 100644
--- a/tutorials/05-fermion-operator.ipynb
+++ b/tutorials/05-fermion-operator.ipynb
@@ -29,10 +29,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.077633Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.077306Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.362479Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.361769Z"
+     "iopub.execute_input": "2023-10-19T16:30:21.670393Z",
+     "iopub.status.busy": "2023-10-19T16:30:21.669989Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.023880Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.023224Z"
     }
    },
    "outputs": [
@@ -40,8 +40,8 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(0), des_a(3)): 0.5,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 1+1j,\n",
+       "    (cre_a(0), des_a(3)): 0.5,\n",
        "    (cre_a(3), des_a(0)): -0.25\n",
        "})"
       ]
@@ -76,17 +76,17 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.367296Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.366261Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.372138Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.371678Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.028811Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.027408Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.034307Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.033759Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j})'"
+       "'FermionOperator({((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j})'"
       ]
      },
      "execution_count": 2,
@@ -110,10 +110,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.375800Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.374921Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.381567Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.381116Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.037944Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.037568Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.044977Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.044445Z"
     }
    },
    "outputs": [
@@ -122,16 +122,16 @@
       "text/plain": [
        "FermionOperator({\n",
        "    (des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
-       "    (cre_a(3), des_a(0)): -0.5,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
-       "    (cre_a(0), des_a(3)): 1,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
+       "    (cre_a(0), des_a(3)): 1,\n",
        "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
-       "    (cre_b(2)): 0-0.25j\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
+       "    (cre_b(2)): 0-0.25j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_a(3), des_a(0)): -0.5\n",
        "})"
       ]
      },
@@ -169,10 +169,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.385304Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.384396Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.390385Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.389901Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.049374Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.048155Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.054897Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.054383Z"
     }
    },
    "outputs": [
@@ -181,16 +181,16 @@
       "text/plain": [
        "FermionOperator({\n",
        "    (des_a(3), des_b(3)): 0-1.25j,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_b(2)): -5\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
+       "    (cre_b(2)): -5,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_a(3), des_a(0)): 0+3j\n",
        "})"
       ]
      },
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.394709Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.393740Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.399514Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.399055Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.058256Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.057797Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.064878Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.064352Z"
     }
    },
    "outputs": [
@@ -230,16 +230,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\n",
-       "    (cre_b(2)): -5,\n",
-       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
-       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
-       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
-       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (des_b(3), des_a(3)): 0+1.25j,\n",
+       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
-       "    (cre_b(1), cre_a(4), des_b(5)): -12+12j\n",
+       "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
+       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,\n",
+       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
+       "    (cre_a(3), des_a(0)): 0+3j,\n",
+       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
+       "    (cre_b(2)): -5\n",
        "})"
       ]
      },
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.403183Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.402262Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.407487Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.407040Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.069240Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.068020Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.074090Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.073516Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.411097Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.410179Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.416471Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.416023Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.078346Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.077123Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.084444Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.083907Z"
     }
    },
    "outputs": [
@@ -340,21 +340,21 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.420049Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.419152Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.426669Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.426204Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.087872Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.087478Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.095690Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.095163Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.11889056-0.13114645j, 0.        +0.j        ,\n",
-       "       0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.        +0.j        ])"
+       "array([0.        +0.j       , 0.        +0.j       ,\n",
+       "       0.        +0.j       , 0.        +0.j       ,\n",
+       "       0.14601055-0.2517831j, 0.        +0.j       ,\n",
+       "       0.        +0.j       , 0.        +0.j       ,\n",
+       "       0.        +0.j       ])"
       ]
      },
      "execution_count": 8,
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-19T14:42:37.430250Z",
-     "iopub.status.busy": "2023-10-19T14:42:37.429345Z",
-     "iopub.status.idle": "2023-10-19T14:42:37.441262Z",
-     "shell.execute_reply": "2023-10-19T14:42:37.440811Z"
+     "iopub.execute_input": "2023-10-19T16:30:22.099160Z",
+     "iopub.status.busy": "2023-10-19T16:30:22.098684Z",
+     "iopub.status.idle": "2023-10-19T16:30:22.112817Z",
+     "shell.execute_reply": "2023-10-19T16:30:22.112282Z"
     }
    },
    "outputs": [