From 6a2c8f174098e732e9bbbc82baef35094d92a66a Mon Sep 17 00:00:00 2001
From: kevinsung <kevinsung@users.noreply.github.com>
Date: Wed, 25 Oct 2023 22:52:38 +0000
Subject: [PATCH] deploy: ddd5f4d35bc5f40282583cf147b5f7cb25b4e6a3

---
 .doctrees/api/ffsim.doctree                   | Bin 464526 -> 466740 bytes
 .doctrees/environment.pickle                  | Bin 1486283 -> 1488945 bytes
 .../nbsphinx/tutorials/01-introduction.ipynb  |  24 ++--
 .../tutorials/02-orbital-rotation.ipynb       |  32 ++---
 .../tutorials/03-double-factorized.ipynb      | 128 +++++++++---------
 .doctrees/nbsphinx/tutorials/04-lucj.ipynb    |  60 ++++----
 .../tutorials/05-entanglement-forging.ipynb   |  32 ++---
 .../tutorials/06-fermion-operator.ipynb       | 126 ++++++++---------
 .../tutorials/03-double-factorized.doctree    | Bin 54750 -> 54828 bytes
 .doctrees/tutorials/04-lucj.doctree           | Bin 38282 -> 38282 bytes
 .../tutorials/05-entanglement-forging.doctree | Bin 15260 -> 15260 bytes
 .../tutorials/06-fermion-operator.doctree     | Bin 41385 -> 41385 bytes
 api/ffsim.html                                |  29 +++-
 searchindex.js                                |   2 +-
 tutorials/01-introduction.ipynb               |  24 ++--
 tutorials/02-orbital-rotation.ipynb           |  32 ++---
 tutorials/03-double-factorized.html           |  48 +++----
 tutorials/03-double-factorized.ipynb          | 128 +++++++++---------
 tutorials/04-lucj.html                        |  28 ++--
 tutorials/04-lucj.ipynb                       |  60 ++++----
 tutorials/05-entanglement-forging.html        |   8 +-
 tutorials/05-entanglement-forging.ipynb       |  32 ++---
 tutorials/06-fermion-operator.html            |  54 ++++----
 tutorials/06-fermion-operator.ipynb           | 126 ++++++++---------
 24 files changed, 500 insertions(+), 473 deletions(-)

diff --git a/.doctrees/api/ffsim.doctree b/.doctrees/api/ffsim.doctree
index ea24b10f4f7624187f1f75f5aa42abb2ee567d88..06017123316c6acc0c9dfe803be6d6b599fbdf78 100644
GIT binary patch
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diff --git a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
index aabe78f3d..11328c287 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": "2023-10-25T22:36:55.806469Z",
-     "iopub.status.busy": "2023-10-25T22:36:55.806037Z",
-     "iopub.status.idle": "2023-10-25T22:36:56.173437Z",
-     "shell.execute_reply": "2023-10-25T22:36:56.172708Z"
+     "iopub.execute_input": "2023-10-25T22:49:45.728598Z",
+     "iopub.status.busy": "2023-10-25T22:49:45.728154Z",
+     "iopub.status.idle": "2023-10-25T22:49:46.110527Z",
+     "shell.execute_reply": "2023-10-25T22:49:46.109715Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:56.178612Z",
-     "iopub.status.busy": "2023-10-25T22:36:56.177304Z",
-     "iopub.status.idle": "2023-10-25T22:36:56.183207Z",
-     "shell.execute_reply": "2023-10-25T22:36:56.182642Z"
+     "iopub.execute_input": "2023-10-25T22:49:46.115961Z",
+     "iopub.status.busy": "2023-10-25T22:49:46.114597Z",
+     "iopub.status.idle": "2023-10-25T22:49:46.120985Z",
+     "shell.execute_reply": "2023-10-25T22:49:46.120363Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:56.187737Z",
-     "iopub.status.busy": "2023-10-25T22:36:56.186648Z",
-     "iopub.status.idle": "2023-10-25T22:36:56.191149Z",
-     "shell.execute_reply": "2023-10-25T22:36:56.190587Z"
+     "iopub.execute_input": "2023-10-25T22:49:46.125500Z",
+     "iopub.status.busy": "2023-10-25T22:49:46.124419Z",
+     "iopub.status.idle": "2023-10-25T22:49:46.129349Z",
+     "shell.execute_reply": "2023-10-25T22:49:46.128546Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index 9abbe1985..f05ba4dfe 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": "2023-10-25T22:36:58.052305Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.052068Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.418054Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.417323Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.191448Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.191046Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.607593Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.606670Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:58.422655Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.422015Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.459609Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.458938Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.612660Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.611183Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.690073Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.689235Z"
     }
    },
    "outputs": [],
@@ -158,10 +158,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:58.463437Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.463084Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.475859Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.475248Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.695786Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.694689Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.709764Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.709040Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:58.478982Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.478632Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.485259Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.484661Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.714702Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.713656Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.720156Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.719563Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index e679311ce..edaf5c8f2 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": "2023-10-25T22:37:00.564527Z",
-     "iopub.status.busy": "2023-10-25T22:37:00.563943Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.040069Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.039225Z"
+     "iopub.execute_input": "2023-10-25T22:49:50.631452Z",
+     "iopub.status.busy": "2023-10-25T22:49:50.630936Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.083516Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.082556Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.043849Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.043504Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.049845Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.049303Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.087434Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.086734Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.094705Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.093973Z"
     }
    },
    "outputs": [
@@ -106,28 +106,28 @@
       "Original representation\n",
       "-----------------------\n",
       "One-body tensor:\n",
-      "[[-8.27478830e-01 -8.52909490e-17]\n",
-      " [-5.57029092e-17 -6.77238770e-01]]\n",
+      "[[-8.27478830e-01 -1.09243819e-16]\n",
+      " [-7.48351655e-17 -6.77238770e-01]]\n",
       "\n",
       "Two-body tensor:\n",
-      "[[[[5.23173938e-01 3.58782168e-17]\n",
-      "   [3.58782168e-17 5.33545754e-01]]\n",
+      "[[[[ 5.23173938e-01 -5.00678144e-19]\n",
+      "   [-5.00678144e-19  5.33545754e-01]]\n",
       "\n",
-      "  [[2.49859013e-17 2.48240570e-01]\n",
-      "   [2.48240570e-01 4.83067333e-17]]]\n",
+      "  [[ 5.85364508e-18  2.48240570e-01]\n",
+      "   [ 2.48240570e-01 -1.17688164e-17]]]\n",
       "\n",
       "\n",
-      " [[[2.49859013e-17 2.48240570e-01]\n",
-      "   [2.48240570e-01 4.83067333e-17]]\n",
+      " [[[ 5.85364508e-18  2.48240570e-01]\n",
+      "   [ 2.48240570e-01 -1.17688164e-17]]\n",
       "\n",
-      "  [[5.33545754e-01 4.01841799e-17]\n",
-      "   [4.01841799e-17 5.53132024e-01]]]]\n",
+      "  [[ 5.33545754e-01  1.05429868e-17]\n",
+      "   [ 1.05429868e-17  5.53132024e-01]]]]\n",
       "\n",
       "Double-factorized representation\n",
       "--------------------------------\n",
       "One-body tensor:\n",
-      "[[-1.21318608e+00 -1.27383424e-16]\n",
-      " [-8.82879498e-17 -1.07792507e+00]]\n",
+      "[[-1.21318608e+00 -1.03109072e-16]\n",
+      " [-8.30334814e-17 -1.07792507e+00]]\n",
       "\n",
       "Diagonal Coulomb matrices:\n",
       "[[[ 5.14653029e-01  5.33545754e-01]\n",
@@ -136,18 +136,18 @@
       " [[ 2.48240570e-01 -2.48240570e-01]\n",
       "  [-2.48240570e-01  2.48240570e-01]]\n",
       "\n",
-      " [[ 2.27521846e-62 -1.39236953e-32]\n",
-      "  [-1.39236953e-32  8.52090881e-03]]]\n",
+      " [[ 1.44655364e-30 -1.11022302e-16]\n",
+      "  [-1.11022302e-16  8.52090881e-03]]]\n",
       "\n",
       "Orbital rotations:\n",
       "[[[ 1.00000000e+00  0.00000000e+00]\n",
       "  [ 0.00000000e+00  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",
-      " [[-1.27830444e-15 -1.00000000e+00]\n",
-      "  [-1.00000000e+00  1.27830444e-15]]]\n"
+      " [[ 7.45733039e-16 -1.00000000e+00]\n",
+      "  [-1.00000000e+00 -7.45733039e-16]]]\n"
      ]
     }
    ],
@@ -226,10 +226,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.053112Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.052436Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.058006Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.057392Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.097615Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.097224Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.103382Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.102656Z"
     }
    },
    "outputs": [],
@@ -284,10 +284,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.061751Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.060649Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.066205Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.065642Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.106760Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.106190Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.111174Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.110496Z"
     }
    },
    "outputs": [],
@@ -324,10 +324,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.069111Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.068667Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.074495Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.073941Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.115052Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.114792Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.121182Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.120373Z"
     }
    },
    "outputs": [
@@ -335,7 +335,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.8377963825937084\n"
+      "Hartree Fock energy: -0.837796382593709\n"
      ]
     }
    ],
@@ -366,10 +366,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.077458Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.076848Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.087132Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.086577Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.125523Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.124134Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.137942Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.137232Z"
     }
    },
    "outputs": [
@@ -377,7 +377,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of evolved state w.r.t. initial state: 0.9696296369955066\n"
+      "Fidelity of evolved state w.r.t. initial state: 0.9696296369955065\n"
      ]
     }
    ],
@@ -408,10 +408,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.090228Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.089559Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.098344Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.097773Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.143052Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.142490Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.155779Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.155041Z"
     }
    },
    "outputs": [
@@ -419,7 +419,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083494\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083491\n"
      ]
     }
    ],
@@ -449,10 +449,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.101276Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.100835Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.145337Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.144745Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.160933Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.159642Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.211316Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.210559Z"
     }
    },
    "outputs": [
@@ -460,7 +460,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109686\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999990623310968\n"
      ]
     }
    ],
@@ -492,10 +492,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.148276Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.147912Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.188137Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.186555Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.215690Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.214603Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.254790Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.254051Z"
     }
    },
    "outputs": [
@@ -503,7 +503,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109686\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999990623310968\n"
      ]
     }
    ],
@@ -534,10 +534,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.191299Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.190992Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.208147Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.207353Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.259870Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.258672Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.277545Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.276466Z"
     }
    },
    "outputs": [
@@ -545,7 +545,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740067\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740071\n"
      ]
     }
    ],
diff --git a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
index 67833f1b8..fffa14560 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": "2023-10-25T22:37:03.486939Z",
-     "iopub.status.busy": "2023-10-25T22:37:03.486686Z",
-     "iopub.status.idle": "2023-10-25T22:37:04.171218Z",
-     "shell.execute_reply": "2023-10-25T22:37:04.170426Z"
+     "iopub.execute_input": "2023-10-25T22:49:53.689996Z",
+     "iopub.status.busy": "2023-10-25T22:49:53.689777Z",
+     "iopub.status.idle": "2023-10-25T22:49:54.502302Z",
+     "shell.execute_reply": "2023-10-25T22:49:54.501564Z"
     }
    },
    "outputs": [
@@ -32,7 +32,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -77.6290254326716  E(CI) = -3.57322412553862  S^2 = 0.0000000\n"
+      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -110,10 +110,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:04.175035Z",
-     "iopub.status.busy": "2023-10-25T22:37:04.174671Z",
-     "iopub.status.idle": "2023-10-25T22:37:04.834102Z",
-     "shell.execute_reply": "2023-10-25T22:37:04.833507Z"
+     "iopub.execute_input": "2023-10-25T22:49:54.506302Z",
+     "iopub.status.busy": "2023-10-25T22:49:54.505497Z",
+     "iopub.status.idle": "2023-10-25T22:49:54.965101Z",
+     "shell.execute_reply": "2023-10-25T22:49:54.964409Z"
     }
    },
    "outputs": [
@@ -121,7 +121,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851268\n"
+      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851462\n"
      ]
     },
     {
@@ -176,10 +176,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:04.838993Z",
-     "iopub.status.busy": "2023-10-25T22:37:04.838311Z",
-     "iopub.status.idle": "2023-10-25T22:38:17.168913Z",
-     "shell.execute_reply": "2023-10-25T22:38:17.168300Z"
+     "iopub.execute_input": "2023-10-25T22:49:54.968428Z",
+     "iopub.status.busy": "2023-10-25T22:49:54.968008Z",
+     "iopub.status.idle": "2023-10-25T22:51:17.439791Z",
+     "shell.execute_reply": "2023-10-25T22:51:17.439126Z"
     }
    },
    "outputs": [
@@ -191,12 +191,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62902198093012\n",
-      "        x: [-2.843e-01  5.591e-01 ... -1.720e-01 -3.600e-01]\n",
-      "      nit: 269\n",
-      "      jac: [ 2.416e-05 -3.126e-05 ... -1.606e-04  9.948e-06]\n",
-      "     nfev: 21316\n",
-      "     njev: 292\n",
+      "      fun: -77.62896682018224\n",
+      "        x: [-1.932e-01  1.104e+00 ... -3.429e-01 -1.010e-01]\n",
+      "      nit: 226\n",
+      "      jac: [ 3.268e-05  8.527e-06 ... -9.123e-04 -3.965e-04]\n",
+      "     nfev: 17593\n",
+      "     njev: 241\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -251,10 +251,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:38:17.173783Z",
-     "iopub.status.busy": "2023-10-25T22:38:17.172653Z",
-     "iopub.status.idle": "2023-10-25T22:39:33.968944Z",
-     "shell.execute_reply": "2023-10-25T22:39:33.968334Z"
+     "iopub.execute_input": "2023-10-25T22:51:17.443422Z",
+     "iopub.status.busy": "2023-10-25T22:51:17.442815Z",
+     "iopub.status.idle": "2023-10-25T22:52:26.644022Z",
+     "shell.execute_reply": "2023-10-25T22:52:26.643271Z"
     }
    },
    "outputs": [
@@ -266,12 +266,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62848215844997\n",
-      "        x: [ 6.198e-01 -6.593e-02 ...  1.183e-01 -1.078e-01]\n",
-      "      nit: 450\n",
-      "      jac: [ 1.492e-04 -2.629e-04 ...  1.435e-04 -3.638e-04]\n",
-      "     nfev: 22701\n",
-      "     njev: 483\n",
+      "      fun: -77.62865917328423\n",
+      "        x: [-1.028e+00 -1.315e+00 ... -4.903e-01  1.494e+00]\n",
+      "      nit: 290\n",
+      "      jac: [-5.969e-05  9.095e-05 ...  5.741e-04 -3.297e-04]\n",
+      "     nfev: 14664\n",
+      "     njev: 312\n",
       " hess_inv: <46x46 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
diff --git a/.doctrees/nbsphinx/tutorials/05-entanglement-forging.ipynb b/.doctrees/nbsphinx/tutorials/05-entanglement-forging.ipynb
index fa8dfa58b..3b672189f 100644
--- a/.doctrees/nbsphinx/tutorials/05-entanglement-forging.ipynb
+++ b/.doctrees/nbsphinx/tutorials/05-entanglement-forging.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:35.902653Z",
-     "iopub.status.busy": "2023-10-25T22:39:35.902244Z",
-     "iopub.status.idle": "2023-10-25T22:39:36.610182Z",
-     "shell.execute_reply": "2023-10-25T22:39:36.609495Z"
+     "iopub.execute_input": "2023-10-25T22:52:28.457365Z",
+     "iopub.status.busy": "2023-10-25T22:52:28.457064Z",
+     "iopub.status.idle": "2023-10-25T22:52:29.067914Z",
+     "shell.execute_reply": "2023-10-25T22:52:29.067063Z"
     }
    },
    "outputs": [
@@ -32,7 +32,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -75.7079508859773  E(CI) = -14.3336207346502  S^2 = 0.0000000\n"
+      "CASCI E = -75.7079508859772  E(CI) = -14.3336207346500  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -90,10 +90,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:36.614713Z",
-     "iopub.status.busy": "2023-10-25T22:39:36.614126Z",
-     "iopub.status.idle": "2023-10-25T22:39:36.641876Z",
-     "shell.execute_reply": "2023-10-25T22:39:36.641194Z"
+     "iopub.execute_input": "2023-10-25T22:52:29.074034Z",
+     "iopub.status.busy": "2023-10-25T22:52:29.072439Z",
+     "iopub.status.idle": "2023-10-25T22:52:29.107737Z",
+     "shell.execute_reply": "2023-10-25T22:52:29.107079Z"
     }
    },
    "outputs": [
@@ -101,7 +101,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -75.68366174447621\n"
+      "Energy at initialialization: -75.68366174447613\n"
      ]
     }
    ],
@@ -135,10 +135,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:36.645471Z",
-     "iopub.status.busy": "2023-10-25T22:39:36.644784Z",
-     "iopub.status.idle": "2023-10-25T22:39:38.706845Z",
-     "shell.execute_reply": "2023-10-25T22:39:38.706152Z"
+     "iopub.execute_input": "2023-10-25T22:52:29.112535Z",
+     "iopub.status.busy": "2023-10-25T22:52:29.111203Z",
+     "iopub.status.idle": "2023-10-25T22:52:32.034045Z",
+     "shell.execute_reply": "2023-10-25T22:52:32.033073Z"
     }
    },
    "outputs": [
@@ -150,8 +150,8 @@
       " message: Maximum number of function evaluations has been exceeded.\n",
       " success: False\n",
       "  status: 2\n",
-      "     fun: -75.69430210093412\n",
-      "       x: [ 1.344e+00  8.447e-02 -1.883e-03  1.105e+00 -1.881e-01]\n",
+      "     fun: -75.69447115688286\n",
+      "       x: [ 1.354e+00  9.455e-02 -3.884e-03  1.094e+00 -2.122e-01]\n",
       "    nfev: 100\n",
       "   maxcv: 0.0\n"
      ]
diff --git a/.doctrees/nbsphinx/tutorials/06-fermion-operator.ipynb b/.doctrees/nbsphinx/tutorials/06-fermion-operator.ipynb
index 300ae3e7f..b2f6037d5 100644
--- a/.doctrees/nbsphinx/tutorials/06-fermion-operator.ipynb
+++ b/.doctrees/nbsphinx/tutorials/06-fermion-operator.ipynb
@@ -29,10 +29,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.366920Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.366331Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.732340Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.731690Z"
+     "iopub.execute_input": "2023-10-25T22:52:33.852859Z",
+     "iopub.status.busy": "2023-10-25T22:52:33.852631Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.239320Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.238688Z"
     }
    },
    "outputs": [
@@ -40,9 +40,9 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0)): -0.25,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 1+1j,\n",
-       "    (cre_a(0), des_a(3)): 0.5\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": "2023-10-25T22:39:40.737597Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.736319Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.743718Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.742835Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.243762Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.243037Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.250376Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.249693Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+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": "2023-10-25T22:39:40.748237Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.747115Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.754695Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.754158Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.255144Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.253705Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.262286Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.261401Z"
     }
    },
    "outputs": [
@@ -121,17 +121,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
        "    (cre_a(3), des_a(0)): -0.5,\n",
+       "    (cre_a(0), des_a(3)): 1,\n",
        "    (cre_b(2)): 0-0.25j,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
        "    (des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
-       "    (cre_a(0), des_a(3)): 1,\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_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
+       "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
+       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j\n",
        "})"
       ]
      },
@@ -169,10 +169,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.759235Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.758153Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.765084Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.764539Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.267159Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.265631Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.272698Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.272094Z"
     }
    },
    "outputs": [
@@ -180,17 +180,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
        "    (cre_a(3), des_a(0)): 0+3j,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_b(2)): -5,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
        "    (des_a(3), des_b(3)): 0-1.25j,\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\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_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
+       "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
+       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j\n",
        "})"
       ]
      },
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.769541Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.768482Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.774962Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.774400Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.277397Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.275959Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.283129Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.282399Z"
     }
    },
    "outputs": [
@@ -230,16 +230,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
-       "    (des_b(3), des_a(3)): 0+1.25j,\n",
-       "    (cre_b(2), cre_a(3), des_a(0)): -1,\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_a(3), des_a(0)): 0+3j,\n",
-       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
+       "    (cre_b(2)): -5,\n",
+       "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
        "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\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_a(0), des_a(3)): 2,\n",
+       "    (des_b(3), des_a(3)): 0+1.25j,\n",
+       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j\n",
        "})"
       ]
      },
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.779369Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.778283Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.784339Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.783767Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.287780Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.286254Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.294121Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.292778Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.789452Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.788382Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.795811Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.795259Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.298274Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.297778Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.304979Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.304437Z"
     }
    },
    "outputs": [
@@ -340,10 +340,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.800327Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.799255Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.808120Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.807530Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.309028Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.308520Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.317214Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.316562Z"
     }
    },
    "outputs": [
@@ -352,7 +352,7 @@
       "text/plain": [
        "array([0.        +0.j        , 0.        +0.j        ,\n",
        "       0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.14416721+0.01183319j, 0.        +0.j        ,\n",
+       "       0.08465914-0.16438186j, 0.        +0.j        ,\n",
        "       0.        +0.j        , 0.        +0.j        ,\n",
        "       0.        +0.j        ])"
       ]
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.812478Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.811398Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.826762Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.826205Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.320550Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.320183Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.336019Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.335310Z"
     }
    },
    "outputs": [
diff --git a/.doctrees/tutorials/03-double-factorized.doctree b/.doctrees/tutorials/03-double-factorized.doctree
index 61df3933ff9f7059c5ecb87d4b6aeedb282a74d4..c6e7bf4ba2298e51501eb4457d0c11c41d9227ce 100644
GIT binary patch
delta 3218
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diff --git a/api/ffsim.html b/api/ffsim.html
index 5294fabef..301dafc01 100644
--- a/api/ffsim.html
+++ b/api/ffsim.html
@@ -298,7 +298,34 @@
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
 <p>A fermionic operator.</p>
 <p>A FermionOperator represents a linear combination of products of fermionic creation
-and annihilation operators.</p>
+and annihilation operators. See <a class="reference internal" href="../tutorials/06-fermion-operator.html"><span class="doc">The FermionOperator class</span></a>
+for an explanation of how to use this class.</p>
+<p>Example:</p>
+<div class="jupyter_cell jupyter_container docutils container">
+<div class="cell_input code_cell docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">ffsim</span>
+
+<span class="n">op</span> <span class="o">=</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">FermionOperator</span><span class="p">(</span>
+    <span class="p">{</span>
+        <span class="p">(</span><span class="n">ffsim</span><span class="o">.</span><span class="n">cre_a</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">des_a</span><span class="p">(</span><span class="mi">3</span><span class="p">)):</span> <span class="mf">0.5</span><span class="p">,</span>
+        <span class="p">(</span><span class="n">ffsim</span><span class="o">.</span><span class="n">cre_a</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">des_a</span><span class="p">(</span><span class="mi">0</span><span class="p">)):</span> <span class="o">-</span><span class="mf">0.25</span><span class="p">,</span>
+        <span class="p">(</span><span class="n">ffsim</span><span class="o">.</span><span class="n">cre_b</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">des_b</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span> <span class="n">ffsim</span><span class="o">.</span><span class="n">cre_a</span><span class="p">(</span><span class="mi">4</span><span class="p">)):</span> <span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="p">,</span>
+    <span class="p">}</span>
+<span class="p">)</span>
+<span class="n">op</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output text_plain highlight-none notranslate"><div class="highlight"><pre><span></span>FermionOperator({
+    (cre_b(1), des_b(5), cre_a(4)): 1+1j,
+    (cre_a(3), des_a(0)): -0.25,
+    (cre_a(0), des_a(3)): 0.5
+})
+</pre></div>
+</div>
+</div>
+</div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>coeffs</strong> (<em>dict</em><em>[</em><em>tuple</em><em>[</em><em>tuple</em><em>[</em><em>bool</em><em>, </em><em>bool</em><em>, </em><em>int</em><em>]</em><em>, </em><em>...</em><em>]</em><em>, </em><em>complex</em><em>]</em>) – The coefficients of the
diff --git a/searchindex.js b/searchindex.js
index 766048bdb..c5c374740 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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"norb (ffsim.doublefactorizedhamiltonian property)": [[0, "ffsim.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.norb"]], "norb (ffsim.molecularhamiltonian property)": [[0, "ffsim.MolecularHamiltonian.norb"]], "norb (ffsim.ucjoperator property)": [[0, "ffsim.UCJOperator.norb"]], "normal_ordered() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.normal_ordered"]], "one_body_tensor (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.one_body_tensor"]], "one_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.one_body_tensor"]], "one_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.one_body_tensor"]], "one_hot() (in module ffsim)": [[0, "ffsim.one_hot"]], "orb (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.orb"]], "orbital_rotations (ffsim.doublefactorizedhamiltonian attribute)": [[0, 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"ffsim.UCJOperator.to_t_amplitudes"]], "to_z_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_z_representation"]], "trace() (in module ffsim)": [[0, "ffsim.trace"]], "two_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.two_body_tensor"]], "two_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.z_representation"]], "contract_diag_coulomb() (in module ffsim.contract)": [[1, "ffsim.contract.contract_diag_coulomb"]], "contract_num_op_sum() (in module ffsim.contract)": [[1, "ffsim.contract.contract_num_op_sum"]], "diag_coulomb_linop() (in module ffsim.contract)": [[1, "ffsim.contract.diag_coulomb_linop"]], "ffsim.contract": [[1, "module-ffsim.contract"]], "num_op_sum_linop() (in module ffsim.contract)": [[1, "ffsim.contract.num_op_sum_linop"]], "one_body_linop() (in module ffsim.contract)": [[1, "ffsim.contract.one_body_linop"]], "apply_matrix_to_slices() (in module ffsim.linalg)": [[2, "ffsim.linalg.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg)": [[2, "ffsim.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[2, "module-ffsim.linalg"]], "givens_decomposition() (in module ffsim.linalg)": [[2, "ffsim.linalg.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_unitary"]], "lup() (in module ffsim.linalg)": [[2, "ffsim.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg)": [[2, "ffsim.linalg.modified_cholesky"]], "reduced_matrix() (in module ffsim.linalg)": [[2, "ffsim.linalg.reduced_matrix"]], "ffsim.random": [[3, "module-ffsim.random"]], "random_antihermitian() (in module ffsim.random)": [[3, "ffsim.random.random_antihermitian"]], "random_hermitian() (in module ffsim.random)": [[3, "ffsim.random.random_hermitian"]], "random_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_orthogonal"]], "random_real_symmetric_matrix() (in module ffsim.random)": [[3, "ffsim.random.random_real_symmetric_matrix"]], "random_special_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_special_orthogonal"]], "random_statevector() (in module ffsim.random)": [[3, "ffsim.random.random_statevector"]], "random_t2_amplitudes() (in module ffsim.random)": [[3, "ffsim.random.random_t2_amplitudes"]], "random_two_body_tensor_real() (in module ffsim.random)": [[3, "ffsim.random.random_two_body_tensor_real"]], "random_unitary() (in module ffsim.random)": [[3, "ffsim.random.random_unitary"]], "ffsim.testing": [[4, "module-ffsim.testing"]], "random_nelec() (in module ffsim.testing)": [[4, "ffsim.testing.random_nelec"]], "random_occupied_orbitals() (in module ffsim.testing)": [[4, "ffsim.testing.random_occupied_orbitals"]]}})
\ No newline at end of file
+Search.setIndex({"docnames": ["api/ffsim", "api/ffsim.contract", "api/ffsim.linalg", "api/ffsim.random", "api/ffsim.testing", "index", "tutorials/01-introduction", "tutorials/02-orbital-rotation", "tutorials/03-double-factorized", "tutorials/04-lucj", "tutorials/05-entanglement-forging", "tutorials/06-fermion-operator"], "filenames": ["api/ffsim.rst", "api/ffsim.contract.rst", "api/ffsim.linalg.rst", "api/ffsim.random.rst", "api/ffsim.testing.rst", "index.rst", "tutorials/01-introduction.ipynb", "tutorials/02-orbital-rotation.ipynb", "tutorials/03-double-factorized.ipynb", "tutorials/04-lucj.ipynb", "tutorials/05-entanglement-forging.ipynb", "tutorials/06-fermion-operator.ipynb"], "titles": ["ffsim", "ffsim.contract", "ffsim.linalg", "ffsim.random", "ffsim.testing", "Welcome to ffsim\u2019s documentation!", "Introduction to ffsim", "Orbital rotations and quadratic Hamiltonians", "Diagonal Coulomb operators and double-factorized Trotter simulation", "The local unitary cluster Jastrow 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Jastrow (UCJ) ansatz": [[9, "The-unitary-cluster-Jastrow-(UCJ)-ansatz"]], "Entanglement forging": [[10, "Entanglement-forging"]], "The FermionOperator class": [[11, "The-FermionOperator-class"]]}, "indexentries": {"doublefactorizedhamiltonian (class in ffsim)": [[0, "ffsim.DoubleFactorizedHamiltonian"]], "fermionaction (class in ffsim)": [[0, "ffsim.FermionAction"]], "fermionoperator (class in ffsim)": [[0, "ffsim.FermionOperator"]], "hopgateansatzoperator (class in ffsim)": [[0, "ffsim.HopGateAnsatzOperator"]], "moleculardata (class in ffsim)": [[0, "ffsim.MolecularData"]], "molecularhamiltonian (class in ffsim)": [[0, "ffsim.MolecularHamiltonian"]], "supportsapplyunitary (class in ffsim)": [[0, "ffsim.SupportsApplyUnitary"]], "supportsapproximateequality (class in ffsim)": [[0, "ffsim.SupportsApproximateEquality"]], "supportslinearoperator (class in ffsim)": [[0, "ffsim.SupportsLinearOperator"]], "supportstrace (class in ffsim)": [[0, "ffsim.SupportsTrace"]], "ucjoperator (class in ffsim)": [[0, "ffsim.UCJOperator"]], "action (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.action"]], "apply_diag_coulomb_evolution() (in module ffsim)": [[0, "ffsim.apply_diag_coulomb_evolution"]], "apply_fsim_gate() (in module ffsim)": [[0, "ffsim.apply_fsim_gate"]], "apply_givens_rotation() (in module ffsim)": [[0, "ffsim.apply_givens_rotation"]], "apply_hop_gate() (in module ffsim)": [[0, "ffsim.apply_hop_gate"]], "apply_num_interaction() (in module ffsim)": [[0, "ffsim.apply_num_interaction"]], "apply_num_num_interaction() (in module ffsim)": [[0, "ffsim.apply_num_num_interaction"]], "apply_num_op_prod_interaction() (in module ffsim)": [[0, "ffsim.apply_num_op_prod_interaction"]], "apply_num_op_sum_evolution() (in module ffsim)": [[0, "ffsim.apply_num_op_sum_evolution"]], "apply_orbital_rotation() (in module ffsim)": [[0, "ffsim.apply_orbital_rotation"]], "apply_tunneling_interaction() (in module ffsim)": [[0, "ffsim.apply_tunneling_interaction"]], "apply_unitary() (in module ffsim)": [[0, "ffsim.apply_unitary"]], "approx_eq() (in module ffsim)": [[0, "ffsim.approx_eq"]], "conserves_particle_number() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.conserves_particle_number"]], "conserves_spin_z() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.conserves_spin_z"]], "constant (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.constant"]], "constant (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.constant"]], "core_energy (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.core_energy"]], "cre() (in module ffsim)": [[0, "ffsim.cre"]], "cre_a() (in module ffsim)": [[0, "ffsim.cre_a"]], "cre_b() (in module ffsim)": [[0, "ffsim.cre_b"]], "des() (in module ffsim)": [[0, "ffsim.des"]], "des_a() (in module ffsim)": [[0, "ffsim.des_a"]], "des_b() (in module ffsim)": [[0, "ffsim.des_b"]], "diag_coulomb_mats (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.diag_coulomb_mats"]], "diag_coulomb_mats_alpha_alpha (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.diag_coulomb_mats_alpha_beta"]], "dim() (in module ffsim)": [[0, "ffsim.dim"]], "dims() (in module ffsim)": [[0, "ffsim.dims"]], "dipole_integrals (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.dipole_integrals"]], "expectation_one_body_power() (in module ffsim)": [[0, "ffsim.expectation_one_body_power"]], "expectation_one_body_product() (in module ffsim)": [[0, "ffsim.expectation_one_body_product"]], "ffsim": [[0, "module-ffsim"]], "final_orbital_rotation (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.final_orbital_rotation"]], "from_hartree_fock() (ffsim.moleculardata static method)": [[0, "ffsim.MolecularData.from_hartree_fock"]], "from_molecular_hamiltonian() (ffsim.doublefactorizedhamiltonian static method)": [[0, "ffsim.DoubleFactorizedHamiltonian.from_molecular_hamiltonian"]], "from_parameters() (ffsim.ucjoperator static method)": [[0, "ffsim.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.ucjoperator static method)": [[0, "ffsim.UCJOperator.from_t_amplitudes"]], "hamiltonian (ffsim.moleculardata property)": [[0, "ffsim.MolecularData.hamiltonian"]], "indices_to_strings() (in module ffsim)": [[0, "ffsim.indices_to_strings"]], "linear_operator() (in module ffsim)": [[0, "ffsim.linear_operator"]], "many_body_order() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.many_body_order"]], "module": [[0, "module-ffsim"], [1, "module-ffsim.contract"], [2, "module-ffsim.linalg"], [3, "module-ffsim.random"], [4, "module-ffsim.testing"]], "multireference_state() (in module ffsim)": [[0, "ffsim.multireference_state"]], "n_reps (ffsim.ucjoperator property)": [[0, "ffsim.UCJOperator.n_reps"]], "nelec (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.nelec"]], "norb (ffsim.doublefactorizedhamiltonian property)": [[0, "ffsim.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.norb"]], "norb (ffsim.molecularhamiltonian property)": [[0, "ffsim.MolecularHamiltonian.norb"]], "norb (ffsim.ucjoperator property)": [[0, "ffsim.UCJOperator.norb"]], "normal_ordered() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.normal_ordered"]], "one_body_tensor (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.one_body_tensor"]], "one_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.one_body_tensor"]], "one_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.one_body_tensor"]], "one_hot() (in module ffsim)": [[0, "ffsim.one_hot"]], "orb (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.orb"]], "orbital_rotations (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.orbital_rotations"]], "orbital_rotations (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.orbital_rotations"]], "orbital_symmetries (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.orbital_symmetries"]], "simulate_qdrift_double_factorized() (in module ffsim)": [[0, "ffsim.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim)": [[0, "ffsim.simulate_trotter_double_factorized"]], "slater_determinant() (in module ffsim)": [[0, "ffsim.slater_determinant"]], "slater_determinant_one_rdm() (in module ffsim)": [[0, "ffsim.slater_determinant_one_rdm"]], "spin (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.spin"]], "to_number_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_number_representation"]], "to_parameters() (ffsim.ucjoperator method)": [[0, "ffsim.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.ucjoperator method)": [[0, "ffsim.UCJOperator.to_t_amplitudes"]], "to_z_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_z_representation"]], "trace() (in module ffsim)": [[0, "ffsim.trace"]], "two_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.two_body_tensor"]], "two_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.z_representation"]], "contract_diag_coulomb() (in module ffsim.contract)": [[1, "ffsim.contract.contract_diag_coulomb"]], "contract_num_op_sum() (in module ffsim.contract)": [[1, "ffsim.contract.contract_num_op_sum"]], "diag_coulomb_linop() (in module ffsim.contract)": [[1, "ffsim.contract.diag_coulomb_linop"]], "ffsim.contract": [[1, "module-ffsim.contract"]], "num_op_sum_linop() (in module ffsim.contract)": [[1, "ffsim.contract.num_op_sum_linop"]], "one_body_linop() (in module ffsim.contract)": [[1, "ffsim.contract.one_body_linop"]], "apply_matrix_to_slices() (in module ffsim.linalg)": [[2, "ffsim.linalg.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg)": [[2, "ffsim.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[2, "module-ffsim.linalg"]], "givens_decomposition() (in module ffsim.linalg)": [[2, "ffsim.linalg.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_unitary"]], "lup() (in module ffsim.linalg)": [[2, "ffsim.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg)": [[2, "ffsim.linalg.modified_cholesky"]], "reduced_matrix() (in module ffsim.linalg)": [[2, "ffsim.linalg.reduced_matrix"]], "ffsim.random": [[3, "module-ffsim.random"]], "random_antihermitian() (in module ffsim.random)": [[3, "ffsim.random.random_antihermitian"]], "random_hermitian() (in module ffsim.random)": [[3, "ffsim.random.random_hermitian"]], "random_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_orthogonal"]], "random_real_symmetric_matrix() (in module ffsim.random)": [[3, "ffsim.random.random_real_symmetric_matrix"]], "random_special_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_special_orthogonal"]], "random_statevector() (in module ffsim.random)": [[3, "ffsim.random.random_statevector"]], "random_t2_amplitudes() (in module ffsim.random)": [[3, "ffsim.random.random_t2_amplitudes"]], "random_two_body_tensor_real() (in module ffsim.random)": [[3, "ffsim.random.random_two_body_tensor_real"]], "random_unitary() (in module ffsim.random)": [[3, "ffsim.random.random_unitary"]], "ffsim.testing": [[4, "module-ffsim.testing"]], "random_nelec() (in module ffsim.testing)": [[4, "ffsim.testing.random_nelec"]], "random_occupied_orbitals() (in module ffsim.testing)": [[4, "ffsim.testing.random_occupied_orbitals"]]}})
\ No newline at end of file
diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb
index aabe78f3d..11328c287 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:55.806469Z",
-     "iopub.status.busy": "2023-10-25T22:36:55.806037Z",
-     "iopub.status.idle": "2023-10-25T22:36:56.173437Z",
-     "shell.execute_reply": "2023-10-25T22:36:56.172708Z"
+     "iopub.execute_input": "2023-10-25T22:49:45.728598Z",
+     "iopub.status.busy": "2023-10-25T22:49:45.728154Z",
+     "iopub.status.idle": "2023-10-25T22:49:46.110527Z",
+     "shell.execute_reply": "2023-10-25T22:49:46.109715Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:56.178612Z",
-     "iopub.status.busy": "2023-10-25T22:36:56.177304Z",
-     "iopub.status.idle": "2023-10-25T22:36:56.183207Z",
-     "shell.execute_reply": "2023-10-25T22:36:56.182642Z"
+     "iopub.execute_input": "2023-10-25T22:49:46.115961Z",
+     "iopub.status.busy": "2023-10-25T22:49:46.114597Z",
+     "iopub.status.idle": "2023-10-25T22:49:46.120985Z",
+     "shell.execute_reply": "2023-10-25T22:49:46.120363Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:56.187737Z",
-     "iopub.status.busy": "2023-10-25T22:36:56.186648Z",
-     "iopub.status.idle": "2023-10-25T22:36:56.191149Z",
-     "shell.execute_reply": "2023-10-25T22:36:56.190587Z"
+     "iopub.execute_input": "2023-10-25T22:49:46.125500Z",
+     "iopub.status.busy": "2023-10-25T22:49:46.124419Z",
+     "iopub.status.idle": "2023-10-25T22:49:46.129349Z",
+     "shell.execute_reply": "2023-10-25T22:49:46.128546Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index 9abbe1985..f05ba4dfe 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": "2023-10-25T22:36:58.052305Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.052068Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.418054Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.417323Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.191448Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.191046Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.607593Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.606670Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:58.422655Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.422015Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.459609Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.458938Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.612660Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.611183Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.690073Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.689235Z"
     }
    },
    "outputs": [],
@@ -158,10 +158,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:58.463437Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.463084Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.475859Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.475248Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.695786Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.694689Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.709764Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.709040Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:36:58.478982Z",
-     "iopub.status.busy": "2023-10-25T22:36:58.478632Z",
-     "iopub.status.idle": "2023-10-25T22:36:58.485259Z",
-     "shell.execute_reply": "2023-10-25T22:36:58.484661Z"
+     "iopub.execute_input": "2023-10-25T22:49:48.714702Z",
+     "iopub.status.busy": "2023-10-25T22:49:48.713656Z",
+     "iopub.status.idle": "2023-10-25T22:49:48.720156Z",
+     "shell.execute_reply": "2023-10-25T22:49:48.719563Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.html b/tutorials/03-double-factorized.html
index c59edd7d7..61bbf1f91 100644
--- a/tutorials/03-double-factorized.html
+++ b/tutorials/03-double-factorized.html
@@ -131,28 +131,28 @@ <h2>Double-factorized representation of the molecular Hamiltonian<a class="heade
 Original representation
 -----------------------
 One-body tensor:
-[[-8.27478830e-01 -8.52909490e-17]
- [-5.57029092e-17 -6.77238770e-01]]
+[[-8.27478830e-01 -1.09243819e-16]
+ [-7.48351655e-17 -6.77238770e-01]]
 
 Two-body tensor:
-[[[[5.23173938e-01 3.58782168e-17]
-   [3.58782168e-17 5.33545754e-01]]
+[[[[ 5.23173938e-01 -5.00678144e-19]
+   [-5.00678144e-19  5.33545754e-01]]
 
-  [[2.49859013e-17 2.48240570e-01]
-   [2.48240570e-01 4.83067333e-17]]]
+  [[ 5.85364508e-18  2.48240570e-01]
+   [ 2.48240570e-01 -1.17688164e-17]]]
 
 
- [[[2.49859013e-17 2.48240570e-01]
-   [2.48240570e-01 4.83067333e-17]]
+ [[[ 5.85364508e-18  2.48240570e-01]
+   [ 2.48240570e-01 -1.17688164e-17]]
 
-  [[5.33545754e-01 4.01841799e-17]
-   [4.01841799e-17 5.53132024e-01]]]]
+  [[ 5.33545754e-01  1.05429868e-17]
+   [ 1.05429868e-17  5.53132024e-01]]]]
 
 Double-factorized representation
 --------------------------------
 One-body tensor:
-[[-1.21318608e+00 -1.27383424e-16]
- [-8.82879498e-17 -1.07792507e+00]]
+[[-1.21318608e+00 -1.03109072e-16]
+ [-8.30334814e-17 -1.07792507e+00]]
 
 Diagonal Coulomb matrices:
 [[[ 5.14653029e-01  5.33545754e-01]
@@ -161,18 +161,18 @@ <h2>Double-factorized representation of the molecular Hamiltonian<a class="heade
  [[ 2.48240570e-01 -2.48240570e-01]
   [-2.48240570e-01  2.48240570e-01]]
 
- [[ 2.27521846e-62 -1.39236953e-32]
-  [-1.39236953e-32  8.52090881e-03]]]
+ [[ 1.44655364e-30 -1.11022302e-16]
+  [-1.11022302e-16  8.52090881e-03]]]
 
 Orbital rotations:
 [[[ 1.00000000e+00  0.00000000e+00]
   [ 0.00000000e+00  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]]
 
- [[-1.27830444e-15 -1.00000000e+00]
-  [-1.00000000e+00  1.27830444e-15]]]
+ [[ 7.45733039e-16 -1.00000000e+00]
+  [-1.00000000e+00 -7.45733039e-16]]]
 </pre></div></div>
 </div>
 </section>
@@ -296,7 +296,7 @@ <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: -0.8377963825937084
+Hartree Fock energy: -0.837796382593709
 </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>
@@ -324,7 +324,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of evolved state w.r.t. initial state: 0.9696296369955066
+Fidelity of evolved state w.r.t. initial state: 0.9696296369955065
 </pre></div></div>
 </div>
 <p>Now, let’s test our implementation.</p>
@@ -351,7 +351,7 @@ <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: 0.9990275744083494
+Fidelity of Trotter-evolved state with exact state: 0.9990275744083491
 </pre></div></div>
 </div>
 <p>The fidelity of the final result can be improved by increasing the number of Trotter steps.</p>
@@ -378,7 +378,7 @@ <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: 0.9999906233109686
+Fidelity of Trotter-evolved state with exact state: 0.999990623310968
 </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>
@@ -407,7 +407,7 @@ <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: 0.9999906233109686
+Fidelity of Trotter-evolved state with exact state: 0.999990623310968
 </pre></div></div>
 </div>
 <p>A higher order formula achieves a higher fidelity with fewer Trotter steps:</p>
@@ -435,7 +435,7 @@ <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: 0.9999999336740067
+Fidelity of Trotter-evolved state with exact state: 0.9999999336740071
 </pre></div></div>
 </div>
 </section>
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index e679311ce..edaf5c8f2 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": "2023-10-25T22:37:00.564527Z",
-     "iopub.status.busy": "2023-10-25T22:37:00.563943Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.040069Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.039225Z"
+     "iopub.execute_input": "2023-10-25T22:49:50.631452Z",
+     "iopub.status.busy": "2023-10-25T22:49:50.630936Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.083516Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.082556Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.043849Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.043504Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.049845Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.049303Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.087434Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.086734Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.094705Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.093973Z"
     }
    },
    "outputs": [
@@ -106,28 +106,28 @@
       "Original representation\n",
       "-----------------------\n",
       "One-body tensor:\n",
-      "[[-8.27478830e-01 -8.52909490e-17]\n",
-      " [-5.57029092e-17 -6.77238770e-01]]\n",
+      "[[-8.27478830e-01 -1.09243819e-16]\n",
+      " [-7.48351655e-17 -6.77238770e-01]]\n",
       "\n",
       "Two-body tensor:\n",
-      "[[[[5.23173938e-01 3.58782168e-17]\n",
-      "   [3.58782168e-17 5.33545754e-01]]\n",
+      "[[[[ 5.23173938e-01 -5.00678144e-19]\n",
+      "   [-5.00678144e-19  5.33545754e-01]]\n",
       "\n",
-      "  [[2.49859013e-17 2.48240570e-01]\n",
-      "   [2.48240570e-01 4.83067333e-17]]]\n",
+      "  [[ 5.85364508e-18  2.48240570e-01]\n",
+      "   [ 2.48240570e-01 -1.17688164e-17]]]\n",
       "\n",
       "\n",
-      " [[[2.49859013e-17 2.48240570e-01]\n",
-      "   [2.48240570e-01 4.83067333e-17]]\n",
+      " [[[ 5.85364508e-18  2.48240570e-01]\n",
+      "   [ 2.48240570e-01 -1.17688164e-17]]\n",
       "\n",
-      "  [[5.33545754e-01 4.01841799e-17]\n",
-      "   [4.01841799e-17 5.53132024e-01]]]]\n",
+      "  [[ 5.33545754e-01  1.05429868e-17]\n",
+      "   [ 1.05429868e-17  5.53132024e-01]]]]\n",
       "\n",
       "Double-factorized representation\n",
       "--------------------------------\n",
       "One-body tensor:\n",
-      "[[-1.21318608e+00 -1.27383424e-16]\n",
-      " [-8.82879498e-17 -1.07792507e+00]]\n",
+      "[[-1.21318608e+00 -1.03109072e-16]\n",
+      " [-8.30334814e-17 -1.07792507e+00]]\n",
       "\n",
       "Diagonal Coulomb matrices:\n",
       "[[[ 5.14653029e-01  5.33545754e-01]\n",
@@ -136,18 +136,18 @@
       " [[ 2.48240570e-01 -2.48240570e-01]\n",
       "  [-2.48240570e-01  2.48240570e-01]]\n",
       "\n",
-      " [[ 2.27521846e-62 -1.39236953e-32]\n",
-      "  [-1.39236953e-32  8.52090881e-03]]]\n",
+      " [[ 1.44655364e-30 -1.11022302e-16]\n",
+      "  [-1.11022302e-16  8.52090881e-03]]]\n",
       "\n",
       "Orbital rotations:\n",
       "[[[ 1.00000000e+00  0.00000000e+00]\n",
       "  [ 0.00000000e+00  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",
-      " [[-1.27830444e-15 -1.00000000e+00]\n",
-      "  [-1.00000000e+00  1.27830444e-15]]]\n"
+      " [[ 7.45733039e-16 -1.00000000e+00]\n",
+      "  [-1.00000000e+00 -7.45733039e-16]]]\n"
      ]
     }
    ],
@@ -226,10 +226,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.053112Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.052436Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.058006Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.057392Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.097615Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.097224Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.103382Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.102656Z"
     }
    },
    "outputs": [],
@@ -284,10 +284,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.061751Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.060649Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.066205Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.065642Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.106760Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.106190Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.111174Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.110496Z"
     }
    },
    "outputs": [],
@@ -324,10 +324,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.069111Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.068667Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.074495Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.073941Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.115052Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.114792Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.121182Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.120373Z"
     }
    },
    "outputs": [
@@ -335,7 +335,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.8377963825937084\n"
+      "Hartree Fock energy: -0.837796382593709\n"
      ]
     }
    ],
@@ -366,10 +366,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.077458Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.076848Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.087132Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.086577Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.125523Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.124134Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.137942Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.137232Z"
     }
    },
    "outputs": [
@@ -377,7 +377,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of evolved state w.r.t. initial state: 0.9696296369955066\n"
+      "Fidelity of evolved state w.r.t. initial state: 0.9696296369955065\n"
      ]
     }
    ],
@@ -408,10 +408,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.090228Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.089559Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.098344Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.097773Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.143052Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.142490Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.155779Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.155041Z"
     }
    },
    "outputs": [
@@ -419,7 +419,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083494\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083491\n"
      ]
     }
    ],
@@ -449,10 +449,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.101276Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.100835Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.145337Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.144745Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.160933Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.159642Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.211316Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.210559Z"
     }
    },
    "outputs": [
@@ -460,7 +460,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109686\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999990623310968\n"
      ]
     }
    ],
@@ -492,10 +492,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.148276Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.147912Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.188137Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.186555Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.215690Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.214603Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.254790Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.254051Z"
     }
    },
    "outputs": [
@@ -503,7 +503,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109686\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999990623310968\n"
      ]
     }
    ],
@@ -534,10 +534,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:01.191299Z",
-     "iopub.status.busy": "2023-10-25T22:37:01.190992Z",
-     "iopub.status.idle": "2023-10-25T22:37:01.208147Z",
-     "shell.execute_reply": "2023-10-25T22:37:01.207353Z"
+     "iopub.execute_input": "2023-10-25T22:49:51.259870Z",
+     "iopub.status.busy": "2023-10-25T22:49:51.258672Z",
+     "iopub.status.idle": "2023-10-25T22:49:51.277545Z",
+     "shell.execute_reply": "2023-10-25T22:49:51.276466Z"
     }
    },
    "outputs": [
@@ -545,7 +545,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740067\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740071\n"
      ]
     }
    ],
diff --git a/tutorials/04-lucj.html b/tutorials/04-lucj.html
index d998b841a..f4fb37cae 100644
--- a/tutorials/04-lucj.html
+++ b/tutorials/04-lucj.html
@@ -96,7 +96,7 @@ <h1>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 converged SCF energy = -77.4456267643962
-CASCI E = -77.6290254326716  E(CI) = -3.57322412553862  S^2 = 0.0000000
+CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000
 </pre></div></div>
 </div>
 <section id="The-unitary-cluster-Jastrow-(UCJ)-ansatz">
@@ -150,7 +150,7 @@ <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) = -77.49387212754473  E_corr = -0.04824536314851268
+E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851462
 Energy at initialialization: -77.46975600021676
 </pre></div></div>
 </div>
@@ -192,12 +192,12 @@ <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: -77.62902198093012
-        x: [-2.843e-01  5.591e-01 ... -1.720e-01 -3.600e-01]
-      nit: 269
-      jac: [ 2.416e-05 -3.126e-05 ... -1.606e-04  9.948e-06]
-     nfev: 21316
-     njev: 292
+      fun: -77.62896682018224
+        x: [-1.932e-01  1.104e+00 ... -3.429e-01 -1.010e-01]
+      nit: 226
+      jac: [ 3.268e-05  8.527e-06 ... -9.123e-04 -3.965e-04]
+     nfev: 17593
+     njev: 241
  hess_inv: &lt;72x72 LbfgsInvHessProduct with dtype=float64&gt;
 </pre></div></div>
 </div>
@@ -258,12 +258,12 @@ <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: -77.62848215844997
-        x: [ 6.198e-01 -6.593e-02 ...  1.183e-01 -1.078e-01]
-      nit: 450
-      jac: [ 1.492e-04 -2.629e-04 ...  1.435e-04 -3.638e-04]
-     nfev: 22701
-     njev: 483
+      fun: -77.62865917328423
+        x: [-1.028e+00 -1.315e+00 ... -4.903e-01  1.494e+00]
+      nit: 290
+      jac: [-5.969e-05  9.095e-05 ...  5.741e-04 -3.297e-04]
+     nfev: 14664
+     njev: 312
  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 67833f1b8..fffa14560 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:03.486939Z",
-     "iopub.status.busy": "2023-10-25T22:37:03.486686Z",
-     "iopub.status.idle": "2023-10-25T22:37:04.171218Z",
-     "shell.execute_reply": "2023-10-25T22:37:04.170426Z"
+     "iopub.execute_input": "2023-10-25T22:49:53.689996Z",
+     "iopub.status.busy": "2023-10-25T22:49:53.689777Z",
+     "iopub.status.idle": "2023-10-25T22:49:54.502302Z",
+     "shell.execute_reply": "2023-10-25T22:49:54.501564Z"
     }
    },
    "outputs": [
@@ -32,7 +32,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -77.6290254326716  E(CI) = -3.57322412553862  S^2 = 0.0000000\n"
+      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -110,10 +110,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:04.175035Z",
-     "iopub.status.busy": "2023-10-25T22:37:04.174671Z",
-     "iopub.status.idle": "2023-10-25T22:37:04.834102Z",
-     "shell.execute_reply": "2023-10-25T22:37:04.833507Z"
+     "iopub.execute_input": "2023-10-25T22:49:54.506302Z",
+     "iopub.status.busy": "2023-10-25T22:49:54.505497Z",
+     "iopub.status.idle": "2023-10-25T22:49:54.965101Z",
+     "shell.execute_reply": "2023-10-25T22:49:54.964409Z"
     }
    },
    "outputs": [
@@ -121,7 +121,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851268\n"
+      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851462\n"
      ]
     },
     {
@@ -176,10 +176,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:37:04.838993Z",
-     "iopub.status.busy": "2023-10-25T22:37:04.838311Z",
-     "iopub.status.idle": "2023-10-25T22:38:17.168913Z",
-     "shell.execute_reply": "2023-10-25T22:38:17.168300Z"
+     "iopub.execute_input": "2023-10-25T22:49:54.968428Z",
+     "iopub.status.busy": "2023-10-25T22:49:54.968008Z",
+     "iopub.status.idle": "2023-10-25T22:51:17.439791Z",
+     "shell.execute_reply": "2023-10-25T22:51:17.439126Z"
     }
    },
    "outputs": [
@@ -191,12 +191,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62902198093012\n",
-      "        x: [-2.843e-01  5.591e-01 ... -1.720e-01 -3.600e-01]\n",
-      "      nit: 269\n",
-      "      jac: [ 2.416e-05 -3.126e-05 ... -1.606e-04  9.948e-06]\n",
-      "     nfev: 21316\n",
-      "     njev: 292\n",
+      "      fun: -77.62896682018224\n",
+      "        x: [-1.932e-01  1.104e+00 ... -3.429e-01 -1.010e-01]\n",
+      "      nit: 226\n",
+      "      jac: [ 3.268e-05  8.527e-06 ... -9.123e-04 -3.965e-04]\n",
+      "     nfev: 17593\n",
+      "     njev: 241\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -251,10 +251,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:38:17.173783Z",
-     "iopub.status.busy": "2023-10-25T22:38:17.172653Z",
-     "iopub.status.idle": "2023-10-25T22:39:33.968944Z",
-     "shell.execute_reply": "2023-10-25T22:39:33.968334Z"
+     "iopub.execute_input": "2023-10-25T22:51:17.443422Z",
+     "iopub.status.busy": "2023-10-25T22:51:17.442815Z",
+     "iopub.status.idle": "2023-10-25T22:52:26.644022Z",
+     "shell.execute_reply": "2023-10-25T22:52:26.643271Z"
     }
    },
    "outputs": [
@@ -266,12 +266,12 @@
       "  message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -77.62848215844997\n",
-      "        x: [ 6.198e-01 -6.593e-02 ...  1.183e-01 -1.078e-01]\n",
-      "      nit: 450\n",
-      "      jac: [ 1.492e-04 -2.629e-04 ...  1.435e-04 -3.638e-04]\n",
-      "     nfev: 22701\n",
-      "     njev: 483\n",
+      "      fun: -77.62865917328423\n",
+      "        x: [-1.028e+00 -1.315e+00 ... -4.903e-01  1.494e+00]\n",
+      "      nit: 290\n",
+      "      jac: [-5.969e-05  9.095e-05 ...  5.741e-04 -3.297e-04]\n",
+      "     nfev: 14664\n",
+      "     njev: 312\n",
       " hess_inv: <46x46 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
diff --git a/tutorials/05-entanglement-forging.html b/tutorials/05-entanglement-forging.html
index 6beed5d3c..5edccb5b7 100644
--- a/tutorials/05-entanglement-forging.html
+++ b/tutorials/05-entanglement-forging.html
@@ -102,7 +102,7 @@ <h1>Entanglement forging<a class="headerlink" href="#Entanglement-forging" title
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 converged SCF energy = -75.6787887956297
-CASCI E = -75.7079508859773  E(CI) = -14.3336207346502  S^2 = 0.0000000
+CASCI E = -75.7079508859772  E(CI) = -14.3336207346500  S^2 = 0.0000000
 </pre></div></div>
 </div>
 <div class="nbinput docutils container">
@@ -139,7 +139,7 @@ <h1>Entanglement forging<a class="headerlink" href="#Entanglement-forging" title
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Energy at initialialization: -75.68366174447621
+Energy at initialialization: -75.68366174447613
 </pre></div></div>
 </div>
 <div class="nbinput docutils container">
@@ -178,8 +178,8 @@ <h1>Entanglement forging<a class="headerlink" href="#Entanglement-forging" title
  message: Maximum number of function evaluations has been exceeded.
  success: False
   status: 2
-     fun: -75.69430210093412
-       x: [ 1.344e+00  8.447e-02 -1.883e-03  1.105e+00 -1.881e-01]
+     fun: -75.69447115688286
+       x: [ 1.354e+00  9.455e-02 -3.884e-03  1.094e+00 -2.122e-01]
     nfev: 100
    maxcv: 0.0
 </pre></div></div>
diff --git a/tutorials/05-entanglement-forging.ipynb b/tutorials/05-entanglement-forging.ipynb
index fa8dfa58b..3b672189f 100644
--- a/tutorials/05-entanglement-forging.ipynb
+++ b/tutorials/05-entanglement-forging.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:35.902653Z",
-     "iopub.status.busy": "2023-10-25T22:39:35.902244Z",
-     "iopub.status.idle": "2023-10-25T22:39:36.610182Z",
-     "shell.execute_reply": "2023-10-25T22:39:36.609495Z"
+     "iopub.execute_input": "2023-10-25T22:52:28.457365Z",
+     "iopub.status.busy": "2023-10-25T22:52:28.457064Z",
+     "iopub.status.idle": "2023-10-25T22:52:29.067914Z",
+     "shell.execute_reply": "2023-10-25T22:52:29.067063Z"
     }
    },
    "outputs": [
@@ -32,7 +32,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -75.7079508859773  E(CI) = -14.3336207346502  S^2 = 0.0000000\n"
+      "CASCI E = -75.7079508859772  E(CI) = -14.3336207346500  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -90,10 +90,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:36.614713Z",
-     "iopub.status.busy": "2023-10-25T22:39:36.614126Z",
-     "iopub.status.idle": "2023-10-25T22:39:36.641876Z",
-     "shell.execute_reply": "2023-10-25T22:39:36.641194Z"
+     "iopub.execute_input": "2023-10-25T22:52:29.074034Z",
+     "iopub.status.busy": "2023-10-25T22:52:29.072439Z",
+     "iopub.status.idle": "2023-10-25T22:52:29.107737Z",
+     "shell.execute_reply": "2023-10-25T22:52:29.107079Z"
     }
    },
    "outputs": [
@@ -101,7 +101,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -75.68366174447621\n"
+      "Energy at initialialization: -75.68366174447613\n"
      ]
     }
    ],
@@ -135,10 +135,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:36.645471Z",
-     "iopub.status.busy": "2023-10-25T22:39:36.644784Z",
-     "iopub.status.idle": "2023-10-25T22:39:38.706845Z",
-     "shell.execute_reply": "2023-10-25T22:39:38.706152Z"
+     "iopub.execute_input": "2023-10-25T22:52:29.112535Z",
+     "iopub.status.busy": "2023-10-25T22:52:29.111203Z",
+     "iopub.status.idle": "2023-10-25T22:52:32.034045Z",
+     "shell.execute_reply": "2023-10-25T22:52:32.033073Z"
     }
    },
    "outputs": [
@@ -150,8 +150,8 @@
       " message: Maximum number of function evaluations has been exceeded.\n",
       " success: False\n",
       "  status: 2\n",
-      "     fun: -75.69430210093412\n",
-      "       x: [ 1.344e+00  8.447e-02 -1.883e-03  1.105e+00 -1.881e-01]\n",
+      "     fun: -75.69447115688286\n",
+      "       x: [ 1.354e+00  9.455e-02 -3.884e-03  1.094e+00 -2.122e-01]\n",
       "    nfev: 100\n",
       "   maxcv: 0.0\n"
      ]
diff --git a/tutorials/06-fermion-operator.html b/tutorials/06-fermion-operator.html
index 0d0b59b92..51db19a6b 100644
--- a/tutorials/06-fermion-operator.html
+++ b/tutorials/06-fermion-operator.html
@@ -78,9 +78,9 @@ <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)): -0.25,
     (cre_b(1), des_b(5), cre_a(4)): 1+1j,
-    (cre_a(0), des_a(3)): 0.5
+    (cre_a(0), des_a(3)): 0.5,
+    (cre_a(3), des_a(0)): -0.25
 })
 </pre></div></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, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+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>
@@ -127,17 +127,17 @@ <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), des_a(3), des_b(3)): 0.0625,
-    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
-    (cre_b(1), des_b(5), cre_a(4)): 2+2j,
+    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
     (cre_a(3), des_a(0)): -0.5,
+    (cre_a(0), des_a(3)): 1,
     (cre_b(2)): 0-0.25j,
-    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
-    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
     (des_a(3), des_b(3)): 0.0625,
-    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
-    (cre_a(0), des_a(3)): 1,
-    (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_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
+    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
+    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
+    (cre_b(1), des_b(5), cre_a(4)): 2+2j,
+    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j
 })
 </pre></div></div>
 </div>
@@ -162,17 +162,17 @@ <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), des_a(3), des_b(3)): 0-0.25j,
-    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
-    (cre_b(1), des_b(5), cre_a(4)): 12-12j,
+    (cre_a(3), des_a(0), cre_b(2)): -1,
     (cre_a(3), des_a(0)): 0+3j,
+    (cre_a(0), des_a(3)): 0-6j,
     (cre_b(2)): -5,
-    (cre_a(0), des_a(3), cre_b(2)): 2,
-    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
     (des_a(3), des_b(3)): 0-1.25j,
-    (cre_a(3), des_a(0), cre_b(2)): -1,
-    (cre_a(0), des_a(3)): 0-6j,
-    (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_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
+    (cre_a(0), des_a(3), cre_b(2)): 2,
+    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,
+    (cre_b(1), des_b(5), cre_a(4)): 12-12j,
+    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j
 })
 </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_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,
-    (des_b(3), des_a(3)): 0+1.25j,
-    (cre_b(2), cre_a(3), des_a(0)): -1,
-    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
-    (cre_a(0), des_a(3)): 0-6j,
     (cre_a(3), des_a(0)): 0+3j,
-    (cre_b(2), cre_a(0), des_a(3)): 2,
+    (cre_a(0), des_a(3)): 0-6j,
     (cre_b(1), cre_a(4), des_b(5)): -12+12j,
+    (cre_b(2)): -5,
+    (cre_b(2), cre_a(3), des_a(0)): -1,
     (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
-    (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_a(0), des_a(3)): 2,
+    (des_b(3), des_a(3)): 0+1.25j,
+    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j
 })
 </pre></div></div>
 </div>
@@ -273,7 +273,7 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="highlight"><pre>
 array([0.        +0.j        , 0.        +0.j        ,
        0.        +0.j        , 0.        +0.j        ,
-       0.14416721+0.01183319j, 0.        +0.j        ,
+       0.08465914-0.16438186j, 0.        +0.j        ,
        0.        +0.j        , 0.        +0.j        ,
        0.        +0.j        ])
 </pre></div></div>
diff --git a/tutorials/06-fermion-operator.ipynb b/tutorials/06-fermion-operator.ipynb
index 300ae3e7f..b2f6037d5 100644
--- a/tutorials/06-fermion-operator.ipynb
+++ b/tutorials/06-fermion-operator.ipynb
@@ -29,10 +29,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.366920Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.366331Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.732340Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.731690Z"
+     "iopub.execute_input": "2023-10-25T22:52:33.852859Z",
+     "iopub.status.busy": "2023-10-25T22:52:33.852631Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.239320Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.238688Z"
     }
    },
    "outputs": [
@@ -40,9 +40,9 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0)): -0.25,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 1+1j,\n",
-       "    (cre_a(0), des_a(3)): 0.5\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": "2023-10-25T22:39:40.737597Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.736319Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.743718Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.742835Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.243762Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.243037Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.250376Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.249693Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 0), (False, False, 3)): 0.5+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": "2023-10-25T22:39:40.748237Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.747115Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.754695Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.754158Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.255144Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.253705Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.262286Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.261401Z"
     }
    },
    "outputs": [
@@ -121,17 +121,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
        "    (cre_a(3), des_a(0)): -0.5,\n",
+       "    (cre_a(0), des_a(3)): 1,\n",
        "    (cre_b(2)): 0-0.25j,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
        "    (des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
-       "    (cre_a(0), des_a(3)): 1,\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_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
+       "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
+       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j\n",
        "})"
       ]
      },
@@ -169,10 +169,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.759235Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.758153Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.765084Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.764539Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.267159Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.265631Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.272698Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.272094Z"
     }
    },
    "outputs": [
@@ -180,17 +180,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
        "    (cre_a(3), des_a(0)): 0+3j,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_b(2)): -5,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
        "    (des_a(3), des_b(3)): 0-1.25j,\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\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_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
+       "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
+       "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j\n",
        "})"
       ]
      },
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.769541Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.768482Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.774962Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.774400Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.277397Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.275959Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.283129Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.282399Z"
     }
    },
    "outputs": [
@@ -230,16 +230,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
-       "    (des_b(3), des_a(3)): 0+1.25j,\n",
-       "    (cre_b(2), cre_a(3), des_a(0)): -1,\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_a(3), des_a(0)): 0+3j,\n",
-       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
+       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
+       "    (cre_b(2)): -5,\n",
+       "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
        "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\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_a(0), des_a(3)): 2,\n",
+       "    (des_b(3), des_a(3)): 0+1.25j,\n",
+       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j\n",
        "})"
       ]
      },
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.779369Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.778283Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.784339Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.783767Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.287780Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.286254Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.294121Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.292778Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.789452Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.788382Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.795811Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.795259Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.298274Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.297778Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.304979Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.304437Z"
     }
    },
    "outputs": [
@@ -340,10 +340,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.800327Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.799255Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.808120Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.807530Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.309028Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.308520Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.317214Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.316562Z"
     }
    },
    "outputs": [
@@ -352,7 +352,7 @@
       "text/plain": [
        "array([0.        +0.j        , 0.        +0.j        ,\n",
        "       0.        +0.j        , 0.        +0.j        ,\n",
-       "       0.14416721+0.01183319j, 0.        +0.j        ,\n",
+       "       0.08465914-0.16438186j, 0.        +0.j        ,\n",
        "       0.        +0.j        , 0.        +0.j        ,\n",
        "       0.        +0.j        ])"
       ]
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-25T22:39:40.812478Z",
-     "iopub.status.busy": "2023-10-25T22:39:40.811398Z",
-     "iopub.status.idle": "2023-10-25T22:39:40.826762Z",
-     "shell.execute_reply": "2023-10-25T22:39:40.826205Z"
+     "iopub.execute_input": "2023-10-25T22:52:34.320550Z",
+     "iopub.status.busy": "2023-10-25T22:52:34.320183Z",
+     "iopub.status.idle": "2023-10-25T22:52:34.336019Z",
+     "shell.execute_reply": "2023-10-25T22:52:34.335310Z"
     }
    },
    "outputs": [