From 5934a5e5bb2d922714381643917ef4d160bb9fad Mon Sep 17 00:00:00 2001
From: kevinsung <kevinsung@users.noreply.github.com>
Date: Fri, 27 Oct 2023 15:56:46 +0000
Subject: [PATCH] deploy: 8c2ee157423f8dde82bab4fa72c90cb2bf7348c9

---
 .doctrees/api/ffsim.contract.doctree          | Bin 67927 -> 78926 bytes
 .doctrees/api/ffsim.doctree                   | Bin 475473 -> 475473 bytes
 .doctrees/environment.pickle                  | Bin 1500441 -> 1516781 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    |  56 ++++----
 .../tutorials/05-entanglement-forging.ipynb   |  28 ++--
 .../tutorials/06-fermion-operator.ipynb       | 126 ++++++++---------
 .../tutorials/03-double-factorized.doctree    | Bin 54592 -> 54670 bytes
 .doctrees/tutorials/04-lucj.doctree           | Bin 38275 -> 38269 bytes
 .../tutorials/05-entanglement-forging.doctree | Bin 15260 -> 15254 bytes
 .../tutorials/06-fermion-operator.doctree     | Bin 41445 -> 41385 bytes
 _modules/ffsim/contract/one_body.html         |  31 ++++-
 api/ffsim.contract.html                       |  32 ++++-
 api/ffsim.html                                |  20 +--
 genindex.html                                 |   2 +
 index.html                                    |   1 +
 objects.inv                                   | Bin 3506 -> 3522 bytes
 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                        |  24 ++--
 tutorials/04-lucj.ipynb                       |  56 ++++----
 tutorials/05-entanglement-forging.html        |   4 +-
 tutorials/05-entanglement-forging.ipynb       |  28 ++--
 tutorials/06-fermion-operator.html            |  54 ++++----
 tutorials/06-fermion-operator.ipynb           | 126 ++++++++---------
 30 files changed, 533 insertions(+), 473 deletions(-)

diff --git a/.doctrees/api/ffsim.contract.doctree b/.doctrees/api/ffsim.contract.doctree
index c81d128e3b277252489d960d1eb8a9823c349996..e6508797584620697975f81f6d6ab4447efdb505 100644
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diff --git a/.doctrees/api/ffsim.doctree b/.doctrees/api/ffsim.doctree
index f2874522abb652b2c6fcd08bccbf568baecd2501..f5ca5f9f9db66fb77a48c7595f430da34dfa7984 100644
GIT binary patch
delta 283
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diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
index 281d8c5fefa0a2e980df118336eebfa7c9b78b62..6746713396126c1988de3bf80a22e097cfd7dafd 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 3797ae9e6..d6e01fa5a 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": "2023-10-27T03:04:57.255539Z",
-     "iopub.status.busy": "2023-10-27T03:04:57.255034Z",
-     "iopub.status.idle": "2023-10-27T03:04:57.653213Z",
-     "shell.execute_reply": "2023-10-27T03:04:57.652569Z"
+     "iopub.execute_input": "2023-10-27T15:56:17.553188Z",
+     "iopub.status.busy": "2023-10-27T15:56:17.552767Z",
+     "iopub.status.idle": "2023-10-27T15:56:17.914376Z",
+     "shell.execute_reply": "2023-10-27T15:56:17.913518Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:04:57.657905Z",
-     "iopub.status.busy": "2023-10-27T03:04:57.656590Z",
-     "iopub.status.idle": "2023-10-27T03:04:57.662682Z",
-     "shell.execute_reply": "2023-10-27T03:04:57.662136Z"
+     "iopub.execute_input": "2023-10-27T15:56:17.918188Z",
+     "iopub.status.busy": "2023-10-27T15:56:17.917631Z",
+     "iopub.status.idle": "2023-10-27T15:56:17.922403Z",
+     "shell.execute_reply": "2023-10-27T15:56:17.921760Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:04:57.667736Z",
-     "iopub.status.busy": "2023-10-27T03:04:57.666400Z",
-     "iopub.status.idle": "2023-10-27T03:04:57.671189Z",
-     "shell.execute_reply": "2023-10-27T03:04:57.670658Z"
+     "iopub.execute_input": "2023-10-27T15:56:17.926658Z",
+     "iopub.status.busy": "2023-10-27T15:56:17.925552Z",
+     "iopub.status.idle": "2023-10-27T15:56:17.930575Z",
+     "shell.execute_reply": "2023-10-27T15:56:17.929762Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index 7699c0f29..4ff87b79a 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": "2023-10-27T03:04:59.630059Z",
-     "iopub.status.busy": "2023-10-27T03:04:59.629560Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.024476Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.023597Z"
+     "iopub.execute_input": "2023-10-27T15:56:19.756312Z",
+     "iopub.status.busy": "2023-10-27T15:56:19.756069Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.124710Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.123784Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:00.028824Z",
-     "iopub.status.busy": "2023-10-27T03:05:00.028106Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.061962Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.061268Z"
+     "iopub.execute_input": "2023-10-27T15:56:20.128851Z",
+     "iopub.status.busy": "2023-10-27T15:56:20.128310Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.167911Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.167175Z"
     }
    },
    "outputs": [],
@@ -158,10 +158,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:00.067442Z",
-     "iopub.status.busy": "2023-10-27T03:05:00.066016Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.079662Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.079034Z"
+     "iopub.execute_input": "2023-10-27T15:56:20.173265Z",
+     "iopub.status.busy": "2023-10-27T15:56:20.172016Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.187030Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.186335Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:00.084489Z",
-     "iopub.status.busy": "2023-10-27T03:05:00.083296Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.090411Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.089817Z"
+     "iopub.execute_input": "2023-10-27T15:56:20.192285Z",
+     "iopub.status.busy": "2023-10-27T15:56:20.191173Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.198482Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.197803Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index c061160c4..867e841ed 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": "2023-10-27T03:05:01.960181Z",
-     "iopub.status.busy": "2023-10-27T03:05:01.959717Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.404039Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.403342Z"
+     "iopub.execute_input": "2023-10-27T15:56:21.878889Z",
+     "iopub.status.busy": "2023-10-27T15:56:21.878510Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.327582Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.326818Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.408011Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.407295Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.417935Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.417313Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.331466Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.330818Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.339396Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.337615Z"
     }
    },
    "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": "2023-10-27T03:05:02.423483Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.421763Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.431334Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.430699Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.342700Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.342346Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.349281Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.348539Z"
     }
    },
    "outputs": [],
@@ -284,10 +284,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.434936Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.434685Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.439093Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.438396Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.352710Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.352274Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.357049Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.356275Z"
     }
    },
    "outputs": [],
@@ -324,10 +324,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.559009Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.558102Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.564371Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.563761Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.360182Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.359836Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.367959Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.367238Z"
     }
    },
    "outputs": [
@@ -335,7 +335,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.8377963825937084\n"
+      "Hartree Fock energy: -0.837796382593709\n"
      ]
     }
    ],
@@ -363,10 +363,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.567736Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.567083Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.584110Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.583071Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.371087Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.370799Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.382769Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.382019Z"
     }
    },
    "outputs": [
@@ -374,7 +374,7 @@
      "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"
      ]
     }
    ],
@@ -405,10 +405,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.587264Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.586808Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.600814Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.599564Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.386352Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.385780Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.395074Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.394453Z"
     }
    },
    "outputs": [
@@ -416,7 +416,7 @@
      "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"
      ]
     }
    ],
@@ -446,10 +446,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.604427Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.603969Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.648867Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.648260Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.398534Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.397827Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.448640Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.447932Z"
     }
    },
    "outputs": [
@@ -457,7 +457,7 @@
      "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"
      ]
     }
    ],
@@ -489,10 +489,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.654063Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.652939Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.679846Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.679254Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.451778Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.451358Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.492907Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.491767Z"
     }
    },
    "outputs": [
@@ -500,7 +500,7 @@
      "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"
      ]
     }
    ],
@@ -531,10 +531,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.684588Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.683495Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.697257Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.696649Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.495880Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.495597Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.514396Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.513618Z"
     }
    },
    "outputs": [
@@ -542,7 +542,7 @@
      "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 d037aca8d..fc59af3b7 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": "2023-10-27T03:05:05.159264Z",
-     "iopub.status.busy": "2023-10-27T03:05:05.159017Z",
-     "iopub.status.idle": "2023-10-27T03:05:05.871208Z",
-     "shell.execute_reply": "2023-10-27T03:05:05.870569Z"
+     "iopub.execute_input": "2023-10-27T15:56:24.886532Z",
+     "iopub.status.busy": "2023-10-27T15:56:24.886278Z",
+     "iopub.status.idle": "2023-10-27T15:56:25.639738Z",
+     "shell.execute_reply": "2023-10-27T15:56:25.638878Z"
     }
    },
    "outputs": [
@@ -25,7 +25,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "converged SCF energy = -77.4456267643962\n"
+      "converged SCF energy = -77.4456267643961\n"
      ]
     },
     {
@@ -110,10 +110,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:05.876664Z",
-     "iopub.status.busy": "2023-10-27T03:05:05.875285Z",
-     "iopub.status.idle": "2023-10-27T03:05:06.651133Z",
-     "shell.execute_reply": "2023-10-27T03:05:06.650529Z"
+     "iopub.execute_input": "2023-10-27T15:56:25.643502Z",
+     "iopub.status.busy": "2023-10-27T15:56:25.642966Z",
+     "iopub.status.idle": "2023-10-27T15:56:25.881461Z",
+     "shell.execute_reply": "2023-10-27T15:56:25.880768Z"
     }
    },
    "outputs": [
@@ -121,14 +121,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754471  E_corr = -0.04824536314851448\n"
+      "E(CCSD) = -77.49387212754468  E_corr = -0.04824536314851557\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -77.46975600021672\n"
+      "Energy at initialialization: -77.46975600021696\n"
      ]
     }
    ],
@@ -173,10 +173,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:06.655856Z",
-     "iopub.status.busy": "2023-10-27T03:05:06.654768Z",
-     "iopub.status.idle": "2023-10-27T03:05:10.593929Z",
-     "shell.execute_reply": "2023-10-27T03:05:10.593304Z"
+     "iopub.execute_input": "2023-10-27T15:56:25.884742Z",
+     "iopub.status.busy": "2023-10-27T15:56:25.884388Z",
+     "iopub.status.idle": "2023-10-27T15:56:31.317001Z",
+     "shell.execute_reply": "2023-10-27T15:56:31.316266Z"
     }
    },
    "outputs": [
@@ -188,12 +188,12 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.51577544983374\n",
-      "        x: [-1.451e-01  1.878e-01 ... -6.238e-01 -6.006e-02]\n",
+      "      fun: -77.5159157550554\n",
+      "        x: [-1.413e-01  1.968e-01 ...  4.266e-01  2.918e-01]\n",
       "      nit: 9\n",
-      "      jac: [ 3.988e-03 -8.249e-03 ... -3.389e-03 -1.711e-03]\n",
-      "     nfev: 1168\n",
-      "     njev: 16\n",
+      "      jac: [ 6.079e-03 -7.610e-03 ...  3.376e-03 -5.228e-03]\n",
+      "     nfev: 1314\n",
+      "     njev: 18\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -246,10 +246,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:10.598208Z",
-     "iopub.status.busy": "2023-10-27T03:05:10.597724Z",
-     "iopub.status.idle": "2023-10-27T03:05:14.139838Z",
-     "shell.execute_reply": "2023-10-27T03:05:14.139253Z"
+     "iopub.execute_input": "2023-10-27T15:56:31.320238Z",
+     "iopub.status.busy": "2023-10-27T15:56:31.319937Z",
+     "iopub.status.idle": "2023-10-27T15:56:35.282027Z",
+     "shell.execute_reply": "2023-10-27T15:56:35.281277Z"
     }
    },
    "outputs": [
@@ -261,10 +261,10 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.45946564739053\n",
-      "        x: [-3.765e-01  8.190e-02 ... -5.784e-01  1.644e-01]\n",
-      "      nit: 16\n",
-      "      jac: [-1.646e-03  9.805e-05 ... -1.137e-05 -1.251e-04]\n",
+      "      fun: -77.45847049044065\n",
+      "        x: [-3.706e-01  8.437e-02 ...  5.969e-01  2.892e-01]\n",
+      "      nit: 15\n",
+      "      jac: [ 4.411e-03 -8.157e-04 ... -6.338e-04  1.933e-04]\n",
       "     nfev: 1034\n",
       "     njev: 22\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 03c556894..24677cfb4 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": "2023-10-27T03:05:16.248103Z",
-     "iopub.status.busy": "2023-10-27T03:05:16.246192Z",
-     "iopub.status.idle": "2023-10-27T03:05:16.873689Z",
-     "shell.execute_reply": "2023-10-27T03:05:16.872788Z"
+     "iopub.execute_input": "2023-10-27T15:56:37.070428Z",
+     "iopub.status.busy": "2023-10-27T15:56:37.070004Z",
+     "iopub.status.idle": "2023-10-27T15:56:37.665177Z",
+     "shell.execute_reply": "2023-10-27T15:56:37.664437Z"
     }
    },
    "outputs": [
@@ -90,10 +90,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:16.877753Z",
-     "iopub.status.busy": "2023-10-27T03:05:16.877167Z",
-     "iopub.status.idle": "2023-10-27T03:05:16.929555Z",
-     "shell.execute_reply": "2023-10-27T03:05:16.928339Z"
+     "iopub.execute_input": "2023-10-27T15:56:37.670102Z",
+     "iopub.status.busy": "2023-10-27T15:56:37.668895Z",
+     "iopub.status.idle": "2023-10-27T15:56:37.698420Z",
+     "shell.execute_reply": "2023-10-27T15:56:37.697754Z"
     }
    },
    "outputs": [
@@ -101,7 +101,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -75.68366174447618\n"
+      "Energy at initialialization: -75.6836617444762\n"
      ]
     }
    ],
@@ -135,10 +135,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:16.935598Z",
-     "iopub.status.busy": "2023-10-27T03:05:16.935182Z",
-     "iopub.status.idle": "2023-10-27T03:05:19.090629Z",
-     "shell.execute_reply": "2023-10-27T03:05:19.089696Z"
+     "iopub.execute_input": "2023-10-27T15:56:37.702992Z",
+     "iopub.status.busy": "2023-10-27T15:56:37.701930Z",
+     "iopub.status.idle": "2023-10-27T15:56:40.173563Z",
+     "shell.execute_reply": "2023-10-27T15:56:40.172738Z"
     }
    },
    "outputs": [
@@ -150,7 +150,7 @@
       " message: Maximum number of function evaluations has been exceeded.\n",
       " success: False\n",
       "  status: 2\n",
-      "     fun: -75.69448131020114\n",
+      "     fun: -75.69448131113485\n",
       "       x: [ 1.354e+00  9.651e-02 -1.863e-03  1.095e+00 -2.132e-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 737161603..17d56189a 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": "2023-10-27T03:05:20.826794Z",
-     "iopub.status.busy": "2023-10-27T03:05:20.826354Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.191528Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.190910Z"
+     "iopub.execute_input": "2023-10-27T15:56:41.814382Z",
+     "iopub.status.busy": "2023-10-27T15:56:41.813941Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.177500Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.176750Z"
     }
    },
    "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_b(1), des_b(5), cre_a(4)): 1+1j\n",
+       "    (cre_a(3), des_a(0)): -0.25\n",
        "})"
       ]
      },
@@ -76,17 +76,17 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.196565Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.195229Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.202666Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.202084Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.180809Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.180437Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.185404Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.184750Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})'"
+       "'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": "2023-10-27T03:05:21.208130Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.206968Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.215617Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.214933Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.188816Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.188104Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.193682Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.192973Z"
     }
    },
    "outputs": [
@@ -121,16 +121,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
-       "    (cre_b(2)): 0-0.25j,\n",
-       "    (cre_a(3), des_a(0)): -0.5,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
-       "    (cre_a(0), des_a(3)): 1,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
        "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
-       "    (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), des_a(3), des_b(3)): -0.25-0.25j,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\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(3), des_a(0), cre_b(2)): 0-0.25j,\n",
+       "    (des_a(3), des_b(3)): 0.0625,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j\n",
        "})"
       ]
@@ -169,10 +169,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.223002Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.219475Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.229733Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.229048Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.196824Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.196346Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.201953Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.201326Z"
     }
    },
    "outputs": [
@@ -180,16 +180,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_b(2)): -5,\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
        "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
-       "    (des_a(3), des_b(3)): 0-1.25j,\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), des_a(3), des_b(3)): -1+1j,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\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(3), des_a(0), cre_b(2)): -1,\n",
+       "    (des_a(3), des_b(3)): 0-1.25j,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 2\n",
        "})"
       ]
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.234131Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.233065Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.240141Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.239585Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.205470Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.205033Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.211108Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.210442Z"
     }
    },
    "outputs": [
@@ -230,14 +230,14 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (des_b(3), des_a(3)): 0+1.25j,\n",
-       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
+       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
+       "    (cre_b(2)): -5,\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",
-       "    (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), des_b(3), des_a(3)): -1+1j,\n",
-       "    (cre_b(2)): -5,\n",
+       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
        "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
        "    (cre_a(3), des_a(0)): 0+3j\n",
        "})"
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.244450Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.243285Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.250663Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.250096Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.214641Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.214210Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.220562Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.219879Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.254249Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.253812Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.262971Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.262375Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.224072Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.223577Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.229192Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.228560Z"
     }
    },
    "outputs": [
@@ -340,21 +340,21 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.267860Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.266431Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.275640Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.275026Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.234118Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.233634Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.242733Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.242056Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([ 0.        +0.j        ,  0.        +0.j        ,\n",
-       "        0.        +0.j        ,  0.        +0.j        ,\n",
-       "       -0.04860684-0.04058205j,  0.        +0.j        ,\n",
-       "        0.        +0.j        ,  0.        +0.j        ,\n",
-       "        0.        +0.j        ])"
+       "array([0.        +0.j        , 0.        +0.j        ,\n",
+       "       0.        +0.j        , 0.        +0.j        ,\n",
+       "       0.10673406+0.06752782j, 0.        +0.j        ,\n",
+       "       0.        +0.j        , 0.        +0.j        ,\n",
+       "       0.        +0.j        ])"
       ]
      },
      "execution_count": 8,
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.280309Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.279234Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.295396Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.294821Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.246326Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.245873Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.261857Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.261249Z"
     }
    },
    "outputs": [
diff --git a/.doctrees/tutorials/03-double-factorized.doctree b/.doctrees/tutorials/03-double-factorized.doctree
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GIT binary patch
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diff --git a/.doctrees/tutorials/04-lucj.doctree b/.doctrees/tutorials/04-lucj.doctree
index 6abf317b574b3a036e7c7ce6762e81a1847054f7..63501513b03020ed56767d332b38e04332ce3e67 100644
GIT binary patch
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diff --git a/.doctrees/tutorials/05-entanglement-forging.doctree b/.doctrees/tutorials/05-entanglement-forging.doctree
index b41ea3e4ee709b8744bd02d8adbda2b8bd4489cf..a77e6ebf973e11c4c1de3dee57ac225a16622f1d 100644
GIT binary patch
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diff --git a/.doctrees/tutorials/06-fermion-operator.doctree b/.doctrees/tutorials/06-fermion-operator.doctree
index c946b96dbb151258bcf83038f9701c2a36e82e6f..22799fab217906a33e0269b938a1d428fa737d2d 100644
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diff --git a/_modules/ffsim/contract/one_body.html b/_modules/ffsim/contract/one_body.html
index f3af91cb0..a712058f0 100644
--- a/_modules/ffsim/contract/one_body.html
+++ b/_modules/ffsim/contract/one_body.html
@@ -57,6 +57,8 @@ <h1>Source code for ffsim.contract.one_body</h1><div class="highlight"><pre>
 <span class="kn">from</span> <span class="nn">ffsim.states</span> <span class="kn">import</span> <span class="n">dim</span>
 
 
+<div class="viewcode-block" id="contract_one_body">
+<a class="viewcode-back" href="../../../api/ffsim.contract.html#ffsim.contract.contract_one_body">[docs]</a>
 <span class="k">def</span> <span class="nf">contract_one_body</span><span class="p">(</span>
     <span class="n">vec</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
     <span class="n">mat</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
@@ -66,6 +68,30 @@ <h1>Source code for ffsim.contract.one_body</h1><div class="highlight"><pre>
     <span class="n">linkstr_index_a</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
     <span class="n">linkstr_index_b</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
 <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+<span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Contract a one-body tensor with a vector.</span>
+
+<span class="sd">    A one-body tensor has the form</span>
+
+<span class="sd">    .. math::</span>
+
+<span class="sd">        \sum_{ij} M_{ij} a^\dagger_i a_j</span>
+
+<span class="sd">    where :math:`M` is a complex-valued matrix.</span>
+
+<span class="sd">    Args:</span>
+<span class="sd">        mat: The one-body tensor.</span>
+<span class="sd">        norb: The number of spatial orbitals.</span>
+<span class="sd">        nelec: The number of alpha and beta electrons.</span>
+<span class="sd">        linkstr_index_a: String index lookup-table for spin alpha, as generated by the</span>
+<span class="sd">            function `pyscf.fci.cistring.gen_linkstr_index`_.</span>
+<span class="sd">        linkstr_index_b: String index lookup-table for spin beta, as generated by the</span>
+<span class="sd">            function `pyscf.fci.cistring.gen_linkstr_index`_.</span>
+
+<span class="sd">    Returns:</span>
+<span class="sd">        A LinearOperator that implements the action of the one-body tensor.</span>
+
+<span class="sd">    .. _pyscf.fci.cistring.gen_linkstr_index: https://pyscf.org/pyscf_api_docs/pyscf.fci.html#pyscf.fci.cistring.gen_linkstr_index</span>
+<span class="sd">    &quot;&quot;&quot;</span>
     <span class="n">link_index</span> <span class="o">=</span> <span class="p">(</span><span class="n">linkstr_index_a</span><span class="p">,</span> <span class="n">linkstr_index_b</span><span class="p">)</span>
     <span class="n">result</span> <span class="o">=</span> <span class="n">contract_1e</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">vec</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">nelec</span><span class="p">,</span> <span class="n">link_index</span><span class="o">=</span><span class="n">link_index</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span>
         <span class="nb">complex</span>
@@ -73,7 +99,8 @@ <h1>Source code for ffsim.contract.one_body</h1><div class="highlight"><pre>
     <span class="n">result</span> <span class="o">+=</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">contract_1e</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">vec</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">nelec</span><span class="p">,</span> <span class="n">link_index</span><span class="o">=</span><span class="n">link_index</span><span class="p">)</span>
     <span class="n">result</span> <span class="o">+=</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">contract_1e</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">vec</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">nelec</span><span class="p">,</span> <span class="n">link_index</span><span class="o">=</span><span class="n">link_index</span><span class="p">)</span>
     <span class="n">result</span> <span class="o">-=</span> <span class="n">contract_1e</span><span class="p">(</span><span class="n">mat</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">vec</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">norb</span><span class="p">,</span> <span class="n">nelec</span><span class="p">,</span> <span class="n">link_index</span><span class="o">=</span><span class="n">link_index</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">result</span>
+    <span class="k">return</span> <span class="n">result</span></div>
+
 
 
 <div class="viewcode-block" id="one_body_linop">
@@ -87,7 +114,7 @@ <h1>Source code for ffsim.contract.one_body</h1><div class="highlight"><pre>
 
 <span class="sd">    .. math::</span>
 
-<span class="sd">        \sum_{ij} M_{ij} a^\dagger{i} a_j</span>
+<span class="sd">        \sum_{ij} M_{ij} a^\dagger_i a_j</span>
 
 <span class="sd">    where :math:`M` is a complex-valued matrix.</span>
 
diff --git a/api/ffsim.contract.html b/api/ffsim.contract.html
index d8d630d82..597d9260c 100644
--- a/api/ffsim.contract.html
+++ b/api/ffsim.contract.html
@@ -105,6 +105,35 @@
 </dl>
 </dd></dl>
 
+<dl class="py function">
+<dt class="sig sig-object py" id="ffsim.contract.contract_one_body">
+<span class="sig-prename descclassname"><span class="pre">ffsim.contract.</span></span><span class="sig-name descname"><span class="pre">contract_one_body</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vec</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norb</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nelec</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">linkstr_index_a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">linkstr_index_b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ffsim/contract/one_body.html#contract_one_body"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.contract.contract_one_body" title="Link to this definition">¶</a></dt>
+<dd><p>Contract a one-body tensor with a vector.</p>
+<p>A one-body tensor has the form</p>
+<div class="math notranslate nohighlight">
+\[\sum_{ij} M_{ij} a^\dagger_i a_j\]</div>
+<p>where <span class="math notranslate nohighlight">\(M\)</span> is a complex-valued matrix.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>mat</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>) – The one-body tensor.</p></li>
+<li><p><strong>norb</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>) – The number of spatial orbitals.</p></li>
+<li><p><strong>nelec</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code>]) – The number of alpha and beta electrons.</p></li>
+<li><p><strong>linkstr_index_a</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>) – String index lookup-table for spin alpha, as generated by the
+function <a class="reference external" href="https://pyscf.org/pyscf_api_docs/pyscf.fci.html#pyscf.fci.cistring.gen_linkstr_index">pyscf.fci.cistring.gen_linkstr_index</a>.</p></li>
+<li><p><strong>linkstr_index_b</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>) – String index lookup-table for spin beta, as generated by the
+function <a class="reference external" href="https://pyscf.org/pyscf_api_docs/pyscf.fci.html#pyscf.fci.cistring.gen_linkstr_index">pyscf.fci.cistring.gen_linkstr_index</a>.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></p>
+</dd>
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p>A LinearOperator that implements the action of the one-body tensor.</p>
+</dd>
+</dl>
+</dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="ffsim.contract.diag_coulomb_linop">
 <span class="sig-prename descclassname"><span class="pre">ffsim.contract.</span></span><span class="sig-name descname"><span class="pre">diag_coulomb_linop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norb</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nelec</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">orbital_rotation</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mat_alpha_beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z_representation</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ffsim/contract/diag_coulomb.html#diag_coulomb_linop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.contract.diag_coulomb_linop" title="Link to this definition">¶</a></dt>
@@ -177,7 +206,7 @@
 <dd><p>Convert a one-body tensor to a linear operator.</p>
 <p>A one-body tensor has the form</p>
 <div class="math notranslate nohighlight">
-\[\sum_{ij} M_{ij} a^\dagger{i} a_j\]</div>
+\[\sum_{ij} M_{ij} a^\dagger_i a_j\]</div>
 <p>where <span class="math notranslate nohighlight">\(M\)</span> is a complex-valued matrix.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -228,6 +257,7 @@ <h3>Navigation</h3>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">ffsim.contract</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="#ffsim.contract.contract_diag_coulomb"><code class="docutils literal notranslate"><span class="pre">contract_diag_coulomb()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="#ffsim.contract.contract_num_op_sum"><code class="docutils literal notranslate"><span class="pre">contract_num_op_sum()</span></code></a></li>
+<li class="toctree-l2"><a class="reference internal" href="#ffsim.contract.contract_one_body"><code class="docutils literal notranslate"><span class="pre">contract_one_body()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="#ffsim.contract.diag_coulomb_linop"><code class="docutils literal notranslate"><span class="pre">diag_coulomb_linop()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="#ffsim.contract.num_op_sum_linop"><code class="docutils literal notranslate"><span class="pre">num_op_sum_linop()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="#ffsim.contract.one_body_linop"><code class="docutils literal notranslate"><span class="pre">one_body_linop()</span></code></a></li>
diff --git a/api/ffsim.html b/api/ffsim.html
index 7d02694e1..4c9039cdc 100644
--- a/api/ffsim.html
+++ b/api/ffsim.html
@@ -318,8 +318,8 @@
 </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_b(1), des_b(5), cre_a(4)): 1+1j,
     (cre_a(0), des_a(3)): 0.5
 })
 </pre></div>
@@ -335,8 +335,8 @@
 <div class="cell_output docutils container">
 <div class="output text_plain highlight-none notranslate"><div class="highlight"><pre><span></span>FermionOperator({
     (cre_a(3), des_a(0)): -0.5,
-    (cre_b(1), des_b(5), cre_a(4)): 2+2j,
-    (cre_a(0), des_a(3)): 1
+    (cre_a(0), des_a(3)): 1,
+    (cre_b(1), des_b(5), cre_a(4)): 2+2j
 })
 </pre></div>
 </div>
@@ -356,11 +356,11 @@
 </div>
 <div class="cell_output docutils container">
 <div class="output text_plain highlight-none notranslate"><div class="highlight"><pre><span></span>FermionOperator({
-    (cre_b(2)): 0+1j,
-    (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,
-    (des_a(3), des_b(3)): -0.25
+    (des_a(3), des_b(3)): -0.25,
+    (cre_b(2)): 0+1j,
+    (cre_a(3), des_a(0)): -0.25
 })
 </pre></div>
 </div>
@@ -374,12 +374,12 @@
 </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), des_a(3), des_b(3)): -0.25-0.25j,
-    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
     (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
-    (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_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
-    (cre_a(3), des_a(0), 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), 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
 })
 </pre></div>
 </div>
diff --git a/genindex.html b/genindex.html
index 95045a7e6..cf8b97387 100644
--- a/genindex.html
+++ b/genindex.html
@@ -111,6 +111,8 @@ <h2 id="C">C</h2>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/ffsim.contract.html#ffsim.contract.contract_num_op_sum">contract_num_op_sum() (in module ffsim.contract)</a>
+</li>
+      <li><a href="api/ffsim.contract.html#ffsim.contract.contract_one_body">contract_one_body() (in module ffsim.contract)</a>
 </li>
       <li><a href="api/ffsim.html#ffsim.MolecularData.core_energy">core_energy (ffsim.MolecularData attribute)</a>
 </li>
diff --git a/index.html b/index.html
index 703972c38..c7c90da99 100644
--- a/index.html
+++ b/index.html
@@ -108,6 +108,7 @@ <h2>API Reference<a class="headerlink" href="#api-reference" title="Link to this
 <li class="toctree-l1"><a class="reference internal" href="api/ffsim.contract.html">ffsim.contract</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="api/ffsim.contract.html#ffsim.contract.contract_diag_coulomb"><code class="docutils literal notranslate"><span class="pre">contract_diag_coulomb()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="api/ffsim.contract.html#ffsim.contract.contract_num_op_sum"><code class="docutils literal notranslate"><span class="pre">contract_num_op_sum()</span></code></a></li>
+<li class="toctree-l2"><a class="reference internal" href="api/ffsim.contract.html#ffsim.contract.contract_one_body"><code class="docutils literal notranslate"><span class="pre">contract_one_body()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="api/ffsim.contract.html#ffsim.contract.diag_coulomb_linop"><code class="docutils literal notranslate"><span class="pre">diag_coulomb_linop()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="api/ffsim.contract.html#ffsim.contract.num_op_sum_linop"><code class="docutils literal notranslate"><span class="pre">num_op_sum_linop()</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="api/ffsim.contract.html#ffsim.contract.one_body_linop"><code class="docutils literal notranslate"><span class="pre">one_body_linop()</span></code></a></li>
diff --git a/objects.inv b/objects.inv
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diff --git a/searchindex.js b/searchindex.js
index 385943532..b2886b7df 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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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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"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 3797ae9e6..d6e01fa5a 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:04:57.255539Z",
-     "iopub.status.busy": "2023-10-27T03:04:57.255034Z",
-     "iopub.status.idle": "2023-10-27T03:04:57.653213Z",
-     "shell.execute_reply": "2023-10-27T03:04:57.652569Z"
+     "iopub.execute_input": "2023-10-27T15:56:17.553188Z",
+     "iopub.status.busy": "2023-10-27T15:56:17.552767Z",
+     "iopub.status.idle": "2023-10-27T15:56:17.914376Z",
+     "shell.execute_reply": "2023-10-27T15:56:17.913518Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:04:57.657905Z",
-     "iopub.status.busy": "2023-10-27T03:04:57.656590Z",
-     "iopub.status.idle": "2023-10-27T03:04:57.662682Z",
-     "shell.execute_reply": "2023-10-27T03:04:57.662136Z"
+     "iopub.execute_input": "2023-10-27T15:56:17.918188Z",
+     "iopub.status.busy": "2023-10-27T15:56:17.917631Z",
+     "iopub.status.idle": "2023-10-27T15:56:17.922403Z",
+     "shell.execute_reply": "2023-10-27T15:56:17.921760Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:04:57.667736Z",
-     "iopub.status.busy": "2023-10-27T03:04:57.666400Z",
-     "iopub.status.idle": "2023-10-27T03:04:57.671189Z",
-     "shell.execute_reply": "2023-10-27T03:04:57.670658Z"
+     "iopub.execute_input": "2023-10-27T15:56:17.926658Z",
+     "iopub.status.busy": "2023-10-27T15:56:17.925552Z",
+     "iopub.status.idle": "2023-10-27T15:56:17.930575Z",
+     "shell.execute_reply": "2023-10-27T15:56:17.929762Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index 7699c0f29..4ff87b79a 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": "2023-10-27T03:04:59.630059Z",
-     "iopub.status.busy": "2023-10-27T03:04:59.629560Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.024476Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.023597Z"
+     "iopub.execute_input": "2023-10-27T15:56:19.756312Z",
+     "iopub.status.busy": "2023-10-27T15:56:19.756069Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.124710Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.123784Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:00.028824Z",
-     "iopub.status.busy": "2023-10-27T03:05:00.028106Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.061962Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.061268Z"
+     "iopub.execute_input": "2023-10-27T15:56:20.128851Z",
+     "iopub.status.busy": "2023-10-27T15:56:20.128310Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.167911Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.167175Z"
     }
    },
    "outputs": [],
@@ -158,10 +158,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:00.067442Z",
-     "iopub.status.busy": "2023-10-27T03:05:00.066016Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.079662Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.079034Z"
+     "iopub.execute_input": "2023-10-27T15:56:20.173265Z",
+     "iopub.status.busy": "2023-10-27T15:56:20.172016Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.187030Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.186335Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:00.084489Z",
-     "iopub.status.busy": "2023-10-27T03:05:00.083296Z",
-     "iopub.status.idle": "2023-10-27T03:05:00.090411Z",
-     "shell.execute_reply": "2023-10-27T03:05:00.089817Z"
+     "iopub.execute_input": "2023-10-27T15:56:20.192285Z",
+     "iopub.status.busy": "2023-10-27T15:56:20.191173Z",
+     "iopub.status.idle": "2023-10-27T15:56:20.198482Z",
+     "shell.execute_reply": "2023-10-27T15:56:20.197803Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.html b/tutorials/03-double-factorized.html
index 2a2da1c44..12e5bc746 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>
@@ -293,7 +293,7 @@ <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>
@@ -321,7 +321,7 @@ <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>
@@ -348,7 +348,7 @@ <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>
@@ -375,7 +375,7 @@ <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>
@@ -404,7 +404,7 @@ <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>
@@ -432,7 +432,7 @@ <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 c061160c4..867e841ed 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": "2023-10-27T03:05:01.960181Z",
-     "iopub.status.busy": "2023-10-27T03:05:01.959717Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.404039Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.403342Z"
+     "iopub.execute_input": "2023-10-27T15:56:21.878889Z",
+     "iopub.status.busy": "2023-10-27T15:56:21.878510Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.327582Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.326818Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.408011Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.407295Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.417935Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.417313Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.331466Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.330818Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.339396Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.337615Z"
     }
    },
    "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": "2023-10-27T03:05:02.423483Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.421763Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.431334Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.430699Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.342700Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.342346Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.349281Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.348539Z"
     }
    },
    "outputs": [],
@@ -284,10 +284,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.434936Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.434685Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.439093Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.438396Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.352710Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.352274Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.357049Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.356275Z"
     }
    },
    "outputs": [],
@@ -324,10 +324,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.559009Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.558102Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.564371Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.563761Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.360182Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.359836Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.367959Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.367238Z"
     }
    },
    "outputs": [
@@ -335,7 +335,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.8377963825937084\n"
+      "Hartree Fock energy: -0.837796382593709\n"
      ]
     }
    ],
@@ -363,10 +363,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.567736Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.567083Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.584110Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.583071Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.371087Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.370799Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.382769Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.382019Z"
     }
    },
    "outputs": [
@@ -374,7 +374,7 @@
      "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"
      ]
     }
    ],
@@ -405,10 +405,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.587264Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.586808Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.600814Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.599564Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.386352Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.385780Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.395074Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.394453Z"
     }
    },
    "outputs": [
@@ -416,7 +416,7 @@
      "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"
      ]
     }
    ],
@@ -446,10 +446,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.604427Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.603969Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.648867Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.648260Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.398534Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.397827Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.448640Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.447932Z"
     }
    },
    "outputs": [
@@ -457,7 +457,7 @@
      "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"
      ]
     }
    ],
@@ -489,10 +489,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.654063Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.652939Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.679846Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.679254Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.451778Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.451358Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.492907Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.491767Z"
     }
    },
    "outputs": [
@@ -500,7 +500,7 @@
      "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"
      ]
     }
    ],
@@ -531,10 +531,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:02.684588Z",
-     "iopub.status.busy": "2023-10-27T03:05:02.683495Z",
-     "iopub.status.idle": "2023-10-27T03:05:02.697257Z",
-     "shell.execute_reply": "2023-10-27T03:05:02.696649Z"
+     "iopub.execute_input": "2023-10-27T15:56:22.495880Z",
+     "iopub.status.busy": "2023-10-27T15:56:22.495597Z",
+     "iopub.status.idle": "2023-10-27T15:56:22.514396Z",
+     "shell.execute_reply": "2023-10-27T15:56:22.513618Z"
     }
    },
    "outputs": [
@@ -542,7 +542,7 @@
      "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 63957239b..3bb5504c9 100644
--- a/tutorials/04-lucj.html
+++ b/tutorials/04-lucj.html
@@ -95,7 +95,7 @@ <h1>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-converged SCF energy = -77.4456267643962
+converged SCF energy = -77.4456267643961
 CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000
 </pre></div></div>
 </div>
@@ -147,8 +147,8 @@ <h2>The unitary cluster Jastrow (UCJ) ansatz<a class="headerlink" href="#The-uni
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-E(CCSD) = -77.49387212754471  E_corr = -0.04824536314851448
-Energy at initialialization: -77.46975600021672
+E(CCSD) = -77.49387212754468  E_corr = -0.04824536314851557
+Energy at initialialization: -77.46975600021696
 </pre></div></div>
 </div>
 <p>To facilitate variational optimization of the ansatz, <code class="docutils literal notranslate"><span class="pre">UCJOperator</span></code> implements methods for conversion to and from a vector of real-valued parameters. The precise relation between a parameter vector and the matrices of the UCJ operator is somewhat complicated. In short, the parameter vector stores the entries of the UCJ matrices in a non-redundant way (for the orbital rotations, the parameter vector actually stores the entries of their generators.)</p>
@@ -187,12 +187,12 @@ <h2>The unitary cluster Jastrow (UCJ) ansatz<a class="headerlink" href="#The-uni
   message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT
   success: False
    status: 1
-      fun: -77.51577544983374
-        x: [-1.451e-01  1.878e-01 ... -6.238e-01 -6.006e-02]
+      fun: -77.5159157550554
+        x: [-1.413e-01  1.968e-01 ...  4.266e-01  2.918e-01]
       nit: 9
-      jac: [ 3.988e-03 -8.249e-03 ... -3.389e-03 -1.711e-03]
-     nfev: 1168
-     njev: 16
+      jac: [ 6.079e-03 -7.610e-03 ...  3.376e-03 -5.228e-03]
+     nfev: 1314
+     njev: 18
  hess_inv: &lt;72x72 LbfgsInvHessProduct with dtype=float64&gt;
 </pre></div></div>
 </div>
@@ -251,10 +251,10 @@ <h2>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
   message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT
   success: False
    status: 1
-      fun: -77.45946564739053
-        x: [-3.765e-01  8.190e-02 ... -5.784e-01  1.644e-01]
-      nit: 16
-      jac: [-1.646e-03  9.805e-05 ... -1.137e-05 -1.251e-04]
+      fun: -77.45847049044065
+        x: [-3.706e-01  8.437e-02 ...  5.969e-01  2.892e-01]
+      nit: 15
+      jac: [ 4.411e-03 -8.157e-04 ... -6.338e-04  1.933e-04]
      nfev: 1034
      njev: 22
  hess_inv: &lt;46x46 LbfgsInvHessProduct with dtype=float64&gt;
diff --git a/tutorials/04-lucj.ipynb b/tutorials/04-lucj.ipynb
index d037aca8d..fc59af3b7 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:05.159264Z",
-     "iopub.status.busy": "2023-10-27T03:05:05.159017Z",
-     "iopub.status.idle": "2023-10-27T03:05:05.871208Z",
-     "shell.execute_reply": "2023-10-27T03:05:05.870569Z"
+     "iopub.execute_input": "2023-10-27T15:56:24.886532Z",
+     "iopub.status.busy": "2023-10-27T15:56:24.886278Z",
+     "iopub.status.idle": "2023-10-27T15:56:25.639738Z",
+     "shell.execute_reply": "2023-10-27T15:56:25.638878Z"
     }
    },
    "outputs": [
@@ -25,7 +25,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "converged SCF energy = -77.4456267643962\n"
+      "converged SCF energy = -77.4456267643961\n"
      ]
     },
     {
@@ -110,10 +110,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:05.876664Z",
-     "iopub.status.busy": "2023-10-27T03:05:05.875285Z",
-     "iopub.status.idle": "2023-10-27T03:05:06.651133Z",
-     "shell.execute_reply": "2023-10-27T03:05:06.650529Z"
+     "iopub.execute_input": "2023-10-27T15:56:25.643502Z",
+     "iopub.status.busy": "2023-10-27T15:56:25.642966Z",
+     "iopub.status.idle": "2023-10-27T15:56:25.881461Z",
+     "shell.execute_reply": "2023-10-27T15:56:25.880768Z"
     }
    },
    "outputs": [
@@ -121,14 +121,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754471  E_corr = -0.04824536314851448\n"
+      "E(CCSD) = -77.49387212754468  E_corr = -0.04824536314851557\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -77.46975600021672\n"
+      "Energy at initialialization: -77.46975600021696\n"
      ]
     }
    ],
@@ -173,10 +173,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:06.655856Z",
-     "iopub.status.busy": "2023-10-27T03:05:06.654768Z",
-     "iopub.status.idle": "2023-10-27T03:05:10.593929Z",
-     "shell.execute_reply": "2023-10-27T03:05:10.593304Z"
+     "iopub.execute_input": "2023-10-27T15:56:25.884742Z",
+     "iopub.status.busy": "2023-10-27T15:56:25.884388Z",
+     "iopub.status.idle": "2023-10-27T15:56:31.317001Z",
+     "shell.execute_reply": "2023-10-27T15:56:31.316266Z"
     }
    },
    "outputs": [
@@ -188,12 +188,12 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.51577544983374\n",
-      "        x: [-1.451e-01  1.878e-01 ... -6.238e-01 -6.006e-02]\n",
+      "      fun: -77.5159157550554\n",
+      "        x: [-1.413e-01  1.968e-01 ...  4.266e-01  2.918e-01]\n",
       "      nit: 9\n",
-      "      jac: [ 3.988e-03 -8.249e-03 ... -3.389e-03 -1.711e-03]\n",
-      "     nfev: 1168\n",
-      "     njev: 16\n",
+      "      jac: [ 6.079e-03 -7.610e-03 ...  3.376e-03 -5.228e-03]\n",
+      "     nfev: 1314\n",
+      "     njev: 18\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -246,10 +246,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:10.598208Z",
-     "iopub.status.busy": "2023-10-27T03:05:10.597724Z",
-     "iopub.status.idle": "2023-10-27T03:05:14.139838Z",
-     "shell.execute_reply": "2023-10-27T03:05:14.139253Z"
+     "iopub.execute_input": "2023-10-27T15:56:31.320238Z",
+     "iopub.status.busy": "2023-10-27T15:56:31.319937Z",
+     "iopub.status.idle": "2023-10-27T15:56:35.282027Z",
+     "shell.execute_reply": "2023-10-27T15:56:35.281277Z"
     }
    },
    "outputs": [
@@ -261,10 +261,10 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.45946564739053\n",
-      "        x: [-3.765e-01  8.190e-02 ... -5.784e-01  1.644e-01]\n",
-      "      nit: 16\n",
-      "      jac: [-1.646e-03  9.805e-05 ... -1.137e-05 -1.251e-04]\n",
+      "      fun: -77.45847049044065\n",
+      "        x: [-3.706e-01  8.437e-02 ...  5.969e-01  2.892e-01]\n",
+      "      nit: 15\n",
+      "      jac: [ 4.411e-03 -8.157e-04 ... -6.338e-04  1.933e-04]\n",
       "     nfev: 1034\n",
       "     njev: 22\n",
       " hess_inv: <46x46 LbfgsInvHessProduct with dtype=float64>\n"
diff --git a/tutorials/05-entanglement-forging.html b/tutorials/05-entanglement-forging.html
index d4ec0b314..9ddad9112 100644
--- a/tutorials/05-entanglement-forging.html
+++ b/tutorials/05-entanglement-forging.html
@@ -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: -75.68366174447618
+Energy at initialialization: -75.6836617444762
 </pre></div></div>
 </div>
 <div class="nbinput docutils container">
@@ -178,7 +178,7 @@ <h1>Entanglement forging<a class="headerlink" href="#Entanglement-forging" title
  message: Maximum number of function evaluations has been exceeded.
  success: False
   status: 2
-     fun: -75.69448131020114
+     fun: -75.69448131113485
        x: [ 1.354e+00  9.651e-02 -1.863e-03  1.095e+00 -2.132e-01]
     nfev: 100
    maxcv: 0.0
diff --git a/tutorials/05-entanglement-forging.ipynb b/tutorials/05-entanglement-forging.ipynb
index 03c556894..24677cfb4 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": "2023-10-27T03:05:16.248103Z",
-     "iopub.status.busy": "2023-10-27T03:05:16.246192Z",
-     "iopub.status.idle": "2023-10-27T03:05:16.873689Z",
-     "shell.execute_reply": "2023-10-27T03:05:16.872788Z"
+     "iopub.execute_input": "2023-10-27T15:56:37.070428Z",
+     "iopub.status.busy": "2023-10-27T15:56:37.070004Z",
+     "iopub.status.idle": "2023-10-27T15:56:37.665177Z",
+     "shell.execute_reply": "2023-10-27T15:56:37.664437Z"
     }
    },
    "outputs": [
@@ -90,10 +90,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:16.877753Z",
-     "iopub.status.busy": "2023-10-27T03:05:16.877167Z",
-     "iopub.status.idle": "2023-10-27T03:05:16.929555Z",
-     "shell.execute_reply": "2023-10-27T03:05:16.928339Z"
+     "iopub.execute_input": "2023-10-27T15:56:37.670102Z",
+     "iopub.status.busy": "2023-10-27T15:56:37.668895Z",
+     "iopub.status.idle": "2023-10-27T15:56:37.698420Z",
+     "shell.execute_reply": "2023-10-27T15:56:37.697754Z"
     }
    },
    "outputs": [
@@ -101,7 +101,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -75.68366174447618\n"
+      "Energy at initialialization: -75.6836617444762\n"
      ]
     }
    ],
@@ -135,10 +135,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:16.935598Z",
-     "iopub.status.busy": "2023-10-27T03:05:16.935182Z",
-     "iopub.status.idle": "2023-10-27T03:05:19.090629Z",
-     "shell.execute_reply": "2023-10-27T03:05:19.089696Z"
+     "iopub.execute_input": "2023-10-27T15:56:37.702992Z",
+     "iopub.status.busy": "2023-10-27T15:56:37.701930Z",
+     "iopub.status.idle": "2023-10-27T15:56:40.173563Z",
+     "shell.execute_reply": "2023-10-27T15:56:40.172738Z"
     }
    },
    "outputs": [
@@ -150,7 +150,7 @@
       " message: Maximum number of function evaluations has been exceeded.\n",
       " success: False\n",
       "  status: 2\n",
-      "     fun: -75.69448131020114\n",
+      "     fun: -75.69448131113485\n",
       "       x: [ 1.354e+00  9.651e-02 -1.863e-03  1.095e+00 -2.132e-01]\n",
       "    nfev: 100\n",
       "   maxcv: 0.0\n"
diff --git a/tutorials/06-fermion-operator.html b/tutorials/06-fermion-operator.html
index 38e2f6905..182a36c29 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_b(1), des_b(5), cre_a(4)): 1+1j
+    (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, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})&#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>
@@ -127,16 +127,16 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
-    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
-    (cre_b(2)): 0-0.25j,
-    (cre_a(3), des_a(0)): -0.5,
-    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
-    (cre_a(0), des_a(3)): 1,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
     (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
-    (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), des_a(3), des_b(3)): -0.25-0.25j,
     (cre_b(1), des_b(5), cre_a(4)): 2+2j,
+    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
+    (cre_a(3), des_a(0)): -0.5,
+    (cre_a(0), des_a(3)): 1,
+    (cre_b(2)): 0-0.25j,
+    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
+    (des_a(3), des_b(3)): 0.0625,
     (cre_a(0), des_a(3), cre_b(2)): 0+0.5j
 })
 </pre></div></div>
@@ -162,16 +162,16 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
-    (cre_a(3), des_a(0), cre_b(2)): -1,
-    (cre_b(2)): -5,
-    (cre_a(3), des_a(0)): 0+3j,
-    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
-    (cre_a(0), des_a(3)): 0-6j,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,
     (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
-    (des_a(3), des_b(3)): 0-1.25j,
-    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
+    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
     (cre_b(1), des_b(5), cre_a(4)): 12-12j,
+    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
+    (cre_a(3), des_a(0)): 0+3j,
+    (cre_a(0), des_a(3)): 0-6j,
+    (cre_b(2)): -5,
+    (cre_a(3), des_a(0), cre_b(2)): -1,
+    (des_a(3), des_b(3)): 0-1.25j,
     (cre_a(0), des_a(3), cre_b(2)): 2
 })
 </pre></div></div>
@@ -193,14 +193,14 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
-    (des_b(3), des_a(3)): 0+1.25j,
-    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
     (cre_b(2), cre_a(3), des_a(0)): -1,
-    (cre_a(0), des_a(3)): 0-6j,
+    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
+    (cre_b(2)): -5,
+    (des_b(3), des_a(3)): 0+1.25j,
     (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
-    (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), des_b(3), des_a(3)): -1+1j,
-    (cre_b(2)): -5,
+    (cre_b(2), cre_a(0), des_a(3)): 2,
     (cre_b(1), cre_a(4), des_b(5)): -12+12j,
     (cre_a(3), des_a(0)): 0+3j
 })
@@ -271,11 +271,11 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-array([ 0.        +0.j        ,  0.        +0.j        ,
-        0.        +0.j        ,  0.        +0.j        ,
-       -0.04860684-0.04058205j,  0.        +0.j        ,
-        0.        +0.j        ,  0.        +0.j        ,
-        0.        +0.j        ])
+array([0.        +0.j        , 0.        +0.j        ,
+       0.        +0.j        , 0.        +0.j        ,
+       0.10673406+0.06752782j, 0.        +0.j        ,
+       0.        +0.j        , 0.        +0.j        ,
+       0.        +0.j        ])
 </pre></div></div>
 </div>
 <p>It can also be passed into most linear algebra routines in <code class="docutils literal notranslate"><span class="pre">scipy.sparse.linalg</span></code>.</p>
diff --git a/tutorials/06-fermion-operator.ipynb b/tutorials/06-fermion-operator.ipynb
index 737161603..17d56189a 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": "2023-10-27T03:05:20.826794Z",
-     "iopub.status.busy": "2023-10-27T03:05:20.826354Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.191528Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.190910Z"
+     "iopub.execute_input": "2023-10-27T15:56:41.814382Z",
+     "iopub.status.busy": "2023-10-27T15:56:41.813941Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.177500Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.176750Z"
     }
    },
    "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_b(1), des_b(5), cre_a(4)): 1+1j\n",
+       "    (cre_a(3), des_a(0)): -0.25\n",
        "})"
       ]
      },
@@ -76,17 +76,17 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.196565Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.195229Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.202666Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.202084Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.180809Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.180437Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.185404Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.184750Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})'"
+       "'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": "2023-10-27T03:05:21.208130Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.206968Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.215617Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.214933Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.188816Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.188104Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.193682Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.192973Z"
     }
    },
    "outputs": [
@@ -121,16 +121,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,\n",
-       "    (cre_b(2)): 0-0.25j,\n",
-       "    (cre_a(3), des_a(0)): -0.5,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
-       "    (cre_a(0), des_a(3)): 1,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,\n",
        "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
-       "    (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), des_a(3), des_b(3)): -0.25-0.25j,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\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(3), des_a(0), cre_b(2)): 0-0.25j,\n",
+       "    (des_a(3), des_b(3)): 0.0625,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j\n",
        "})"
       ]
@@ -169,10 +169,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.223002Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.219475Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.229733Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.229048Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.196824Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.196346Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.201953Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.201326Z"
     }
    },
    "outputs": [
@@ -180,16 +180,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_b(2)): -5,\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\n",
-       "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
        "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
-       "    (des_a(3), des_b(3)): 0-1.25j,\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), des_a(3), des_b(3)): -1+1j,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
+       "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\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(3), des_a(0), cre_b(2)): -1,\n",
+       "    (des_a(3), des_b(3)): 0-1.25j,\n",
        "    (cre_a(0), des_a(3), cre_b(2)): 2\n",
        "})"
       ]
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.234131Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.233065Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.240141Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.239585Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.205470Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.205033Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.211108Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.210442Z"
     }
    },
    "outputs": [
@@ -230,14 +230,14 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (des_b(3), des_a(3)): 0+1.25j,\n",
-       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
-       "    (cre_a(0), des_a(3)): 0-6j,\n",
+       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
+       "    (cre_b(2)): -5,\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",
-       "    (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), des_b(3), des_a(3)): -1+1j,\n",
-       "    (cre_b(2)): -5,\n",
+       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
        "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
        "    (cre_a(3), des_a(0)): 0+3j\n",
        "})"
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.244450Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.243285Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.250663Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.250096Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.214641Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.214210Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.220562Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.219879Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.254249Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.253812Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.262971Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.262375Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.224072Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.223577Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.229192Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.228560Z"
     }
    },
    "outputs": [
@@ -340,21 +340,21 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.267860Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.266431Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.275640Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.275026Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.234118Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.233634Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.242733Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.242056Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([ 0.        +0.j        ,  0.        +0.j        ,\n",
-       "        0.        +0.j        ,  0.        +0.j        ,\n",
-       "       -0.04860684-0.04058205j,  0.        +0.j        ,\n",
-       "        0.        +0.j        ,  0.        +0.j        ,\n",
-       "        0.        +0.j        ])"
+       "array([0.        +0.j        , 0.        +0.j        ,\n",
+       "       0.        +0.j        , 0.        +0.j        ,\n",
+       "       0.10673406+0.06752782j, 0.        +0.j        ,\n",
+       "       0.        +0.j        , 0.        +0.j        ,\n",
+       "       0.        +0.j        ])"
       ]
      },
      "execution_count": 8,
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-27T03:05:21.280309Z",
-     "iopub.status.busy": "2023-10-27T03:05:21.279234Z",
-     "iopub.status.idle": "2023-10-27T03:05:21.295396Z",
-     "shell.execute_reply": "2023-10-27T03:05:21.294821Z"
+     "iopub.execute_input": "2023-10-27T15:56:42.246326Z",
+     "iopub.status.busy": "2023-10-27T15:56:42.245873Z",
+     "iopub.status.idle": "2023-10-27T15:56:42.261857Z",
+     "shell.execute_reply": "2023-10-27T15:56:42.261249Z"
     }
    },
    "outputs": [