From 21ed625122c789b2619faa2ad430365192632d8f Mon Sep 17 00:00:00 2001
From: kevinsung <kevinsung@users.noreply.github.com>
Date: Thu, 26 Oct 2023 21:54:46 +0000
Subject: [PATCH] deploy: e3ddac7faee44e8e4e95821b2f81bc175760027c

---
 .doctrees/api/ffsim.doctree                   | Bin 475643 -> 475473 bytes
 .doctrees/environment.pickle                  | Bin 1500412 -> 1499475 bytes
 .../nbsphinx/tutorials/01-introduction.ipynb  |  24 ++--
 .../tutorials/02-orbital-rotation.ipynb       |  32 ++---
 .../tutorials/03-double-factorized.ipynb      |  80 ++++++------
 .doctrees/nbsphinx/tutorials/04-lucj.ipynb    |  56 ++++-----
 .../tutorials/05-entanglement-forging.ipynb   |  30 ++---
 .../tutorials/06-fermion-operator.ipynb       | 114 +++++++++---------
 .doctrees/tutorials/04-lucj.doctree           | Bin 38275 -> 38269 bytes
 .../tutorials/05-entanglement-forging.doctree | Bin 15254 -> 15260 bytes
 .../tutorials/06-fermion-operator.doctree     | Bin 41445 -> 41445 bytes
 .../double_factorized_hamiltonian.html        |   2 +-
 .../hamiltonians/molecular_hamiltonian.html   |   2 +-
 _modules/ffsim/molecular_data.html            |  23 +---
 _modules/ffsim/variational/hopgate.html       |   2 +-
 _modules/ffsim/variational/ucj.html           |   2 +-
 api/ffsim.html                                |  16 +--
 searchindex.js                                |   2 +-
 tutorials/01-introduction.ipynb               |  24 ++--
 tutorials/02-orbital-rotation.ipynb           |  32 ++---
 tutorials/03-double-factorized.ipynb          |  80 ++++++------
 tutorials/04-lucj.html                        |  24 ++--
 tutorials/04-lucj.ipynb                       |  56 ++++-----
 tutorials/05-entanglement-forging.html        |   6 +-
 tutorials/05-entanglement-forging.ipynb       |  30 ++---
 tutorials/06-fermion-operator.html            |  42 +++----
 tutorials/06-fermion-operator.ipynb           | 114 +++++++++---------
 27 files changed, 386 insertions(+), 407 deletions(-)

diff --git a/.doctrees/api/ffsim.doctree b/.doctrees/api/ffsim.doctree
index 8f3cd36e1eb0bac10156e8b8f603af200584cc83..29e74e7e385a325db9cb65d159401f3d4fef4d51 100644
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diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
index 5150edb8b62ce08734d0b9e566d95e7c16a7d179..928acc897f1715a49021b04e90096c27b109576b 100644
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diff --git a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
index 738bf9af0..542a28d4f 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": "2023-10-26T15:40:42.829408Z",
-     "iopub.status.busy": "2023-10-26T15:40:42.829034Z",
-     "iopub.status.idle": "2023-10-26T15:40:43.115107Z",
-     "shell.execute_reply": "2023-10-26T15:40:43.114553Z"
+     "iopub.execute_input": "2023-10-26T21:54:24.626048Z",
+     "iopub.status.busy": "2023-10-26T21:54:24.625502Z",
+     "iopub.status.idle": "2023-10-26T21:54:24.916794Z",
+     "shell.execute_reply": "2023-10-26T21:54:24.916239Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:43.119123Z",
-     "iopub.status.busy": "2023-10-26T15:40:43.118055Z",
-     "iopub.status.idle": "2023-10-26T15:40:43.123141Z",
-     "shell.execute_reply": "2023-10-26T15:40:43.122678Z"
+     "iopub.execute_input": "2023-10-26T21:54:24.921005Z",
+     "iopub.status.busy": "2023-10-26T21:54:24.919903Z",
+     "iopub.status.idle": "2023-10-26T21:54:24.925012Z",
+     "shell.execute_reply": "2023-10-26T21:54:24.924548Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:43.126861Z",
-     "iopub.status.busy": "2023-10-26T15:40:43.125985Z",
-     "iopub.status.idle": "2023-10-26T15:40:43.129804Z",
-     "shell.execute_reply": "2023-10-26T15:40:43.129341Z"
+     "iopub.execute_input": "2023-10-26T21:54:24.928816Z",
+     "iopub.status.busy": "2023-10-26T21:54:24.927921Z",
+     "iopub.status.idle": "2023-10-26T21:54:24.931868Z",
+     "shell.execute_reply": "2023-10-26T21:54:24.931405Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index d540c77ff..e59b1f447 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": "2023-10-26T15:40:44.747012Z",
-     "iopub.status.busy": "2023-10-26T15:40:44.746660Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.026053Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.025508Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.554827Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.554540Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.838397Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.837851Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:45.030774Z",
-     "iopub.status.busy": "2023-10-26T15:40:45.029736Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.055723Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.055244Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.843035Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.841994Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.867230Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.866712Z"
     }
    },
    "outputs": [],
@@ -158,10 +158,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:45.059575Z",
-     "iopub.status.busy": "2023-10-26T15:40:45.058663Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.069563Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.069067Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.871420Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.870428Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.881346Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.880817Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:45.073324Z",
-     "iopub.status.busy": "2023-10-26T15:40:45.072401Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.077945Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.077473Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.885340Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.884395Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.890064Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.889582Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index 4191a3e16..aff25e788 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": "2023-10-26T15:40:46.698076Z",
-     "iopub.status.busy": "2023-10-26T15:40:46.697722Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.057254Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.056722Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.517494Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.517144Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.859683Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.859174Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.061559Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.060504Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.068182Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.067706Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.863775Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.862781Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.870588Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.870125Z"
     }
    },
    "outputs": [
@@ -226,10 +226,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.071132Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.070637Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.076297Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.075779Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.874583Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.873677Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.879229Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.878771Z"
     }
    },
    "outputs": [],
@@ -284,10 +284,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.078619Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.078279Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.081964Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.081501Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.882477Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.882071Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.885968Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.885523Z"
     }
    },
    "outputs": [],
@@ -324,10 +324,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.155592Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.154994Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.159928Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.159315Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.952107Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.951382Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.957168Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.956674Z"
     }
    },
    "outputs": [
@@ -363,10 +363,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.162336Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.162145Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.172569Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.171964Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.959983Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.959396Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.968750Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.968270Z"
     }
    },
    "outputs": [
@@ -405,10 +405,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.175110Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.174657Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.183808Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.183279Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.971329Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.970763Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.979373Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.978932Z"
     }
    },
    "outputs": [
@@ -446,10 +446,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.186320Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.186131Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.219836Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.219385Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.981881Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.981327Z",
+     "iopub.status.idle": "2023-10-26T21:54:29.016188Z",
+     "shell.execute_reply": "2023-10-26T21:54:29.015742Z"
     }
    },
    "outputs": [
@@ -489,10 +489,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.222288Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.222014Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.243532Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.243081Z"
+     "iopub.execute_input": "2023-10-26T21:54:29.019498Z",
+     "iopub.status.busy": "2023-10-26T21:54:29.018429Z",
+     "iopub.status.idle": "2023-10-26T21:54:29.038774Z",
+     "shell.execute_reply": "2023-10-26T21:54:29.038333Z"
     }
    },
    "outputs": [
@@ -531,10 +531,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.246063Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.245776Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.255612Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.255186Z"
+     "iopub.execute_input": "2023-10-26T21:54:29.042307Z",
+     "iopub.status.busy": "2023-10-26T21:54:29.041422Z",
+     "iopub.status.idle": "2023-10-26T21:54:29.052280Z",
+     "shell.execute_reply": "2023-10-26T21:54:29.051815Z"
     }
    },
    "outputs": [
diff --git a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
index 09ba4aa87..a11f8d251 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": "2023-10-26T15:40:49.173908Z",
-     "iopub.status.busy": "2023-10-26T15:40:49.173566Z",
-     "iopub.status.idle": "2023-10-26T15:40:49.721773Z",
-     "shell.execute_reply": "2023-10-26T15:40:49.721209Z"
+     "iopub.execute_input": "2023-10-26T21:54:30.789283Z",
+     "iopub.status.busy": "2023-10-26T21:54:30.788907Z",
+     "iopub.status.idle": "2023-10-26T21:54:31.461048Z",
+     "shell.execute_reply": "2023-10-26T21:54:31.460505Z"
     }
    },
    "outputs": [
@@ -32,7 +32,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000\n"
+      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -110,10 +110,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:49.724841Z",
-     "iopub.status.busy": "2023-10-26T15:40:49.724494Z",
-     "iopub.status.idle": "2023-10-26T15:40:50.692531Z",
-     "shell.execute_reply": "2023-10-26T15:40:50.691938Z"
+     "iopub.execute_input": "2023-10-26T21:54:31.465293Z",
+     "iopub.status.busy": "2023-10-26T21:54:31.464287Z",
+     "iopub.status.idle": "2023-10-26T21:54:31.898474Z",
+     "shell.execute_reply": "2023-10-26T21:54:31.897988Z"
     }
    },
    "outputs": [
@@ -121,14 +121,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851454\n"
+      "E(CCSD) = -77.49387212754476  E_corr = -0.0482453631485149\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -77.46975600021693\n"
+      "Energy at initialialization: -77.46975600021689\n"
      ]
     }
    ],
@@ -173,10 +173,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:50.695286Z",
-     "iopub.status.busy": "2023-10-26T15:40:50.694948Z",
-     "iopub.status.idle": "2023-10-26T15:40:54.086057Z",
-     "shell.execute_reply": "2023-10-26T15:40:54.085582Z"
+     "iopub.execute_input": "2023-10-26T21:54:31.903123Z",
+     "iopub.status.busy": "2023-10-26T21:54:31.901767Z",
+     "iopub.status.idle": "2023-10-26T21:54:34.814416Z",
+     "shell.execute_reply": "2023-10-26T21:54:34.813892Z"
     }
    },
    "outputs": [
@@ -188,12 +188,12 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.51588951609632\n",
-      "        x: [-1.450e-01  1.879e-01 ... -6.233e-01 -5.993e-02]\n",
+      "      fun: -77.51554916701404\n",
+      "        x: [-1.569e-01  1.944e-01 ... -6.056e-01  1.983e-01]\n",
       "      nit: 9\n",
-      "      jac: [ 4.106e-03 -8.635e-03 ... -2.993e-03 -1.670e-03]\n",
-      "     nfev: 1168\n",
-      "     njev: 16\n",
+      "      jac: [-8.171e-03 -3.966e-03 ... -9.706e-03  1.509e-03]\n",
+      "     nfev: 1022\n",
+      "     njev: 14\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -246,10 +246,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:54.088721Z",
-     "iopub.status.busy": "2023-10-26T15:40:54.088365Z",
-     "iopub.status.idle": "2023-10-26T15:40:57.233669Z",
-     "shell.execute_reply": "2023-10-26T15:40:57.233141Z"
+     "iopub.execute_input": "2023-10-26T21:54:34.817935Z",
+     "iopub.status.busy": "2023-10-26T21:54:34.817539Z",
+     "iopub.status.idle": "2023-10-26T21:54:37.520155Z",
+     "shell.execute_reply": "2023-10-26T21:54:37.519545Z"
     }
    },
    "outputs": [
@@ -261,10 +261,10 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.46007276424072\n",
-      "        x: [-3.689e-01  8.946e-02 ... -5.942e-01  1.631e-01]\n",
-      "      nit: 16\n",
-      "      jac: [-1.563e-04  3.979e-04 ...  4.633e-04 -1.531e-03]\n",
+      "      fun: -77.46262558981611\n",
+      "        x: [-3.094e-01  6.744e-02 ... -4.668e-01  2.137e-01]\n",
+      "      nit: 17\n",
+      "      jac: [-1.587e-03  1.123e-04 ... -4.022e-04  3.425e-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 af60c1c26..ca695411a 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": "2023-10-26T15:40:58.912815Z",
-     "iopub.status.busy": "2023-10-26T15:40:58.912459Z",
-     "iopub.status.idle": "2023-10-26T15:40:59.499610Z",
-     "shell.execute_reply": "2023-10-26T15:40:59.498969Z"
+     "iopub.execute_input": "2023-10-26T21:54:39.107848Z",
+     "iopub.status.busy": "2023-10-26T21:54:39.107649Z",
+     "iopub.status.idle": "2023-10-26T21:54:39.723354Z",
+     "shell.execute_reply": "2023-10-26T21:54:39.722809Z"
     }
    },
    "outputs": [
@@ -90,10 +90,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:59.502796Z",
-     "iopub.status.busy": "2023-10-26T15:40:59.502470Z",
-     "iopub.status.idle": "2023-10-26T15:40:59.525012Z",
-     "shell.execute_reply": "2023-10-26T15:40:59.524526Z"
+     "iopub.execute_input": "2023-10-26T21:54:39.727688Z",
+     "iopub.status.busy": "2023-10-26T21:54:39.726626Z",
+     "iopub.status.idle": "2023-10-26T21:54:39.749064Z",
+     "shell.execute_reply": "2023-10-26T21:54:39.748609Z"
     }
    },
    "outputs": [
@@ -101,7 +101,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -75.6836617444762\n"
+      "Energy at initialialization: -75.68366174447623\n"
      ]
     }
    ],
@@ -135,10 +135,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:59.528033Z",
-     "iopub.status.busy": "2023-10-26T15:40:59.527659Z",
-     "iopub.status.idle": "2023-10-26T15:41:01.268404Z",
-     "shell.execute_reply": "2023-10-26T15:41:01.267819Z"
+     "iopub.execute_input": "2023-10-26T21:54:39.752628Z",
+     "iopub.status.busy": "2023-10-26T21:54:39.751733Z",
+     "iopub.status.idle": "2023-10-26T21:54:41.490438Z",
+     "shell.execute_reply": "2023-10-26T21:54:41.489666Z"
     }
    },
    "outputs": [
@@ -150,8 +150,8 @@
       " message: Maximum number of function evaluations has been exceeded.\n",
       " success: False\n",
       "  status: 2\n",
-      "     fun: -75.69434198374157\n",
-      "       x: [ 1.352e+00  8.664e-02 -2.940e-03  1.104e+00 -1.913e-01]\n",
+      "     fun: -75.69430210107313\n",
+      "       x: [ 1.344e+00  8.447e-02 -1.883e-03  1.105e+00 -1.881e-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 42ade8376..00beecc14 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": "2023-10-26T15:41:02.558992Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.558609Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.841652Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.841145Z"
+     "iopub.execute_input": "2023-10-26T21:54:42.975850Z",
+     "iopub.status.busy": "2023-10-26T21:54:42.975373Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.267057Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.266479Z"
     }
    },
    "outputs": [
@@ -40,9 +40,9 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 1+1j,\n",
+       "    (cre_a(0), des_a(3)): 0.5,\n",
        "    (cre_a(3), des_a(0)): -0.25,\n",
-       "    (cre_a(0), des_a(3)): 0.5\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 1+1j\n",
        "})"
       ]
      },
@@ -76,17 +76,17 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.844287Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.843875Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.848987Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.848434Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.270889Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.269857Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.275030Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.274490Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j})'"
+       "'FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})'"
       ]
      },
      "execution_count": 2,
@@ -110,10 +110,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.851513Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.851326Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.857252Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.856741Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.277738Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.277491Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.283561Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.283042Z"
     }
    },
    "outputs": [
@@ -121,17 +121,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
+       "    (des_a(3), des_b(3)): 0.0625,\n",
+       "    (cre_b(2)): 0-0.25j,\n",
        "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\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), des_a(3), des_b(3)): 0.0625,\n",
        "    (cre_a(0), des_a(3)): 1,\n",
+       "    (cre_a(3), des_a(0)): -0.5,\n",
        "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
-       "    (des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
-       "    (cre_a(3), des_a(0)): -0.5\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": "2023-10-26T15:41:02.860132Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.859935Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.865132Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.864630Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.286372Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.286147Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.290042Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.289581Z"
     }
    },
    "outputs": [
@@ -180,17 +180,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
+       "    (des_a(3), des_b(3)): 0-1.25j,\n",
+       "    (cre_b(2)): -5,\n",
        "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
        "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_b(2)): -5,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
        "    (cre_a(0), des_a(3)): 0-6j,\n",
+       "    (cre_a(3), des_a(0)): 0+3j,\n",
        "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
-       "    (des_a(3), des_b(3)): 0-1.25j,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
-       "    (cre_a(3), des_a(0)): 0+3j\n",
+       "    (cre_a(0), des_a(3), cre_b(2)): 2\n",
        "})"
       ]
      },
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.867808Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.867617Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.872638Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.872124Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.292578Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.292031Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.295877Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.295425Z"
     }
    },
    "outputs": [
@@ -230,16 +230,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\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), cre_a(0), des_a(3)): 2,\n",
        "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
-       "    (cre_b(2)): -5,\n",
-       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (des_b(3), des_a(3)): 0+1.25j,\n",
+       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
-       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j\n",
+       "    (cre_b(2)): -5,\n",
+       "    (cre_a(3), des_a(0)): 0+3j,\n",
+       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,\n",
+       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
+       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
+       "    (cre_a(0), des_a(3)): 0-6j\n",
        "})"
       ]
      },
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.875652Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.875246Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.880572Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.880030Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.298353Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.297816Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.301192Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.300757Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.883281Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.883085Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.888675Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.888143Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.303693Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.303108Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.307884Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.307438Z"
     }
    },
    "outputs": [
@@ -340,10 +340,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.891351Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.891153Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.898806Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.898298Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.310238Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.309883Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.315265Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.314809Z"
     }
    },
    "outputs": [
@@ -352,7 +352,7 @@
       "text/plain": [
        "array([ 0.        +0.j        ,  0.        +0.j        ,\n",
        "        0.        +0.j        ,  0.        +0.j        ,\n",
-       "       -0.11189423+0.03187888j,  0.        +0.j        ,\n",
+       "       -0.15345942+0.16296314j,  0.        +0.j        ,\n",
        "        0.        +0.j        ,  0.        +0.j        ,\n",
        "        0.        +0.j        ])"
       ]
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.901540Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.901345Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.912867Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.912344Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.317609Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.317233Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.328565Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.328121Z"
     }
    },
    "outputs": [
diff --git a/.doctrees/tutorials/04-lucj.doctree b/.doctrees/tutorials/04-lucj.doctree
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GIT binary patch
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diff --git a/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html b/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
index 5ee208715..cfc20fd2c 100644
--- a/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
+++ b/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
@@ -57,7 +57,7 @@ <h1>Source code for ffsim.hamiltonians.double_factorized_hamiltonian</h1><div cl
 
 <div class="viewcode-block" id="DoubleFactorizedHamiltonian">
 <a class="viewcode-back" href="../../../api/ffsim.html#ffsim.DoubleFactorizedHamiltonian">[docs]</a>
-<span class="nd">@dataclasses</span><span class="o">.</span><span class="n">dataclass</span>
+<span class="nd">@dataclasses</span><span class="o">.</span><span class="n">dataclass</span><span class="p">(</span><span class="n">frozen</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="k">class</span> <span class="nc">DoubleFactorizedHamiltonian</span><span class="p">:</span>
 <span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;A Hamiltonian in the double-factorized form of the low rank decomposition.</span>
 
diff --git a/_modules/ffsim/hamiltonians/molecular_hamiltonian.html b/_modules/ffsim/hamiltonians/molecular_hamiltonian.html
index c361f9d5a..6ab03218f 100644
--- a/_modules/ffsim/hamiltonians/molecular_hamiltonian.html
+++ b/_modules/ffsim/hamiltonians/molecular_hamiltonian.html
@@ -61,7 +61,7 @@ <h1>Source code for ffsim.hamiltonians.molecular_hamiltonian</h1><div class="hig
 
 <div class="viewcode-block" id="MolecularHamiltonian">
 <a class="viewcode-back" href="../../../api/ffsim.html#ffsim.MolecularHamiltonian">[docs]</a>
-<span class="nd">@dataclasses</span><span class="o">.</span><span class="n">dataclass</span>
+<span class="nd">@dataclasses</span><span class="o">.</span><span class="n">dataclass</span><span class="p">(</span><span class="n">frozen</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="k">class</span> <span class="nc">MolecularHamiltonian</span><span class="p">:</span>
 <span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;A molecular Hamiltonian.</span>
 
diff --git a/_modules/ffsim/molecular_data.html b/_modules/ffsim/molecular_data.html
index f1add6eb4..a124b1ec4 100644
--- a/_modules/ffsim/molecular_data.html
+++ b/_modules/ffsim/molecular_data.html
@@ -93,7 +93,7 @@ <h1>Source code for ffsim.molecular_data</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="MolecularData">
 <a class="viewcode-back" href="../../api/ffsim.html#ffsim.MolecularData">[docs]</a>
-<span class="nd">@dataclasses</span><span class="o">.</span><span class="n">dataclass</span>
+<span class="nd">@dataclasses</span><span class="o">.</span><span class="n">dataclass</span><span class="p">(</span><span class="n">frozen</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="k">class</span> <span class="nc">MolecularData</span><span class="p">:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;Class for storing molecular data.</span>
 
@@ -115,27 +115,6 @@ <h1>Source code for ffsim.molecular_data</h1><div class="highlight"><pre>
     <span class="n">dipole_integrals</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
     <span class="n">orbital_symmetries</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
 
-    <span class="c1"># TODO remove this after Python 3.10 dataclasses allows keyword-only arguments</span>
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
-        <span class="bp">self</span><span class="p">,</span>
-        <span class="o">*</span><span class="p">,</span>
-        <span class="n">norb</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
-        <span class="n">nelec</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
-        <span class="n">core_energy</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
-        <span class="n">one_body_tensor</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">two_body_tensor</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">dipole_integrals</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-        <span class="n">orbital_symmetries</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-    <span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">norb</span> <span class="o">=</span> <span class="n">norb</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">nelec</span> <span class="o">=</span> <span class="n">nelec</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">core_energy</span> <span class="o">=</span> <span class="n">core_energy</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">one_body_tensor</span> <span class="o">=</span> <span class="n">one_body_tensor</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">two_body_tensor</span> <span class="o">=</span> <span class="n">two_body_tensor</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">dipole_integrals</span> <span class="o">=</span> <span class="n">dipole_integrals</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">orbital_symmetries</span> <span class="o">=</span> <span class="n">orbital_symmetries</span>
-        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
-
     <span class="nd">@property</span>
     <span class="k">def</span> <span class="nf">hamiltonian</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">MolecularHamiltonian</span><span class="p">:</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;The Hamiltonian defined by the molecular data.&quot;&quot;&quot;</span>
diff --git a/_modules/ffsim/variational/hopgate.html b/_modules/ffsim/variational/hopgate.html
index 089bc83b3..afae037b3 100644
--- a/_modules/ffsim/variational/hopgate.html
+++ b/_modules/ffsim/variational/hopgate.html
@@ -59,7 +59,7 @@ <h1>Source code for ffsim.variational.hopgate</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="HopGateAnsatzOperator">
 <a class="viewcode-back" href="../../../api/ffsim.html#ffsim.HopGateAnsatzOperator">[docs]</a>
-<span class="nd">@dataclass</span>
+<span class="nd">@dataclass</span><span class="p">(</span><span class="n">frozen</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="k">class</span> <span class="nc">HopGateAnsatzOperator</span><span class="p">:</span>
 <span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;A hop gate ansatz operator.&quot;&quot;&quot;</span>
 
diff --git a/_modules/ffsim/variational/ucj.html b/_modules/ffsim/variational/ucj.html
index 5fa9d820e..fe96be51a 100644
--- a/_modules/ffsim/variational/ucj.html
+++ b/_modules/ffsim/variational/ucj.html
@@ -63,7 +63,7 @@ <h1>Source code for ffsim.variational.ucj</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="UCJOperator">
 <a class="viewcode-back" href="../../../api/ffsim.html#ffsim.UCJOperator">[docs]</a>
-<span class="nd">@dataclass</span>
+<span class="nd">@dataclass</span><span class="p">(</span><span class="n">frozen</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="k">class</span> <span class="nc">UCJOperator</span><span class="p">:</span>
 <span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;A unitary cluster Jastrow operator.</span>
 
diff --git a/api/ffsim.html b/api/ffsim.html
index 39c388057..cb95c32d4 100644
--- a/api/ffsim.html
+++ b/api/ffsim.html
@@ -318,9 +318,9 @@
 </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(0), des_a(3)): 0.5,
-    (cre_a(3), des_a(0)): -0.25
+    (cre_a(3), des_a(0)): -0.25,
+    (cre_b(1), des_b(5), cre_a(4)): 1+1j
 })
 </pre></div>
 </div>
@@ -356,9 +356,9 @@
 </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(0), des_a(3)): 0.5,
     (cre_b(1), des_b(5), cre_a(4)): 1+1j,
+    (cre_b(2)): 0+1j,
     (cre_a(3), des_a(0)): -0.25,
     (des_a(3), des_b(3)): -0.25
 })
@@ -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_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(0), des_a(3), des_a(3), des_b(3)): -0.125,
+    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
-    (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), des_a(3), des_b(3)): -0.25-0.25j,
+    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
+    (cre_a(3), des_a(0), cre_b(2)): 0-0.25j
 })
 </pre></div>
 </div>
@@ -468,7 +468,7 @@
 
 <dl class="py class">
 <dt class="sig sig-object py" id="ffsim.MolecularData">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">ffsim.</span></span><span class="sig-name descname"><span class="pre">MolecularData</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</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="n"><span class="pre">core_energy</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">one_body_tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">two_body_tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dipole_integrals</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">orbital_symmetries</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ffsim/molecular_data.html#MolecularData"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.MolecularData" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">ffsim.</span></span><span class="sig-name descname"><span class="pre">MolecularData</span></span><span class="sig-paren">(</span><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="n"><span class="pre">core_energy</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">one_body_tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">two_body_tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dipole_integrals</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">orbital_symmetries</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/ffsim/molecular_data.html#MolecularData"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#ffsim.MolecularData" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
 <p>Class for storing molecular data.</p>
 <dl class="py attribute">
diff --git a/searchindex.js b/searchindex.js
index f5ddb59be..d6750bcbf 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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"diag_coulomb_mats_alpha_alpha (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.diag_coulomb_mats_alpha_beta"]], "dim() (in module ffsim)": [[0, "ffsim.dim"]], "dims() (in module ffsim)": [[0, "ffsim.dims"]], "dipole_integrals (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.dipole_integrals"]], "expectation_one_body_power() (in module ffsim)": [[0, "ffsim.expectation_one_body_power"]], "expectation_one_body_product() (in module ffsim)": [[0, "ffsim.expectation_one_body_product"]], "ffsim": [[0, "module-ffsim"]], "final_orbital_rotation (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.final_orbital_rotation"]], "from_hartree_fock() (ffsim.moleculardata static method)": [[0, "ffsim.MolecularData.from_hartree_fock"]], "from_molecular_hamiltonian() (ffsim.doublefactorizedhamiltonian static method)": [[0, "ffsim.DoubleFactorizedHamiltonian.from_molecular_hamiltonian"]], "from_parameters() (ffsim.ucjoperator static method)": [[0, "ffsim.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.ucjoperator static method)": [[0, "ffsim.UCJOperator.from_t_amplitudes"]], "hamiltonian (ffsim.moleculardata property)": [[0, "ffsim.MolecularData.hamiltonian"]], "hartree_fock_state() (in module ffsim)": [[0, "ffsim.hartree_fock_state"]], "indices_to_strings() (in module ffsim)": [[0, "ffsim.indices_to_strings"]], "linear_operator() (in module ffsim)": [[0, "ffsim.linear_operator"]], "many_body_order() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.many_body_order"]], "module": [[0, "module-ffsim"], [1, "module-ffsim.contract"], [2, "module-ffsim.linalg"], [3, "module-ffsim.random"], [4, "module-ffsim.testing"]], "multireference_state() (in module ffsim)": [[0, "ffsim.multireference_state"]], "n_reps (ffsim.ucjoperator property)": [[0, "ffsim.UCJOperator.n_reps"]], "nelec (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.nelec"]], "norb (ffsim.doublefactorizedhamiltonian property)": [[0, "ffsim.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.norb"]], "norb (ffsim.molecularhamiltonian property)": [[0, "ffsim.MolecularHamiltonian.norb"]], "norb (ffsim.ucjoperator property)": [[0, "ffsim.UCJOperator.norb"]], "normal_ordered() (ffsim.fermionoperator method)": [[0, "ffsim.FermionOperator.normal_ordered"]], "one_body_tensor (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.one_body_tensor"]], "one_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.one_body_tensor"]], "one_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.one_body_tensor"]], "one_hot() (in module ffsim)": [[0, "ffsim.one_hot"]], "orb (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.orb"]], "orbital_rotations (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.orbital_rotations"]], "orbital_rotations (ffsim.ucjoperator attribute)": [[0, "ffsim.UCJOperator.orbital_rotations"]], "orbital_symmetries (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.orbital_symmetries"]], "simulate_qdrift_double_factorized() (in module ffsim)": [[0, "ffsim.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim)": [[0, "ffsim.simulate_trotter_double_factorized"]], "slater_determinant() (in module ffsim)": [[0, "ffsim.slater_determinant"]], "slater_determinant_one_rdm() (in module ffsim)": [[0, "ffsim.slater_determinant_one_rdm"]], "spin (ffsim.fermionaction attribute)": [[0, "ffsim.FermionAction.spin"]], "to_number_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_number_representation"]], "to_parameters() (ffsim.ucjoperator method)": [[0, "ffsim.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.ucjoperator method)": [[0, "ffsim.UCJOperator.to_t_amplitudes"]], "to_z_representation() (ffsim.doublefactorizedhamiltonian method)": [[0, "ffsim.DoubleFactorizedHamiltonian.to_z_representation"]], "trace() (in module ffsim)": [[0, "ffsim.trace"]], "two_body_tensor (ffsim.moleculardata attribute)": [[0, "ffsim.MolecularData.two_body_tensor"]], "two_body_tensor (ffsim.molecularhamiltonian attribute)": [[0, "ffsim.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.doublefactorizedhamiltonian attribute)": [[0, "ffsim.DoubleFactorizedHamiltonian.z_representation"]], "contract_diag_coulomb() (in module ffsim.contract)": [[1, "ffsim.contract.contract_diag_coulomb"]], "contract_num_op_sum() (in module ffsim.contract)": [[1, "ffsim.contract.contract_num_op_sum"]], "diag_coulomb_linop() (in module ffsim.contract)": [[1, "ffsim.contract.diag_coulomb_linop"]], "ffsim.contract": [[1, "module-ffsim.contract"]], "num_op_sum_linop() (in module ffsim.contract)": [[1, "ffsim.contract.num_op_sum_linop"]], "one_body_linop() (in module ffsim.contract)": [[1, "ffsim.contract.one_body_linop"]], "apply_matrix_to_slices() (in module ffsim.linalg)": [[2, "ffsim.linalg.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg)": [[2, "ffsim.linalg.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg)": [[2, "ffsim.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[2, "module-ffsim.linalg"]], "givens_decomposition() (in module ffsim.linalg)": [[2, "ffsim.linalg.givens_decomposition"]], "is_antihermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg)": [[2, "ffsim.linalg.is_unitary"]], "lup() (in module ffsim.linalg)": [[2, "ffsim.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg)": [[2, "ffsim.linalg.modified_cholesky"]], "reduced_matrix() (in module ffsim.linalg)": [[2, "ffsim.linalg.reduced_matrix"]], "ffsim.random": [[3, "module-ffsim.random"]], "random_antihermitian() (in module ffsim.random)": [[3, "ffsim.random.random_antihermitian"]], "random_hermitian() (in module ffsim.random)": [[3, "ffsim.random.random_hermitian"]], "random_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_orthogonal"]], "random_real_symmetric_matrix() (in module ffsim.random)": [[3, "ffsim.random.random_real_symmetric_matrix"]], "random_special_orthogonal() (in module ffsim.random)": [[3, "ffsim.random.random_special_orthogonal"]], "random_statevector() (in module ffsim.random)": [[3, "ffsim.random.random_statevector"]], "random_t2_amplitudes() (in module ffsim.random)": [[3, "ffsim.random.random_t2_amplitudes"]], "random_two_body_tensor_real() (in module ffsim.random)": [[3, "ffsim.random.random_two_body_tensor_real"]], "random_unitary() (in module ffsim.random)": [[3, "ffsim.random.random_unitary"]], "ffsim.testing": [[4, "module-ffsim.testing"]], "random_nelec() (in module ffsim.testing)": [[4, "ffsim.testing.random_nelec"]], "random_occupied_orbitals() (in module ffsim.testing)": [[4, "ffsim.testing.random_occupied_orbitals"]]}})
\ No newline at end of file
+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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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 738bf9af0..542a28d4f 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:42.829408Z",
-     "iopub.status.busy": "2023-10-26T15:40:42.829034Z",
-     "iopub.status.idle": "2023-10-26T15:40:43.115107Z",
-     "shell.execute_reply": "2023-10-26T15:40:43.114553Z"
+     "iopub.execute_input": "2023-10-26T21:54:24.626048Z",
+     "iopub.status.busy": "2023-10-26T21:54:24.625502Z",
+     "iopub.status.idle": "2023-10-26T21:54:24.916794Z",
+     "shell.execute_reply": "2023-10-26T21:54:24.916239Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:43.119123Z",
-     "iopub.status.busy": "2023-10-26T15:40:43.118055Z",
-     "iopub.status.idle": "2023-10-26T15:40:43.123141Z",
-     "shell.execute_reply": "2023-10-26T15:40:43.122678Z"
+     "iopub.execute_input": "2023-10-26T21:54:24.921005Z",
+     "iopub.status.busy": "2023-10-26T21:54:24.919903Z",
+     "iopub.status.idle": "2023-10-26T21:54:24.925012Z",
+     "shell.execute_reply": "2023-10-26T21:54:24.924548Z"
     }
    },
    "outputs": [],
@@ -93,10 +93,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:43.126861Z",
-     "iopub.status.busy": "2023-10-26T15:40:43.125985Z",
-     "iopub.status.idle": "2023-10-26T15:40:43.129804Z",
-     "shell.execute_reply": "2023-10-26T15:40:43.129341Z"
+     "iopub.execute_input": "2023-10-26T21:54:24.928816Z",
+     "iopub.status.busy": "2023-10-26T21:54:24.927921Z",
+     "iopub.status.idle": "2023-10-26T21:54:24.931868Z",
+     "shell.execute_reply": "2023-10-26T21:54:24.931405Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index d540c77ff..e59b1f447 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": "2023-10-26T15:40:44.747012Z",
-     "iopub.status.busy": "2023-10-26T15:40:44.746660Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.026053Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.025508Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.554827Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.554540Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.838397Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.837851Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:45.030774Z",
-     "iopub.status.busy": "2023-10-26T15:40:45.029736Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.055723Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.055244Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.843035Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.841994Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.867230Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.866712Z"
     }
    },
    "outputs": [],
@@ -158,10 +158,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:45.059575Z",
-     "iopub.status.busy": "2023-10-26T15:40:45.058663Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.069563Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.069067Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.871420Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.870428Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.881346Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.880817Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:45.073324Z",
-     "iopub.status.busy": "2023-10-26T15:40:45.072401Z",
-     "iopub.status.idle": "2023-10-26T15:40:45.077945Z",
-     "shell.execute_reply": "2023-10-26T15:40:45.077473Z"
+     "iopub.execute_input": "2023-10-26T21:54:26.885340Z",
+     "iopub.status.busy": "2023-10-26T21:54:26.884395Z",
+     "iopub.status.idle": "2023-10-26T21:54:26.890064Z",
+     "shell.execute_reply": "2023-10-26T21:54:26.889582Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index 4191a3e16..aff25e788 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": "2023-10-26T15:40:46.698076Z",
-     "iopub.status.busy": "2023-10-26T15:40:46.697722Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.057254Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.056722Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.517494Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.517144Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.859683Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.859174Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.061559Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.060504Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.068182Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.067706Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.863775Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.862781Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.870588Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.870125Z"
     }
    },
    "outputs": [
@@ -226,10 +226,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.071132Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.070637Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.076297Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.075779Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.874583Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.873677Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.879229Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.878771Z"
     }
    },
    "outputs": [],
@@ -284,10 +284,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.078619Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.078279Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.081964Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.081501Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.882477Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.882071Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.885968Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.885523Z"
     }
    },
    "outputs": [],
@@ -324,10 +324,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.155592Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.154994Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.159928Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.159315Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.952107Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.951382Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.957168Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.956674Z"
     }
    },
    "outputs": [
@@ -363,10 +363,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.162336Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.162145Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.172569Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.171964Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.959983Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.959396Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.968750Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.968270Z"
     }
    },
    "outputs": [
@@ -405,10 +405,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.175110Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.174657Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.183808Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.183279Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.971329Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.970763Z",
+     "iopub.status.idle": "2023-10-26T21:54:28.979373Z",
+     "shell.execute_reply": "2023-10-26T21:54:28.978932Z"
     }
    },
    "outputs": [
@@ -446,10 +446,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.186320Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.186131Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.219836Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.219385Z"
+     "iopub.execute_input": "2023-10-26T21:54:28.981881Z",
+     "iopub.status.busy": "2023-10-26T21:54:28.981327Z",
+     "iopub.status.idle": "2023-10-26T21:54:29.016188Z",
+     "shell.execute_reply": "2023-10-26T21:54:29.015742Z"
     }
    },
    "outputs": [
@@ -489,10 +489,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.222288Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.222014Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.243532Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.243081Z"
+     "iopub.execute_input": "2023-10-26T21:54:29.019498Z",
+     "iopub.status.busy": "2023-10-26T21:54:29.018429Z",
+     "iopub.status.idle": "2023-10-26T21:54:29.038774Z",
+     "shell.execute_reply": "2023-10-26T21:54:29.038333Z"
     }
    },
    "outputs": [
@@ -531,10 +531,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:47.246063Z",
-     "iopub.status.busy": "2023-10-26T15:40:47.245776Z",
-     "iopub.status.idle": "2023-10-26T15:40:47.255612Z",
-     "shell.execute_reply": "2023-10-26T15:40:47.255186Z"
+     "iopub.execute_input": "2023-10-26T21:54:29.042307Z",
+     "iopub.status.busy": "2023-10-26T21:54:29.041422Z",
+     "iopub.status.idle": "2023-10-26T21:54:29.052280Z",
+     "shell.execute_reply": "2023-10-26T21:54:29.051815Z"
     }
    },
    "outputs": [
diff --git a/tutorials/04-lucj.html b/tutorials/04-lucj.html
index 2ff465c19..5fdff9766 100644
--- a/tutorials/04-lucj.html
+++ b/tutorials/04-lucj.html
@@ -96,7 +96,7 @@ <h1>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 converged SCF energy = -77.4456267643962
-CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000
+CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000
 </pre></div></div>
 </div>
 <section id="The-unitary-cluster-Jastrow-(UCJ)-ansatz">
@@ -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) = -77.49387212754473  E_corr = -0.04824536314851454
-Energy at initialialization: -77.46975600021693
+E(CCSD) = -77.49387212754476  E_corr = -0.0482453631485149
+Energy at initialialization: -77.46975600021689
 </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: -77.51588951609632
-        x: [-1.450e-01  1.879e-01 ... -6.233e-01 -5.993e-02]
+      fun: -77.51554916701404
+        x: [-1.569e-01  1.944e-01 ... -6.056e-01  1.983e-01]
       nit: 9
-      jac: [ 4.106e-03 -8.635e-03 ... -2.993e-03 -1.670e-03]
-     nfev: 1168
-     njev: 16
+      jac: [-8.171e-03 -3.966e-03 ... -9.706e-03  1.509e-03]
+     nfev: 1022
+     njev: 14
  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: -77.46007276424072
-        x: [-3.689e-01  8.946e-02 ... -5.942e-01  1.631e-01]
-      nit: 16
-      jac: [-1.563e-04  3.979e-04 ...  4.633e-04 -1.531e-03]
+      fun: -77.46262558981611
+        x: [-3.094e-01  6.744e-02 ... -4.668e-01  2.137e-01]
+      nit: 17
+      jac: [-1.587e-03  1.123e-04 ... -4.022e-04  3.425e-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 09ba4aa87..a11f8d251 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:49.173908Z",
-     "iopub.status.busy": "2023-10-26T15:40:49.173566Z",
-     "iopub.status.idle": "2023-10-26T15:40:49.721773Z",
-     "shell.execute_reply": "2023-10-26T15:40:49.721209Z"
+     "iopub.execute_input": "2023-10-26T21:54:30.789283Z",
+     "iopub.status.busy": "2023-10-26T21:54:30.788907Z",
+     "iopub.status.idle": "2023-10-26T21:54:31.461048Z",
+     "shell.execute_reply": "2023-10-26T21:54:31.460505Z"
     }
    },
    "outputs": [
@@ -32,7 +32,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553863  S^2 = 0.0000000\n"
+      "CASCI E = -77.6290254326717  E(CI) = -3.57322412553862  S^2 = 0.0000000\n"
      ]
     }
    ],
@@ -110,10 +110,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:49.724841Z",
-     "iopub.status.busy": "2023-10-26T15:40:49.724494Z",
-     "iopub.status.idle": "2023-10-26T15:40:50.692531Z",
-     "shell.execute_reply": "2023-10-26T15:40:50.691938Z"
+     "iopub.execute_input": "2023-10-26T21:54:31.465293Z",
+     "iopub.status.busy": "2023-10-26T21:54:31.464287Z",
+     "iopub.status.idle": "2023-10-26T21:54:31.898474Z",
+     "shell.execute_reply": "2023-10-26T21:54:31.897988Z"
     }
    },
    "outputs": [
@@ -121,14 +121,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -77.49387212754473  E_corr = -0.04824536314851454\n"
+      "E(CCSD) = -77.49387212754476  E_corr = -0.0482453631485149\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -77.46975600021693\n"
+      "Energy at initialialization: -77.46975600021689\n"
      ]
     }
    ],
@@ -173,10 +173,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:50.695286Z",
-     "iopub.status.busy": "2023-10-26T15:40:50.694948Z",
-     "iopub.status.idle": "2023-10-26T15:40:54.086057Z",
-     "shell.execute_reply": "2023-10-26T15:40:54.085582Z"
+     "iopub.execute_input": "2023-10-26T21:54:31.903123Z",
+     "iopub.status.busy": "2023-10-26T21:54:31.901767Z",
+     "iopub.status.idle": "2023-10-26T21:54:34.814416Z",
+     "shell.execute_reply": "2023-10-26T21:54:34.813892Z"
     }
    },
    "outputs": [
@@ -188,12 +188,12 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.51588951609632\n",
-      "        x: [-1.450e-01  1.879e-01 ... -6.233e-01 -5.993e-02]\n",
+      "      fun: -77.51554916701404\n",
+      "        x: [-1.569e-01  1.944e-01 ... -6.056e-01  1.983e-01]\n",
       "      nit: 9\n",
-      "      jac: [ 4.106e-03 -8.635e-03 ... -2.993e-03 -1.670e-03]\n",
-      "     nfev: 1168\n",
-      "     njev: 16\n",
+      "      jac: [-8.171e-03 -3.966e-03 ... -9.706e-03  1.509e-03]\n",
+      "     nfev: 1022\n",
+      "     njev: 14\n",
       " hess_inv: <72x72 LbfgsInvHessProduct with dtype=float64>\n"
      ]
     }
@@ -246,10 +246,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:54.088721Z",
-     "iopub.status.busy": "2023-10-26T15:40:54.088365Z",
-     "iopub.status.idle": "2023-10-26T15:40:57.233669Z",
-     "shell.execute_reply": "2023-10-26T15:40:57.233141Z"
+     "iopub.execute_input": "2023-10-26T21:54:34.817935Z",
+     "iopub.status.busy": "2023-10-26T21:54:34.817539Z",
+     "iopub.status.idle": "2023-10-26T21:54:37.520155Z",
+     "shell.execute_reply": "2023-10-26T21:54:37.519545Z"
     }
    },
    "outputs": [
@@ -261,10 +261,10 @@
       "  message: STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT\n",
       "  success: False\n",
       "   status: 1\n",
-      "      fun: -77.46007276424072\n",
-      "        x: [-3.689e-01  8.946e-02 ... -5.942e-01  1.631e-01]\n",
-      "      nit: 16\n",
-      "      jac: [-1.563e-04  3.979e-04 ...  4.633e-04 -1.531e-03]\n",
+      "      fun: -77.46262558981611\n",
+      "        x: [-3.094e-01  6.744e-02 ... -4.668e-01  2.137e-01]\n",
+      "      nit: 17\n",
+      "      jac: [-1.587e-03  1.123e-04 ... -4.022e-04  3.425e-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 50a53a5d6..0efcb3747 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: -75.6836617444762
+Energy at initialialization: -75.68366174447623
 </pre></div></div>
 </div>
 <div class="nbinput docutils container">
@@ -178,8 +178,8 @@ <h1>Entanglement forging<a class="headerlink" href="#Entanglement-forging" title
  message: Maximum number of function evaluations has been exceeded.
  success: False
   status: 2
-     fun: -75.69434198374157
-       x: [ 1.352e+00  8.664e-02 -2.940e-03  1.104e+00 -1.913e-01]
+     fun: -75.69430210107313
+       x: [ 1.344e+00  8.447e-02 -1.883e-03  1.105e+00 -1.881e-01]
     nfev: 100
    maxcv: 0.0
 </pre></div></div>
diff --git a/tutorials/05-entanglement-forging.ipynb b/tutorials/05-entanglement-forging.ipynb
index af60c1c26..ca695411a 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": "2023-10-26T15:40:58.912815Z",
-     "iopub.status.busy": "2023-10-26T15:40:58.912459Z",
-     "iopub.status.idle": "2023-10-26T15:40:59.499610Z",
-     "shell.execute_reply": "2023-10-26T15:40:59.498969Z"
+     "iopub.execute_input": "2023-10-26T21:54:39.107848Z",
+     "iopub.status.busy": "2023-10-26T21:54:39.107649Z",
+     "iopub.status.idle": "2023-10-26T21:54:39.723354Z",
+     "shell.execute_reply": "2023-10-26T21:54:39.722809Z"
     }
    },
    "outputs": [
@@ -90,10 +90,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:59.502796Z",
-     "iopub.status.busy": "2023-10-26T15:40:59.502470Z",
-     "iopub.status.idle": "2023-10-26T15:40:59.525012Z",
-     "shell.execute_reply": "2023-10-26T15:40:59.524526Z"
+     "iopub.execute_input": "2023-10-26T21:54:39.727688Z",
+     "iopub.status.busy": "2023-10-26T21:54:39.726626Z",
+     "iopub.status.idle": "2023-10-26T21:54:39.749064Z",
+     "shell.execute_reply": "2023-10-26T21:54:39.748609Z"
     }
    },
    "outputs": [
@@ -101,7 +101,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -75.6836617444762\n"
+      "Energy at initialialization: -75.68366174447623\n"
      ]
     }
    ],
@@ -135,10 +135,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:40:59.528033Z",
-     "iopub.status.busy": "2023-10-26T15:40:59.527659Z",
-     "iopub.status.idle": "2023-10-26T15:41:01.268404Z",
-     "shell.execute_reply": "2023-10-26T15:41:01.267819Z"
+     "iopub.execute_input": "2023-10-26T21:54:39.752628Z",
+     "iopub.status.busy": "2023-10-26T21:54:39.751733Z",
+     "iopub.status.idle": "2023-10-26T21:54:41.490438Z",
+     "shell.execute_reply": "2023-10-26T21:54:41.489666Z"
     }
    },
    "outputs": [
@@ -150,8 +150,8 @@
       " message: Maximum number of function evaluations has been exceeded.\n",
       " success: False\n",
       "  status: 2\n",
-      "     fun: -75.69434198374157\n",
-      "       x: [ 1.352e+00  8.664e-02 -2.940e-03  1.104e+00 -1.913e-01]\n",
+      "     fun: -75.69430210107313\n",
+      "       x: [ 1.344e+00  8.447e-02 -1.883e-03  1.105e+00 -1.881e-01]\n",
       "    nfev: 100\n",
       "   maxcv: 0.0\n"
      ]
diff --git a/tutorials/06-fermion-operator.html b/tutorials/06-fermion-operator.html
index c5e5a64f0..c0d0a546b 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_b(1), des_b(5), cre_a(4)): 1+1j,
+    (cre_a(0), des_a(3)): 0.5,
     (cre_a(3), des_a(0)): -0.25,
-    (cre_a(0), des_a(3)): 0.5
+    (cre_b(1), des_b(5), cre_a(4)): 1+1j
 })
 </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, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j})&#39;
+&#39;FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})&#39;
 </pre></div></div>
 </div>
 <p>FermionOperators support arithmetic operations. Note that when multiplying a FermionOperator by a scalar, the scalar must go on the left, i.e. <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">*</span> <span class="pre">op</span></code> and not <code class="docutils literal notranslate"><span class="pre">op</span> <span class="pre">*</span> <span class="pre">2</span></code>.</p>
@@ -127,17 +127,17 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
+    (des_a(3), des_b(3)): 0.0625,
+    (cre_b(2)): 0-0.25j,
     (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,
+    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
     (cre_a(3), des_a(0), cre_b(2)): 0-0.25j,
-    (cre_b(2)): 0-0.25j,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0.0625,
     (cre_a(0), des_a(3)): 1,
+    (cre_a(3), des_a(0)): -0.5,
     (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,
-    (des_a(3), des_b(3)): 0.0625,
-    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,
-    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,
     (cre_b(1), des_b(5), cre_a(4)): 2+2j,
-    (cre_a(3), des_a(0)): -0.5
+    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j
 })
 </pre></div></div>
 </div>
@@ -162,17 +162,17 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
+    (des_a(3), des_b(3)): 0-1.25j,
+    (cre_b(2)): -5,
     (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,
+    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
     (cre_a(3), des_a(0), cre_b(2)): -1,
-    (cre_b(2)): -5,
     (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,
     (cre_a(0), des_a(3)): 0-6j,
+    (cre_a(3), des_a(0)): 0+3j,
     (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,
-    (des_a(3), des_b(3)): 0-1.25j,
-    (cre_a(0), des_a(3), cre_b(2)): 2,
-    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,
     (cre_b(1), des_b(5), cre_a(4)): 12-12j,
-    (cre_a(3), des_a(0)): 0+3j
+    (cre_a(0), des_a(3), cre_b(2)): 2
 })
 </pre></div></div>
 </div>
@@ -193,16 +193,16 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="output_area docutils container">
 <div class="highlight"><pre>
 FermionOperator({
-    (cre_a(3), des_a(0)): 0+3j,
-    (cre_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), cre_a(0), des_a(3)): 2,
     (cre_b(2), cre_a(3), des_a(0)): -1,
-    (cre_b(2)): -5,
-    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
     (des_b(3), des_a(3)): 0+1.25j,
+    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,
     (cre_b(1), cre_a(4), des_b(5)): -12+12j,
-    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j
+    (cre_b(2)): -5,
+    (cre_a(3), des_a(0)): 0+3j,
+    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,
+    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,
+    (cre_b(2), cre_a(0), des_a(3)): 2,
+    (cre_a(0), des_a(3)): 0-6j
 })
 </pre></div></div>
 </div>
@@ -273,7 +273,7 @@ <h1>The FermionOperator class<a class="headerlink" href="#The-FermionOperator-cl
 <div class="highlight"><pre>
 array([ 0.        +0.j        ,  0.        +0.j        ,
         0.        +0.j        ,  0.        +0.j        ,
-       -0.11189423+0.03187888j,  0.        +0.j        ,
+       -0.15345942+0.16296314j,  0.        +0.j        ,
         0.        +0.j        ,  0.        +0.j        ,
         0.        +0.j        ])
 </pre></div></div>
diff --git a/tutorials/06-fermion-operator.ipynb b/tutorials/06-fermion-operator.ipynb
index 42ade8376..00beecc14 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": "2023-10-26T15:41:02.558992Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.558609Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.841652Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.841145Z"
+     "iopub.execute_input": "2023-10-26T21:54:42.975850Z",
+     "iopub.status.busy": "2023-10-26T21:54:42.975373Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.267057Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.266479Z"
     }
    },
    "outputs": [
@@ -40,9 +40,9 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_b(1), des_b(5), cre_a(4)): 1+1j,\n",
+       "    (cre_a(0), des_a(3)): 0.5,\n",
        "    (cre_a(3), des_a(0)): -0.25,\n",
-       "    (cre_a(0), des_a(3)): 0.5\n",
+       "    (cre_b(1), des_b(5), cre_a(4)): 1+1j\n",
        "})"
       ]
      },
@@ -76,17 +76,17 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.844287Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.843875Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.848987Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.848434Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.270889Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.269857Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.275030Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.274490Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'FermionOperator({((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, False, 0), (False, False, 3)): 0.5+0j})'"
+       "'FermionOperator({((True, False, 0), (False, False, 3)): 0.5+0j, ((True, False, 3), (False, False, 0)): -0.25+0j, ((True, True, 1), (False, True, 5), (True, False, 4)): 1+1j})'"
       ]
      },
      "execution_count": 2,
@@ -110,10 +110,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.851513Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.851326Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.857252Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.856741Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.277738Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.277491Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.283561Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.283042Z"
     }
    },
    "outputs": [
@@ -121,17 +121,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
+       "    (des_a(3), des_b(3)): 0.0625,\n",
+       "    (cre_b(2)): 0-0.25j,\n",
        "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -0.25-0.25j,\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\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), des_a(3), des_b(3)): 0.0625,\n",
        "    (cre_a(0), des_a(3)): 1,\n",
+       "    (cre_a(3), des_a(0)): -0.5,\n",
        "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): -1+1j,\n",
-       "    (des_a(3), des_b(3)): 0.0625,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 0+0.5j,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): -0.125,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 2+2j,\n",
-       "    (cre_a(3), des_a(0)): -0.5\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": "2023-10-26T15:41:02.860132Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.859935Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.865132Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.864630Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.286372Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.286147Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.290042Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.289581Z"
     }
    },
    "outputs": [
@@ -180,17 +180,17 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
+       "    (des_a(3), des_b(3)): 0-1.25j,\n",
+       "    (cre_b(2)): -5,\n",
        "    (cre_b(1), des_b(5), cre_a(4), des_a(3), des_b(3)): -1+1j,\n",
+       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
        "    (cre_a(3), des_a(0), cre_b(2)): -1,\n",
-       "    (cre_b(2)): -5,\n",
        "    (cre_a(3), des_a(0), des_a(3), des_b(3)): 0-0.25j,\n",
        "    (cre_a(0), des_a(3)): 0-6j,\n",
+       "    (cre_a(3), des_a(0)): 0+3j,\n",
        "    (cre_b(1), des_b(5), cre_a(4), cre_b(2)): 4+4j,\n",
-       "    (des_a(3), des_b(3)): 0-1.25j,\n",
-       "    (cre_a(0), des_a(3), cre_b(2)): 2,\n",
-       "    (cre_a(0), des_a(3), des_a(3), des_b(3)): 0+0.5j,\n",
        "    (cre_b(1), des_b(5), cre_a(4)): 12-12j,\n",
-       "    (cre_a(3), des_a(0)): 0+3j\n",
+       "    (cre_a(0), des_a(3), cre_b(2)): 2\n",
        "})"
       ]
      },
@@ -219,10 +219,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.867808Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.867617Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.872638Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.872124Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.292578Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.292031Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.295877Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.295425Z"
     }
    },
    "outputs": [
@@ -230,16 +230,16 @@
      "data": {
       "text/plain": [
        "FermionOperator({\n",
-       "    (cre_a(3), des_a(0)): 0+3j,\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), cre_a(0), des_a(3)): 2,\n",
        "    (cre_b(2), cre_a(3), des_a(0)): -1,\n",
-       "    (cre_b(2)): -5,\n",
-       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (des_b(3), des_a(3)): 0+1.25j,\n",
+       "    (cre_a(3), des_b(3), des_a(3), des_a(0)): 0+0.25j,\n",
        "    (cre_b(1), cre_a(4), des_b(5)): -12+12j,\n",
-       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j\n",
+       "    (cre_b(2)): -5,\n",
+       "    (cre_a(3), des_a(0)): 0+3j,\n",
+       "    (cre_b(2), cre_b(1), cre_a(4), des_b(5)): 4+4j,\n",
+       "    (cre_b(1), cre_a(4), des_b(5), des_b(3), des_a(3)): -1+1j,\n",
+       "    (cre_b(2), cre_a(0), des_a(3)): 2,\n",
+       "    (cre_a(0), des_a(3)): 0-6j\n",
        "})"
       ]
      },
@@ -264,10 +264,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.875652Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.875246Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.880572Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.880030Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.298353Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.297816Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.301192Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.300757Z"
     }
    },
    "outputs": [
@@ -297,10 +297,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.883281Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.883085Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.888675Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.888143Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.303693Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.303108Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.307884Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.307438Z"
     }
    },
    "outputs": [
@@ -340,10 +340,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.891351Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.891153Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.898806Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.898298Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.310238Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.309883Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.315265Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.314809Z"
     }
    },
    "outputs": [
@@ -352,7 +352,7 @@
       "text/plain": [
        "array([ 0.        +0.j        ,  0.        +0.j        ,\n",
        "        0.        +0.j        ,  0.        +0.j        ,\n",
-       "       -0.11189423+0.03187888j,  0.        +0.j        ,\n",
+       "       -0.15345942+0.16296314j,  0.        +0.j        ,\n",
        "        0.        +0.j        ,  0.        +0.j        ,\n",
        "        0.        +0.j        ])"
       ]
@@ -379,10 +379,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-10-26T15:41:02.901540Z",
-     "iopub.status.busy": "2023-10-26T15:41:02.901345Z",
-     "iopub.status.idle": "2023-10-26T15:41:02.912867Z",
-     "shell.execute_reply": "2023-10-26T15:41:02.912344Z"
+     "iopub.execute_input": "2023-10-26T21:54:43.317609Z",
+     "iopub.status.busy": "2023-10-26T21:54:43.317233Z",
+     "iopub.status.idle": "2023-10-26T21:54:43.328565Z",
+     "shell.execute_reply": "2023-10-26T21:54:43.328121Z"
     }
    },
    "outputs": [