diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
index 5e63c0f2f..6e640b12d 100644
Binary files a/.doctrees/environment.pickle and b/.doctrees/environment.pickle differ
diff --git a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
index ad7d9f2a8..6029431d7 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": "2023-09-07T15:26:40.890186Z",
-     "iopub.status.busy": "2023-09-07T15:26:40.889998Z",
-     "iopub.status.idle": "2023-09-07T15:26:41.155566Z",
-     "shell.execute_reply": "2023-09-07T15:26:41.155021Z"
+     "iopub.execute_input": "2023-09-18T02:05:03.658805Z",
+     "iopub.status.busy": "2023-09-18T02:05:03.658381Z",
+     "iopub.status.idle": "2023-09-18T02:05:03.955093Z",
+     "shell.execute_reply": "2023-09-18T02:05:03.954447Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:41.160196Z",
-     "iopub.status.busy": "2023-09-07T15:26:41.158882Z",
-     "iopub.status.idle": "2023-09-07T15:26:41.164122Z",
-     "shell.execute_reply": "2023-09-07T15:26:41.163663Z"
+     "iopub.execute_input": "2023-09-18T02:05:03.959523Z",
+     "iopub.status.busy": "2023-09-18T02:05:03.958887Z",
+     "iopub.status.idle": "2023-09-18T02:05:03.962807Z",
+     "shell.execute_reply": "2023-09-18T02:05:03.962347Z"
     }
    },
    "outputs": [],
@@ -92,10 +92,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:41.167258Z",
-     "iopub.status.busy": "2023-09-07T15:26:41.166917Z",
-     "iopub.status.idle": "2023-09-07T15:26:41.170732Z",
-     "shell.execute_reply": "2023-09-07T15:26:41.170270Z"
+     "iopub.execute_input": "2023-09-18T02:05:03.966673Z",
+     "iopub.status.busy": "2023-09-18T02:05:03.965624Z",
+     "iopub.status.idle": "2023-09-18T02:05:03.969627Z",
+     "shell.execute_reply": "2023-09-18T02:05:03.969180Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index 37d0723e8..5a83bace4 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": "2023-09-07T15:26:42.794994Z",
-     "iopub.status.busy": "2023-09-07T15:26:42.794511Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.059300Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.058758Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.512787Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.512357Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.805381Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.804805Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:43.063803Z",
-     "iopub.status.busy": "2023-09-07T15:26:43.062723Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.087233Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.086742Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.808773Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.808218Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.831943Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.831473Z"
     }
    },
    "outputs": [],
@@ -160,10 +160,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:43.091091Z",
-     "iopub.status.busy": "2023-09-07T15:26:43.090131Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.101373Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.100898Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.835698Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.834771Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.845616Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.845143Z"
     }
    },
    "outputs": [],
@@ -203,10 +203,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:43.105118Z",
-     "iopub.status.busy": "2023-09-07T15:26:43.104198Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.109678Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.109212Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.849173Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.848283Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.853696Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.853238Z"
     }
    },
    "outputs": [],
diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index ba7048cc6..1389dccd5 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": "2023-09-07T15:26:44.545162Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.544972Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.921112Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.920522Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.523673Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.523282Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.948579Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.947852Z"
     }
    },
    "outputs": [
@@ -93,10 +93,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.926467Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.925211Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.934235Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.933024Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.962923Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.962413Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.968633Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.968167Z"
     }
    },
    "outputs": [
@@ -111,44 +111,44 @@
       " [-3.07220771e-16 -6.77238770e-01]]\n",
       "\n",
       "Two-body tensor:\n",
-      "[[[[5.23173938e-01 1.94289029e-16]\n",
-      "   [1.94289029e-16 5.33545754e-01]]\n",
+      "[[[[5.23173938e-01 1.57437591e-16]\n",
+      "   [1.57437591e-16 5.33545754e-01]]\n",
       "\n",
-      "  [[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]]\n",
+      "  [[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]]\n",
       "\n",
       "\n",
-      " [[[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]\n",
+      " [[[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]\n",
       "\n",
-      "  [[5.33545754e-01 1.11022302e-16]\n",
-      "   [1.11022302e-16 5.53132024e-01]]]]\n",
+      "  [[5.33545754e-01 1.24884750e-16]\n",
+      "   [1.24884750e-16 5.53132024e-01]]]]\n",
       "\n",
       "Double-factorized representation\n",
       "--------------------------------\n",
       "One-body tensor:\n",
-      "[[-1.21318608e+00 -4.05183033e-16]\n",
-      " [-4.59876437e-16 -1.07792507e+00]]\n",
+      "[[-1.21318608e+00 -4.25870402e-16]\n",
+      " [-4.76015378e-16 -1.07792507e+00]]\n",
       "\n",
       "Diagonal Coulomb matrices:\n",
-      "[[[ 5.14653029e-001  5.33545754e-001]\n",
-      "  [ 5.33545754e-001  5.53132024e-001]]\n",
+      "[[[ 5.14653029e-01  5.33545754e-01]\n",
+      "  [ 5.33545754e-01  5.53132024e-01]]\n",
       "\n",
-      " [[ 2.48240570e-001 -2.48240570e-001]\n",
-      "  [-2.48240570e-001  2.48240570e-001]]\n",
+      " [[ 2.48240570e-01 -2.48240570e-01]\n",
+      "  [-2.48240570e-01  2.48240570e-01]]\n",
       "\n",
-      " [[ 5.96958401e-121 -7.13206008e-062]\n",
-      "  [-7.13206008e-062  8.52090881e-003]]]\n",
+      " [[ 1.50800163e-59 -3.58462611e-31]\n",
+      "  [-3.58462611e-31  8.52090881e-03]]]\n",
       "\n",
       "Orbital rotations:\n",
-      "[[[-1.00000000e+00  4.25128053e-15]\n",
-      "  [ 4.25128053e-15  1.00000000e+00]]\n",
+      "[[[-1.00000000e+00  8.24520980e-15]\n",
+      "  [ 8.24520980e-15  1.00000000e+00]]\n",
       "\n",
-      " [[ 7.07106781e-01 -7.07106781e-01]\n",
-      "  [-7.07106781e-01 -7.07106781e-01]]\n",
+      " [[-7.07106781e-01 -7.07106781e-01]\n",
+      "  [ 7.07106781e-01 -7.07106781e-01]]\n",
       "\n",
-      " [[ 2.89310728e-30 -1.00000000e+00]\n",
-      "  [-1.00000000e+00 -2.89310728e-30]]]\n"
+      " [[ 6.48603030e-15 -1.00000000e+00]\n",
+      "  [-1.00000000e+00 -6.48603030e-15]]]\n"
      ]
     }
    ],
@@ -227,10 +227,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.937097Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.936719Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.941442Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.940888Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.971383Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.970957Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.975813Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.975336Z"
     }
    },
    "outputs": [],
@@ -285,10 +285,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.943853Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.943661Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.947511Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.946949Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.978268Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.977905Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.981583Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.981127Z"
     }
    },
    "outputs": [],
@@ -325,10 +325,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.949838Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.949656Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.954241Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.953674Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.984042Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.983658Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.988160Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.987706Z"
     }
    },
    "outputs": [
@@ -336,7 +336,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.837796382593709\n"
+      "Hartree Fock energy: -0.8377963825937088\n"
      ]
     }
    ],
@@ -367,10 +367,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.957218Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.957027Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.976975Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.976401Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.990630Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.990253Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.998852Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.998404Z"
     }
    },
    "outputs": [
@@ -409,10 +409,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.979271Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.979089Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.986473Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.985937Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.001256Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.000883Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.008185Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.007713Z"
     }
    },
    "outputs": [
@@ -420,7 +420,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083491\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999027574408349\n"
      ]
     }
    ],
@@ -450,10 +450,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.990312Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.990026Z",
-     "iopub.status.idle": "2023-09-07T15:26:45.024328Z",
-     "shell.execute_reply": "2023-09-07T15:26:45.023790Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.010462Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.010158Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.045650Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.045200Z"
     }
    },
    "outputs": [
@@ -461,7 +461,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -493,10 +493,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:45.026743Z",
-     "iopub.status.busy": "2023-09-07T15:26:45.026527Z",
-     "iopub.status.idle": "2023-09-07T15:26:45.054074Z",
-     "shell.execute_reply": "2023-09-07T15:26:45.053560Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.048369Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.048062Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.075448Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.075010Z"
     }
    },
    "outputs": [
@@ -504,7 +504,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -535,10 +535,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:45.056440Z",
-     "iopub.status.busy": "2023-09-07T15:26:45.056262Z",
-     "iopub.status.idle": "2023-09-07T15:26:45.070133Z",
-     "shell.execute_reply": "2023-09-07T15:26:45.069612Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.077880Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.077582Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.089522Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.089090Z"
     }
    },
    "outputs": [
@@ -546,7 +546,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740059\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740057\n"
      ]
     }
    ],
diff --git a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
index e090a9cbd..ce73d31a9 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": "2023-09-07T15:26:47.013441Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.013236Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.355236Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.354722Z"
+     "iopub.execute_input": "2023-09-18T02:05:09.969349Z",
+     "iopub.status.busy": "2023-09-18T02:05:09.968911Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.339028Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.338496Z"
     }
    },
    "outputs": [
@@ -80,10 +80,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.361071Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.360482Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.505657Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.505182Z"
+     "iopub.execute_input": "2023-09-18T02:05:10.342145Z",
+     "iopub.status.busy": "2023-09-18T02:05:10.341656Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.440591Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.440086Z"
     }
    },
    "outputs": [
@@ -91,14 +91,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -0.970773076716434  E_corr = -0.1329766941227252\n"
+      "E(CCSD) = -0.9707730767164341  E_corr = -0.1329766941227253\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -0.9696246123746335\n"
+      "Energy at initialialization: -0.9696246123746332\n"
      ]
     }
    ],
@@ -145,10 +145,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.510068Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.508909Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.651624Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.651122Z"
+     "iopub.execute_input": "2023-09-18T02:05:10.443357Z",
+     "iopub.status.busy": "2023-09-18T02:05:10.442931Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.598491Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.597968Z"
     }
    },
    "outputs": [
@@ -160,15 +160,15 @@
       "  message: Optimization terminated successfully.\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -0.970773075391498\n",
+      "      fun: -0.9707730753913614\n",
       "        x: [-2.678e-01  2.678e-01 ... -1.970e+00 -1.970e+00]\n",
       "      nit: 2\n",
-      "      jac: [-5.960e-08  0.000e+00 ... -2.980e-08 -1.490e-07]\n",
-      " hess_inv: [[ 1.000e+00  0.000e+00 ...  1.364e-12 -2.206e-13]\n",
+      "      jac: [ 1.490e-08  0.000e+00 ...  9.686e-08 -1.714e-07]\n",
+      " hess_inv: [[ 1.000e+00  0.000e+00 ...  4.080e-13 -3.192e-13]\n",
       "            [ 0.000e+00  1.000e+00 ...  0.000e+00  0.000e+00]\n",
       "            ...\n",
-      "            [ 1.364e-12  0.000e+00 ...  1.000e+00  1.818e-12]\n",
-      "            [-2.206e-13  0.000e+00 ...  1.818e-12  1.000e+00]]\n",
+      "            [ 4.080e-13  0.000e+00 ...  1.000e+00 -2.505e-12]\n",
+      "            [-3.192e-13  0.000e+00 ... -2.505e-12  1.000e+00]]\n",
       "     nfev: 63\n",
       "     njev: 3\n"
      ]
@@ -222,10 +222,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.655633Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.654532Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.820397Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.819778Z"
+     "iopub.execute_input": "2023-09-18T02:05:10.601282Z",
+     "iopub.status.busy": "2023-09-18T02:05:10.600952Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.746486Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.745975Z"
     }
    },
    "outputs": [
@@ -237,15 +237,15 @@
       "  message: Optimization terminated successfully.\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -0.9707730754179825\n",
+      "      fun: -0.9707730754179815\n",
       "        x: [ 2.678e-01 -2.678e-01 ... -1.970e+00 -1.970e+00]\n",
       "      nit: 4\n",
-      "      jac: [ 0.000e+00  0.000e+00 ...  8.196e-08 -7.451e-08]\n",
+      "      jac: [ 0.000e+00  0.000e+00 ... -4.470e-08 -2.980e-08]\n",
       " hess_inv: [[ 1.000e+00  0.000e+00 ...  0.000e+00  0.000e+00]\n",
       "            [ 0.000e+00  1.000e+00 ...  0.000e+00  0.000e+00]\n",
       "            ...\n",
-      "            [ 0.000e+00  0.000e+00 ...  1.000e+00  2.029e-10]\n",
-      "            [ 0.000e+00  0.000e+00 ...  2.029e-10  1.000e+00]]\n",
+      "            [ 0.000e+00  0.000e+00 ...  1.000e+00 -6.132e-10]\n",
+      "            [ 0.000e+00  0.000e+00 ... -6.132e-10  1.000e+00]]\n",
       "     nfev: 75\n",
       "     njev: 5\n"
      ]
diff --git a/.doctrees/tutorials/03-double-factorized.doctree b/.doctrees/tutorials/03-double-factorized.doctree
index f54f0264c..09a268958 100644
Binary files a/.doctrees/tutorials/03-double-factorized.doctree and b/.doctrees/tutorials/03-double-factorized.doctree differ
diff --git a/.doctrees/tutorials/04-lucj.doctree b/.doctrees/tutorials/04-lucj.doctree
index 66221ca8f..34d6b2460 100644
Binary files a/.doctrees/tutorials/04-lucj.doctree and b/.doctrees/tutorials/04-lucj.doctree differ
diff --git a/_modules/ffsim/contract/diag_coulomb.html b/_modules/ffsim/contract/diag_coulomb.html
index 10d4d530b..c7570e367 100644
--- a/_modules/ffsim/contract/diag_coulomb.html
+++ b/_modules/ffsim/contract/diag_coulomb.html
@@ -375,7 +375,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/contract/hamiltonian.html b/_modules/ffsim/contract/hamiltonian.html
index 4adbdcd53..9c81b0dc4 100644
--- a/_modules/ffsim/contract/hamiltonian.html
+++ b/_modules/ffsim/contract/hamiltonian.html
@@ -250,7 +250,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/contract/num_op_sum.html b/_modules/ffsim/contract/num_op_sum.html
index 4c74f24b8..c47f6cf4c 100644
--- a/_modules/ffsim/contract/num_op_sum.html
+++ b/_modules/ffsim/contract/num_op_sum.html
@@ -271,7 +271,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/gates/diag_coulomb.html b/_modules/ffsim/gates/diag_coulomb.html
index 819e82d8b..43a948cc8 100644
--- a/_modules/ffsim/gates/diag_coulomb.html
+++ b/_modules/ffsim/gates/diag_coulomb.html
@@ -261,7 +261,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/gates/gates.html b/_modules/ffsim/gates/gates.html
index 5fc9ac743..d5cec41a1 100644
--- a/_modules/ffsim/gates/gates.html
+++ b/_modules/ffsim/gates/gates.html
@@ -324,7 +324,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/gates/num_op_sum.html b/_modules/ffsim/gates/num_op_sum.html
index e65666b1a..dc4b8a37a 100644
--- a/_modules/ffsim/gates/num_op_sum.html
+++ b/_modules/ffsim/gates/num_op_sum.html
@@ -224,7 +224,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/gates/orbital_rotation.html b/_modules/ffsim/gates/orbital_rotation.html
index a19022c35..80c941f94 100644
--- a/_modules/ffsim/gates/orbital_rotation.html
+++ b/_modules/ffsim/gates/orbital_rotation.html
@@ -450,7 +450,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html b/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
index cbed98fbc..49b47b7b1 100644
--- a/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
+++ b/_modules/ffsim/hamiltonians/double_factorized_hamiltonian.html
@@ -404,7 +404,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/hamiltonians/molecular_hamiltonian.html b/_modules/ffsim/hamiltonians/molecular_hamiltonian.html
index 1de558773..9d117fe24 100644
--- a/_modules/ffsim/hamiltonians/molecular_hamiltonian.html
+++ b/_modules/ffsim/hamiltonians/molecular_hamiltonian.html
@@ -167,7 +167,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/linalg/double_factorized.html b/_modules/ffsim/linalg/double_factorized.html
index f2880d561..97ccac904 100644
--- a/_modules/ffsim/linalg/double_factorized.html
+++ b/_modules/ffsim/linalg/double_factorized.html
@@ -610,7 +610,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/linalg/givens.html b/_modules/ffsim/linalg/givens.html
index 70cb01f1d..e7130d95c 100644
--- a/_modules/ffsim/linalg/givens.html
+++ b/_modules/ffsim/linalg/givens.html
@@ -260,7 +260,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/linalg/linalg.html b/_modules/ffsim/linalg/linalg.html
index 2f3efe449..c32ff5671 100644
--- a/_modules/ffsim/linalg/linalg.html
+++ b/_modules/ffsim/linalg/linalg.html
@@ -149,7 +149,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/linalg/predicates.html b/_modules/ffsim/linalg/predicates.html
index d084db7a4..e388ba40f 100644
--- a/_modules/ffsim/linalg/predicates.html
+++ b/_modules/ffsim/linalg/predicates.html
@@ -238,7 +238,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/molecular_data.html b/_modules/ffsim/molecular_data.html
index 588fa798e..d3dbe91ad 100644
--- a/_modules/ffsim/molecular_data.html
+++ b/_modules/ffsim/molecular_data.html
@@ -232,7 +232,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/protocols/linear_operator.html b/_modules/ffsim/protocols/linear_operator.html
index 183c669f9..be37f9964 100644
--- a/_modules/ffsim/protocols/linear_operator.html
+++ b/_modules/ffsim/protocols/linear_operator.html
@@ -140,7 +140,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/protocols/trace.html b/_modules/ffsim/protocols/trace.html
index 895c41450..93a33da69 100644
--- a/_modules/ffsim/protocols/trace.html
+++ b/_modules/ffsim/protocols/trace.html
@@ -138,7 +138,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/random.html b/_modules/ffsim/random.html
index 8ce52b819..a9bd6d896 100644
--- a/_modules/ffsim/random.html
+++ b/_modules/ffsim/random.html
@@ -326,7 +326,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/slow.html b/_modules/ffsim/slow.html
index 611e8e076..e65be3bea 100644
--- a/_modules/ffsim/slow.html
+++ b/_modules/ffsim/slow.html
@@ -426,7 +426,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/states.html b/_modules/ffsim/states.html
index 0734d3567..a3f7f0226 100644
--- a/_modules/ffsim/states.html
+++ b/_modules/ffsim/states.html
@@ -239,7 +239,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/testing.html b/_modules/ffsim/testing.html
index 30aa72ab4..5f0b82a5b 100644
--- a/_modules/ffsim/testing.html
+++ b/_modules/ffsim/testing.html
@@ -152,7 +152,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/trotter/qdrift.html b/_modules/ffsim/trotter/qdrift.html
index c5eae08c4..6cd3c6024 100644
--- a/_modules/ffsim/trotter/qdrift.html
+++ b/_modules/ffsim/trotter/qdrift.html
@@ -784,7 +784,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/trotter/trotter.html b/_modules/ffsim/trotter/trotter.html
index 2598e7a8e..0cb786121 100644
--- a/_modules/ffsim/trotter/trotter.html
+++ b/_modules/ffsim/trotter/trotter.html
@@ -277,7 +277,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/variational/lucj.html b/_modules/ffsim/variational/lucj.html
index c2e3533c6..dac096a80 100644
--- a/_modules/ffsim/variational/lucj.html
+++ b/_modules/ffsim/variational/lucj.html
@@ -464,7 +464,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/ffsim/wick.html b/_modules/ffsim/wick.html
index b1f84975f..f8b03a625 100644
--- a/_modules/ffsim/wick.html
+++ b/_modules/ffsim/wick.html
@@ -216,7 +216,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/_modules/index.html b/_modules/index.html
index 3005040e6..23b0d577a 100644
--- a/_modules/index.html
+++ b/_modules/index.html
@@ -116,7 +116,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
     </div>
diff --git a/api/generated/ffsim.contract.html b/api/generated/ffsim.contract.html
index bb1941564..aa58e9588 100644
--- a/api/generated/ffsim.contract.html
+++ b/api/generated/ffsim.contract.html
@@ -296,7 +296,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
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-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
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-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
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-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
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-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
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(ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation"]], "two_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation"]], "apply_matrix_to_slices() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[4, "module-ffsim.linalg"]], "ffsim.linalg.double_factorized": [[4, "module-ffsim.linalg.double_factorized"]], "ffsim.linalg.givens": [[4, "module-ffsim.linalg.givens"]], "ffsim.linalg.linalg": [[4, "module-ffsim.linalg.linalg"]], "ffsim.linalg.predicates": [[4, "module-ffsim.linalg.predicates"]], "givens_decomposition() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_decomposition"]], "givens_matrix() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_matrix"]], "is_antihermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_unitary"]], "lup() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.modified_cholesky"]], "optimal_diag_coulomb_mats() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.optimal_diag_coulomb_mats"]], "supportslinearoperator (class in ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.SupportsLinearOperator"]], "supportstrace (class in ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.SupportsTrace"]], "ffsim.protocols": [[5, "module-ffsim.protocols"]], "ffsim.protocols.linear_operator": [[5, "module-ffsim.protocols.linear_operator"]], "ffsim.protocols.trace": [[5, "module-ffsim.protocols.trace"]], "linear_operator() (in module ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.linear_operator"]], "trace() (in module ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.trace"]], "expectation_squared_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.expectation_squared_diag_coulomb"]], "ffsim.trotter": [[6, "module-ffsim.trotter"]], "ffsim.trotter.qdrift": [[6, "module-ffsim.trotter.qdrift"]], "ffsim.trotter.trotter": [[6, "module-ffsim.trotter.trotter"]], "one_body_square_decomposition() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.one_body_square_decomposition"]], "qdrift_probabilities() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.qdrift_probabilities"]], "simulate_qdrift_double_factorized() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim.trotter.trotter)": [[6, "ffsim.trotter.trotter.simulate_trotter_double_factorized"]], "spectral_norm_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_diag_coulomb"]], "spectral_norm_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_one_body_tensor"]], "variance_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_diag_coulomb"]], "variance_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_one_body_tensor"]], "ucjoperator (class in ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.UCJOperator"]], "apply_ucj_operator() (in module ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.apply_ucj_operator"]], "diag_coulomb_mats_alpha_alpha (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_beta"]], "ffsim.variational": [[7, "module-ffsim.variational"]], "ffsim.variational.lucj": [[7, "module-ffsim.variational.lucj"]], "final_orbital_rotation (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.final_orbital_rotation"]], "from_parameters() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_t_amplitudes"]], "n_reps (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.n_reps"]], "norb (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.norb"]], "orbital_rotations (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.orbital_rotations"]], "to_parameters() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_t_amplitudes"]]}})
\ No newline at end of file
+Search.setIndex({"docnames": ["api/generated/ffsim", "api/generated/ffsim.contract", "api/generated/ffsim.gates", "api/generated/ffsim.hamiltonians", "api/generated/ffsim.linalg", "api/generated/ffsim.protocols", "api/generated/ffsim.trotter", "api/generated/ffsim.variational", "api/generated/modules", "api/index", "index", "tutorials/01-introduction", "tutorials/02-orbital-rotation", "tutorials/03-double-factorized", "tutorials/04-lucj", "tutorials/index"], "filenames": ["api/generated/ffsim.rst", "api/generated/ffsim.contract.rst", "api/generated/ffsim.gates.rst", "api/generated/ffsim.hamiltonians.rst", "api/generated/ffsim.linalg.rst", "api/generated/ffsim.protocols.rst", "api/generated/ffsim.trotter.rst", "api/generated/ffsim.variational.rst", "api/generated/modules.rst", "api/index.rst", "index.rst", "tutorials/01-introduction.ipynb", "tutorials/02-orbital-rotation.ipynb", "tutorials/03-double-factorized.ipynb", "tutorials/04-lucj.ipynb", "tutorials/index.rst"], "titles": ["ffsim package", "ffsim.contract package", "ffsim.gates package", "ffsim.hamiltonians package", "ffsim.linalg package", "ffsim.protocols package", "ffsim.trotter package", "ffsim.variational package", "ffsim", "API reference", "ffsim documentation", "Introduction to ffsim", "Orbital rotations and quadratic Hamiltonians", "Diagonal Coulomb operators and double-factorized Trotter simulation", "The local unitary cluster Jastrow (LUCJ) ansatz", "Tutorials"], "terms": {"contract": [0, 8, 9, 12], "diag_coulomb": [0, 8], "contract_diag_coulomb": [0, 1], "diag_coulomb_linop": [0, 1], "hamiltonian": [0, 6, 8, 9, 14, 15], "hamiltonian_linop": [0, 1, 12], "hamiltonian_trac": [0, 1], "num_op_sum": [0, 8], "contract_num_op_sum": [0, 1], "num_op_sum_linop": [0, 1], "gate": [0, 8, 9, 14], "apply_diag_coulomb_evolut": [0, 2, 13], "apply_givens_rot": [0, 2], "apply_num_interact": [0, 2], "apply_num_op_prod_interact": [0, 2], "apply_tunneling_interact": [0, 2], "apply_num_op_sum_evolut": [0, 2, 12, 13], "orbital_rot": [0, 1, 3, 4, 6, 7, 8, 11, 12, 13], "apply_orbital_rot": [0, 2, 11, 12], "gen_orbital_rotation_index": [0, 2], "double_factorized_hamiltonian": [0, 8, 13], "doublefactorizedhamiltonian": [0, 3, 6, 13], "one_body_tensor": [0, 1, 3, 6, 12, 13], "diag_coulomb_mat": [0, 3, 6, 13], "constant": [0, 1, 3, 13, 14], "z_represent": [0, 1, 2, 3, 6], "norb": [0, 1, 2, 3, 5, 6, 7, 11, 12, 13, 14], "to_number_represent": [0, 3], "to_z_represent": [0, 3], "molecular_hamiltonian": [0, 8], "molecularhamiltonian": [0, 3], "two_body_tensor": [0, 1, 3, 4, 13], "linalg": [0, 8, 9, 12, 13], "double_factor": [0, 8], "double_factorized_t2": [0, 4], "modified_choleski": [0, 4], "optimal_diag_coulomb_mat": [0, 4], "given": [0, 1, 2, 6, 8, 12, 13], "apply_matrix_to_slic": [0, 4], "givens_decomposit": [0, 4], "givens_matrix": [0, 4], "expm_multiply_taylor": [0, 4], "lup": [0, 4], "predic": [0, 8], "is_antihermitian": [0, 4], "is_hermitian": [0, 4], "is_orthogon": [0, 4], "is_real_symmetr": [0, 4], 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(ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.diag_coulomb_mats"]], "double_factorized_hamiltonian() (in module ffsim.hamiltonians.double_factorized_hamiltonian)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.double_factorized_hamiltonian"]], "ffsim.hamiltonians": [[3, "module-ffsim.hamiltonians"]], "ffsim.hamiltonians.double_factorized_hamiltonian": [[3, "module-ffsim.hamiltonians.double_factorized_hamiltonian"]], "ffsim.hamiltonians.molecular_hamiltonian": [[3, "module-ffsim.hamiltonians.molecular_hamiltonian"]], "norb (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian property)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.norb"]], "norb (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian property)": [[3, 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(ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian method)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.to_z_representation"]], "two_body_tensor (ffsim.hamiltonians.molecular_hamiltonian.molecularhamiltonian attribute)": [[3, "ffsim.hamiltonians.molecular_hamiltonian.MolecularHamiltonian.two_body_tensor"]], "z_representation (ffsim.hamiltonians.double_factorized_hamiltonian.doublefactorizedhamiltonian attribute)": [[3, "ffsim.hamiltonians.double_factorized_hamiltonian.DoubleFactorizedHamiltonian.z_representation"]], "apply_matrix_to_slices() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.apply_matrix_to_slices"]], "double_factorized() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized"]], "double_factorized_t2() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.double_factorized_t2"]], "expm_multiply_taylor() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.expm_multiply_taylor"]], "ffsim.linalg": [[4, "module-ffsim.linalg"]], "ffsim.linalg.double_factorized": [[4, "module-ffsim.linalg.double_factorized"]], "ffsim.linalg.givens": [[4, "module-ffsim.linalg.givens"]], "ffsim.linalg.linalg": [[4, "module-ffsim.linalg.linalg"]], "ffsim.linalg.predicates": [[4, "module-ffsim.linalg.predicates"]], "givens_decomposition() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_decomposition"]], "givens_matrix() (in module ffsim.linalg.givens)": [[4, "ffsim.linalg.givens.givens_matrix"]], "is_antihermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_antihermitian"]], "is_hermitian() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_hermitian"]], "is_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_orthogonal"]], "is_real_symmetric() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_real_symmetric"]], "is_special_orthogonal() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_special_orthogonal"]], "is_unitary() (in module ffsim.linalg.predicates)": [[4, "ffsim.linalg.predicates.is_unitary"]], "lup() (in module ffsim.linalg.linalg)": [[4, "ffsim.linalg.linalg.lup"]], "modified_cholesky() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.modified_cholesky"]], "optimal_diag_coulomb_mats() (in module ffsim.linalg.double_factorized)": [[4, "ffsim.linalg.double_factorized.optimal_diag_coulomb_mats"]], "supportslinearoperator (class in ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.SupportsLinearOperator"]], "supportstrace (class in ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.SupportsTrace"]], "ffsim.protocols": [[5, "module-ffsim.protocols"]], "ffsim.protocols.linear_operator": [[5, "module-ffsim.protocols.linear_operator"]], "ffsim.protocols.trace": [[5, "module-ffsim.protocols.trace"]], "linear_operator() (in module ffsim.protocols.linear_operator)": [[5, "ffsim.protocols.linear_operator.linear_operator"]], "trace() (in module ffsim.protocols.trace)": [[5, "ffsim.protocols.trace.trace"]], "expectation_squared_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.expectation_squared_diag_coulomb"]], "ffsim.trotter": [[6, "module-ffsim.trotter"]], "ffsim.trotter.qdrift": [[6, "module-ffsim.trotter.qdrift"]], "ffsim.trotter.trotter": [[6, "module-ffsim.trotter.trotter"]], "one_body_square_decomposition() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.one_body_square_decomposition"]], "qdrift_probabilities() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.qdrift_probabilities"]], "simulate_qdrift_double_factorized() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.simulate_qdrift_double_factorized"]], "simulate_trotter_double_factorized() (in module ffsim.trotter.trotter)": [[6, "ffsim.trotter.trotter.simulate_trotter_double_factorized"]], "spectral_norm_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_diag_coulomb"]], "spectral_norm_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.spectral_norm_one_body_tensor"]], "variance_diag_coulomb() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_diag_coulomb"]], "variance_one_body_tensor() (in module ffsim.trotter.qdrift)": [[6, "ffsim.trotter.qdrift.variance_one_body_tensor"]], "ucjoperator (class in ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.UCJOperator"]], "apply_ucj_operator() (in module ffsim.variational.lucj)": [[7, "ffsim.variational.lucj.apply_ucj_operator"]], "diag_coulomb_mats_alpha_alpha (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_alpha"]], "diag_coulomb_mats_alpha_beta (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.diag_coulomb_mats_alpha_beta"]], "ffsim.variational": [[7, "module-ffsim.variational"]], "ffsim.variational.lucj": [[7, "module-ffsim.variational.lucj"]], "final_orbital_rotation (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.final_orbital_rotation"]], "from_parameters() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_parameters"]], "from_t_amplitudes() (ffsim.variational.lucj.ucjoperator static method)": [[7, "ffsim.variational.lucj.UCJOperator.from_t_amplitudes"]], "n_reps (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.n_reps"]], "norb (ffsim.variational.lucj.ucjoperator property)": [[7, "ffsim.variational.lucj.UCJOperator.norb"]], "orbital_rotations (ffsim.variational.lucj.ucjoperator attribute)": [[7, "ffsim.variational.lucj.UCJOperator.orbital_rotations"]], "to_parameters() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_parameters"]], "to_t_amplitudes() (ffsim.variational.lucj.ucjoperator method)": [[7, "ffsim.variational.lucj.UCJOperator.to_t_amplitudes"]]}})
\ No newline at end of file
diff --git a/tutorials/01-introduction.html b/tutorials/01-introduction.html
index 23354e262..866040844 100644
--- a/tutorials/01-introduction.html
+++ b/tutorials/01-introduction.html
@@ -161,7 +161,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
       |
diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb
index ad7d9f2a8..6029431d7 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:40.890186Z",
-     "iopub.status.busy": "2023-09-07T15:26:40.889998Z",
-     "iopub.status.idle": "2023-09-07T15:26:41.155566Z",
-     "shell.execute_reply": "2023-09-07T15:26:41.155021Z"
+     "iopub.execute_input": "2023-09-18T02:05:03.658805Z",
+     "iopub.status.busy": "2023-09-18T02:05:03.658381Z",
+     "iopub.status.idle": "2023-09-18T02:05:03.955093Z",
+     "shell.execute_reply": "2023-09-18T02:05:03.954447Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:41.160196Z",
-     "iopub.status.busy": "2023-09-07T15:26:41.158882Z",
-     "iopub.status.idle": "2023-09-07T15:26:41.164122Z",
-     "shell.execute_reply": "2023-09-07T15:26:41.163663Z"
+     "iopub.execute_input": "2023-09-18T02:05:03.959523Z",
+     "iopub.status.busy": "2023-09-18T02:05:03.958887Z",
+     "iopub.status.idle": "2023-09-18T02:05:03.962807Z",
+     "shell.execute_reply": "2023-09-18T02:05:03.962347Z"
     }
    },
    "outputs": [],
@@ -92,10 +92,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:41.167258Z",
-     "iopub.status.busy": "2023-09-07T15:26:41.166917Z",
-     "iopub.status.idle": "2023-09-07T15:26:41.170732Z",
-     "shell.execute_reply": "2023-09-07T15:26:41.170270Z"
+     "iopub.execute_input": "2023-09-18T02:05:03.966673Z",
+     "iopub.status.busy": "2023-09-18T02:05:03.965624Z",
+     "iopub.status.idle": "2023-09-18T02:05:03.969627Z",
+     "shell.execute_reply": "2023-09-18T02:05:03.969180Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.html b/tutorials/02-orbital-rotation.html
index 1a19cae2e..88e0cf24b 100644
--- a/tutorials/02-orbital-rotation.html
+++ b/tutorials/02-orbital-rotation.html
@@ -229,7 +229,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
       |
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index 37d0723e8..5a83bace4 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": "2023-09-07T15:26:42.794994Z",
-     "iopub.status.busy": "2023-09-07T15:26:42.794511Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.059300Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.058758Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.512787Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.512357Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.805381Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.804805Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:43.063803Z",
-     "iopub.status.busy": "2023-09-07T15:26:43.062723Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.087233Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.086742Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.808773Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.808218Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.831943Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.831473Z"
     }
    },
    "outputs": [],
@@ -160,10 +160,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:43.091091Z",
-     "iopub.status.busy": "2023-09-07T15:26:43.090131Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.101373Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.100898Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.835698Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.834771Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.845616Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.845143Z"
     }
    },
    "outputs": [],
@@ -203,10 +203,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:43.105118Z",
-     "iopub.status.busy": "2023-09-07T15:26:43.104198Z",
-     "iopub.status.idle": "2023-09-07T15:26:43.109678Z",
-     "shell.execute_reply": "2023-09-07T15:26:43.109212Z"
+     "iopub.execute_input": "2023-09-18T02:05:05.849173Z",
+     "iopub.status.busy": "2023-09-18T02:05:05.848283Z",
+     "iopub.status.idle": "2023-09-18T02:05:05.853696Z",
+     "shell.execute_reply": "2023-09-18T02:05:05.853238Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.html b/tutorials/03-double-factorized.html
index 669da39f7..8b6da9752 100644
--- a/tutorials/03-double-factorized.html
+++ b/tutorials/03-double-factorized.html
@@ -136,44 +136,44 @@ <h2>Double-factorized representation of the molecular Hamiltonian<a class="heade
  [-3.07220771e-16 -6.77238770e-01]]
 
 Two-body tensor:
-[[[[5.23173938e-01 1.94289029e-16]
-   [1.94289029e-16 5.33545754e-01]]
+[[[[5.23173938e-01 1.57437591e-16]
+   [1.57437591e-16 5.33545754e-01]]
 
-  [[1.94289029e-16 2.48240570e-01]
-   [2.48240570e-01 8.32667268e-17]]]
+  [[2.12704463e-16 2.48240570e-01]
+   [2.48240570e-01 1.61492903e-16]]]
 
 
- [[[1.94289029e-16 2.48240570e-01]
-   [2.48240570e-01 8.32667268e-17]]
+ [[[2.12704463e-16 2.48240570e-01]
+   [2.48240570e-01 1.61492903e-16]]
 
-  [[5.33545754e-01 1.11022302e-16]
-   [1.11022302e-16 5.53132024e-01]]]]
+  [[5.33545754e-01 1.24884750e-16]
+   [1.24884750e-16 5.53132024e-01]]]]
 
 Double-factorized representation
 --------------------------------
 One-body tensor:
-[[-1.21318608e+00 -4.05183033e-16]
- [-4.59876437e-16 -1.07792507e+00]]
+[[-1.21318608e+00 -4.25870402e-16]
+ [-4.76015378e-16 -1.07792507e+00]]
 
 Diagonal Coulomb matrices:
-[[[ 5.14653029e-001  5.33545754e-001]
-  [ 5.33545754e-001  5.53132024e-001]]
+[[[ 5.14653029e-01  5.33545754e-01]
+  [ 5.33545754e-01  5.53132024e-01]]
 
- [[ 2.48240570e-001 -2.48240570e-001]
-  [-2.48240570e-001  2.48240570e-001]]
+ [[ 2.48240570e-01 -2.48240570e-01]
+  [-2.48240570e-01  2.48240570e-01]]
 
- [[ 5.96958401e-121 -7.13206008e-062]
-  [-7.13206008e-062  8.52090881e-003]]]
+ [[ 1.50800163e-59 -3.58462611e-31]
+  [-3.58462611e-31  8.52090881e-03]]]
 
 Orbital rotations:
-[[[-1.00000000e+00  4.25128053e-15]
-  [ 4.25128053e-15  1.00000000e+00]]
+[[[-1.00000000e+00  8.24520980e-15]
+  [ 8.24520980e-15  1.00000000e+00]]
 
- [[ 7.07106781e-01 -7.07106781e-01]
-  [-7.07106781e-01 -7.07106781e-01]]
+ [[-7.07106781e-01 -7.07106781e-01]
+  [ 7.07106781e-01 -7.07106781e-01]]
 
- [[ 2.89310728e-30 -1.00000000e+00]
-  [-1.00000000e+00 -2.89310728e-30]]]
+ [[ 6.48603030e-15 -1.00000000e+00]
+  [-1.00000000e+00 -6.48603030e-15]]]
 </pre></div></div>
 </div>
 </section>
@@ -297,7 +297,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Hartree Fock energy: -0.837796382593709
+Hartree Fock energy: -0.8377963825937088
 </pre></div></div>
 </div>
 <p>Now, we set the evolution time and calculate the exact result of time evolution by directly exponentiating the Hamiltonian using SciPy. Later, we will compare the result of our approximate time evolution with this exact result.</p>
@@ -352,7 +352,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9990275744083491
+Fidelity of Trotter-evolved state with exact state: 0.999027574408349
 </pre></div></div>
 </div>
 <p>The fidelity of the final result can be improved by increasing the number of Trotter steps.</p>
@@ -379,7 +379,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9999906233109653
+Fidelity of Trotter-evolved state with exact state: 0.9999906233109657
 </pre></div></div>
 </div>
 <p>As mentioned above, ffsim already includes functionality for Trotter simulation of double-factorized Hamiltonians. The implementation in ffsim includes higher-order Trotter-Suzuki formulas. The first-order asymmetric formula that we just implemented corresponds to <code class="docutils literal notranslate"><span class="pre">order=0</span></code> in ffsim’s implementation. <code class="docutils literal notranslate"><span class="pre">order=1</span></code> corresponds to the first-order symmetric (commonly known as the second-order) formula, <code class="docutils literal notranslate"><span class="pre">order=2</span></code> corresponds to the second-order symmetric (fourth-order) formula, and so on.</p>
@@ -408,7 +408,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9999906233109653
+Fidelity of Trotter-evolved state with exact state: 0.9999906233109657
 </pre></div></div>
 </div>
 <p>A higher order formula achieves a higher fidelity with fewer Trotter steps:</p>
@@ -436,7 +436,7 @@ <h3>Implementing Trotter simulation of the double-factorized Hamiltonian<a class
 </div>
 <div class="output_area docutils container">
 <div class="highlight"><pre>
-Fidelity of Trotter-evolved state with exact state: 0.9999999336740059
+Fidelity of Trotter-evolved state with exact state: 0.9999999336740057
 </pre></div></div>
 </div>
 </section>
@@ -503,7 +503,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
       |
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index ba7048cc6..1389dccd5 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": "2023-09-07T15:26:44.545162Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.544972Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.921112Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.920522Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.523673Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.523282Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.948579Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.947852Z"
     }
    },
    "outputs": [
@@ -93,10 +93,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.926467Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.925211Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.934235Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.933024Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.962923Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.962413Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.968633Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.968167Z"
     }
    },
    "outputs": [
@@ -111,44 +111,44 @@
       " [-3.07220771e-16 -6.77238770e-01]]\n",
       "\n",
       "Two-body tensor:\n",
-      "[[[[5.23173938e-01 1.94289029e-16]\n",
-      "   [1.94289029e-16 5.33545754e-01]]\n",
+      "[[[[5.23173938e-01 1.57437591e-16]\n",
+      "   [1.57437591e-16 5.33545754e-01]]\n",
       "\n",
-      "  [[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]]\n",
+      "  [[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]]\n",
       "\n",
       "\n",
-      " [[[1.94289029e-16 2.48240570e-01]\n",
-      "   [2.48240570e-01 8.32667268e-17]]\n",
+      " [[[2.12704463e-16 2.48240570e-01]\n",
+      "   [2.48240570e-01 1.61492903e-16]]\n",
       "\n",
-      "  [[5.33545754e-01 1.11022302e-16]\n",
-      "   [1.11022302e-16 5.53132024e-01]]]]\n",
+      "  [[5.33545754e-01 1.24884750e-16]\n",
+      "   [1.24884750e-16 5.53132024e-01]]]]\n",
       "\n",
       "Double-factorized representation\n",
       "--------------------------------\n",
       "One-body tensor:\n",
-      "[[-1.21318608e+00 -4.05183033e-16]\n",
-      " [-4.59876437e-16 -1.07792507e+00]]\n",
+      "[[-1.21318608e+00 -4.25870402e-16]\n",
+      " [-4.76015378e-16 -1.07792507e+00]]\n",
       "\n",
       "Diagonal Coulomb matrices:\n",
-      "[[[ 5.14653029e-001  5.33545754e-001]\n",
-      "  [ 5.33545754e-001  5.53132024e-001]]\n",
+      "[[[ 5.14653029e-01  5.33545754e-01]\n",
+      "  [ 5.33545754e-01  5.53132024e-01]]\n",
       "\n",
-      " [[ 2.48240570e-001 -2.48240570e-001]\n",
-      "  [-2.48240570e-001  2.48240570e-001]]\n",
+      " [[ 2.48240570e-01 -2.48240570e-01]\n",
+      "  [-2.48240570e-01  2.48240570e-01]]\n",
       "\n",
-      " [[ 5.96958401e-121 -7.13206008e-062]\n",
-      "  [-7.13206008e-062  8.52090881e-003]]]\n",
+      " [[ 1.50800163e-59 -3.58462611e-31]\n",
+      "  [-3.58462611e-31  8.52090881e-03]]]\n",
       "\n",
       "Orbital rotations:\n",
-      "[[[-1.00000000e+00  4.25128053e-15]\n",
-      "  [ 4.25128053e-15  1.00000000e+00]]\n",
+      "[[[-1.00000000e+00  8.24520980e-15]\n",
+      "  [ 8.24520980e-15  1.00000000e+00]]\n",
       "\n",
-      " [[ 7.07106781e-01 -7.07106781e-01]\n",
-      "  [-7.07106781e-01 -7.07106781e-01]]\n",
+      " [[-7.07106781e-01 -7.07106781e-01]\n",
+      "  [ 7.07106781e-01 -7.07106781e-01]]\n",
       "\n",
-      " [[ 2.89310728e-30 -1.00000000e+00]\n",
-      "  [-1.00000000e+00 -2.89310728e-30]]]\n"
+      " [[ 6.48603030e-15 -1.00000000e+00]\n",
+      "  [-1.00000000e+00 -6.48603030e-15]]]\n"
      ]
     }
    ],
@@ -227,10 +227,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.937097Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.936719Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.941442Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.940888Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.971383Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.970957Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.975813Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.975336Z"
     }
    },
    "outputs": [],
@@ -285,10 +285,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.943853Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.943661Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.947511Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.946949Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.978268Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.977905Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.981583Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.981127Z"
     }
    },
    "outputs": [],
@@ -325,10 +325,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.949838Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.949656Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.954241Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.953674Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.984042Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.983658Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.988160Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.987706Z"
     }
    },
    "outputs": [
@@ -336,7 +336,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hartree Fock energy: -0.837796382593709\n"
+      "Hartree Fock energy: -0.8377963825937088\n"
      ]
     }
    ],
@@ -367,10 +367,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.957218Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.957027Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.976975Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.976401Z"
+     "iopub.execute_input": "2023-09-18T02:05:07.990630Z",
+     "iopub.status.busy": "2023-09-18T02:05:07.990253Z",
+     "iopub.status.idle": "2023-09-18T02:05:07.998852Z",
+     "shell.execute_reply": "2023-09-18T02:05:07.998404Z"
     }
    },
    "outputs": [
@@ -409,10 +409,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.979271Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.979089Z",
-     "iopub.status.idle": "2023-09-07T15:26:44.986473Z",
-     "shell.execute_reply": "2023-09-07T15:26:44.985937Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.001256Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.000883Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.008185Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.007713Z"
     }
    },
    "outputs": [
@@ -420,7 +420,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9990275744083491\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.999027574408349\n"
      ]
     }
    ],
@@ -450,10 +450,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:44.990312Z",
-     "iopub.status.busy": "2023-09-07T15:26:44.990026Z",
-     "iopub.status.idle": "2023-09-07T15:26:45.024328Z",
-     "shell.execute_reply": "2023-09-07T15:26:45.023790Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.010462Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.010158Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.045650Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.045200Z"
     }
    },
    "outputs": [
@@ -461,7 +461,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -493,10 +493,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:45.026743Z",
-     "iopub.status.busy": "2023-09-07T15:26:45.026527Z",
-     "iopub.status.idle": "2023-09-07T15:26:45.054074Z",
-     "shell.execute_reply": "2023-09-07T15:26:45.053560Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.048369Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.048062Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.075448Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.075010Z"
     }
    },
    "outputs": [
@@ -504,7 +504,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109653\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999906233109657\n"
      ]
     }
    ],
@@ -535,10 +535,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:45.056440Z",
-     "iopub.status.busy": "2023-09-07T15:26:45.056262Z",
-     "iopub.status.idle": "2023-09-07T15:26:45.070133Z",
-     "shell.execute_reply": "2023-09-07T15:26:45.069612Z"
+     "iopub.execute_input": "2023-09-18T02:05:08.077880Z",
+     "iopub.status.busy": "2023-09-18T02:05:08.077582Z",
+     "iopub.status.idle": "2023-09-18T02:05:08.089522Z",
+     "shell.execute_reply": "2023-09-18T02:05:08.089090Z"
     }
    },
    "outputs": [
@@ -546,7 +546,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740059\n"
+      "Fidelity of Trotter-evolved state with exact state: 0.9999999336740057\n"
      ]
     }
    ],
diff --git a/tutorials/04-lucj.html b/tutorials/04-lucj.html
index 8acc8ad1a..8931af849 100644
--- a/tutorials/04-lucj.html
+++ b/tutorials/04-lucj.html
@@ -125,8 +125,8 @@ <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) = -0.970773076716434  E_corr = -0.1329766941227252
-Energy at initialialization: -0.9696246123746335
+E(CCSD) = -0.9707730767164341  E_corr = -0.1329766941227253
+Energy at initialialization: -0.9696246123746332
 </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>
@@ -165,15 +165,15 @@ <h2>The unitary cluster Jastrow (UCJ) ansatz<a class="headerlink" href="#The-uni
   message: Optimization terminated successfully.
   success: True
    status: 0
-      fun: -0.970773075391498
+      fun: -0.9707730753913614
         x: [-2.678e-01  2.678e-01 ... -1.970e+00 -1.970e+00]
       nit: 2
-      jac: [-5.960e-08  0.000e+00 ... -2.980e-08 -1.490e-07]
- hess_inv: [[ 1.000e+00  0.000e+00 ...  1.364e-12 -2.206e-13]
+      jac: [ 1.490e-08  0.000e+00 ...  9.686e-08 -1.714e-07]
+ hess_inv: [[ 1.000e+00  0.000e+00 ...  4.080e-13 -3.192e-13]
             [ 0.000e+00  1.000e+00 ...  0.000e+00  0.000e+00]
             ...
-            [ 1.364e-12  0.000e+00 ...  1.000e+00  1.818e-12]
-            [-2.206e-13  0.000e+00 ...  1.818e-12  1.000e+00]]
+            [ 4.080e-13  0.000e+00 ...  1.000e+00 -2.505e-12]
+            [-3.192e-13  0.000e+00 ... -2.505e-12  1.000e+00]]
      nfev: 63
      njev: 3
 </pre></div></div>
@@ -236,15 +236,15 @@ <h2>The local unitary cluster Jastrow (LUCJ) ansatz<a class="headerlink" href="#
   message: Optimization terminated successfully.
   success: True
    status: 0
-      fun: -0.9707730754179825
+      fun: -0.9707730754179815
         x: [ 2.678e-01 -2.678e-01 ... -1.970e+00 -1.970e+00]
       nit: 4
-      jac: [ 0.000e+00  0.000e+00 ...  8.196e-08 -7.451e-08]
+      jac: [ 0.000e+00  0.000e+00 ... -4.470e-08 -2.980e-08]
  hess_inv: [[ 1.000e+00  0.000e+00 ...  0.000e+00  0.000e+00]
             [ 0.000e+00  1.000e+00 ...  0.000e+00  0.000e+00]
             ...
-            [ 0.000e+00  0.000e+00 ...  1.000e+00  2.029e-10]
-            [ 0.000e+00  0.000e+00 ...  2.029e-10  1.000e+00]]
+            [ 0.000e+00  0.000e+00 ...  1.000e+00 -6.132e-10]
+            [ 0.000e+00  0.000e+00 ... -6.132e-10  1.000e+00]]
      nfev: 75
      njev: 5
 </pre></div></div>
@@ -312,7 +312,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
       |
diff --git a/tutorials/04-lucj.ipynb b/tutorials/04-lucj.ipynb
index e090a9cbd..ce73d31a9 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.013441Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.013236Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.355236Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.354722Z"
+     "iopub.execute_input": "2023-09-18T02:05:09.969349Z",
+     "iopub.status.busy": "2023-09-18T02:05:09.968911Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.339028Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.338496Z"
     }
    },
    "outputs": [
@@ -80,10 +80,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.361071Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.360482Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.505657Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.505182Z"
+     "iopub.execute_input": "2023-09-18T02:05:10.342145Z",
+     "iopub.status.busy": "2023-09-18T02:05:10.341656Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.440591Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.440086Z"
     }
    },
    "outputs": [
@@ -91,14 +91,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E(CCSD) = -0.970773076716434  E_corr = -0.1329766941227252\n"
+      "E(CCSD) = -0.9707730767164341  E_corr = -0.1329766941227253\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Energy at initialialization: -0.9696246123746335\n"
+      "Energy at initialialization: -0.9696246123746332\n"
      ]
     }
    ],
@@ -145,10 +145,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.510068Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.508909Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.651624Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.651122Z"
+     "iopub.execute_input": "2023-09-18T02:05:10.443357Z",
+     "iopub.status.busy": "2023-09-18T02:05:10.442931Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.598491Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.597968Z"
     }
    },
    "outputs": [
@@ -160,15 +160,15 @@
       "  message: Optimization terminated successfully.\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -0.970773075391498\n",
+      "      fun: -0.9707730753913614\n",
       "        x: [-2.678e-01  2.678e-01 ... -1.970e+00 -1.970e+00]\n",
       "      nit: 2\n",
-      "      jac: [-5.960e-08  0.000e+00 ... -2.980e-08 -1.490e-07]\n",
-      " hess_inv: [[ 1.000e+00  0.000e+00 ...  1.364e-12 -2.206e-13]\n",
+      "      jac: [ 1.490e-08  0.000e+00 ...  9.686e-08 -1.714e-07]\n",
+      " hess_inv: [[ 1.000e+00  0.000e+00 ...  4.080e-13 -3.192e-13]\n",
       "            [ 0.000e+00  1.000e+00 ...  0.000e+00  0.000e+00]\n",
       "            ...\n",
-      "            [ 1.364e-12  0.000e+00 ...  1.000e+00  1.818e-12]\n",
-      "            [-2.206e-13  0.000e+00 ...  1.818e-12  1.000e+00]]\n",
+      "            [ 4.080e-13  0.000e+00 ...  1.000e+00 -2.505e-12]\n",
+      "            [-3.192e-13  0.000e+00 ... -2.505e-12  1.000e+00]]\n",
       "     nfev: 63\n",
       "     njev: 3\n"
      ]
@@ -222,10 +222,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-07T15:26:47.655633Z",
-     "iopub.status.busy": "2023-09-07T15:26:47.654532Z",
-     "iopub.status.idle": "2023-09-07T15:26:47.820397Z",
-     "shell.execute_reply": "2023-09-07T15:26:47.819778Z"
+     "iopub.execute_input": "2023-09-18T02:05:10.601282Z",
+     "iopub.status.busy": "2023-09-18T02:05:10.600952Z",
+     "iopub.status.idle": "2023-09-18T02:05:10.746486Z",
+     "shell.execute_reply": "2023-09-18T02:05:10.745975Z"
     }
    },
    "outputs": [
@@ -237,15 +237,15 @@
       "  message: Optimization terminated successfully.\n",
       "  success: True\n",
       "   status: 0\n",
-      "      fun: -0.9707730754179825\n",
+      "      fun: -0.9707730754179815\n",
       "        x: [ 2.678e-01 -2.678e-01 ... -1.970e+00 -1.970e+00]\n",
       "      nit: 4\n",
-      "      jac: [ 0.000e+00  0.000e+00 ...  8.196e-08 -7.451e-08]\n",
+      "      jac: [ 0.000e+00  0.000e+00 ... -4.470e-08 -2.980e-08]\n",
       " hess_inv: [[ 1.000e+00  0.000e+00 ...  0.000e+00  0.000e+00]\n",
       "            [ 0.000e+00  1.000e+00 ...  0.000e+00  0.000e+00]\n",
       "            ...\n",
-      "            [ 0.000e+00  0.000e+00 ...  1.000e+00  2.029e-10]\n",
-      "            [ 0.000e+00  0.000e+00 ...  2.029e-10  1.000e+00]]\n",
+      "            [ 0.000e+00  0.000e+00 ...  1.000e+00 -6.132e-10]\n",
+      "            [ 0.000e+00  0.000e+00 ... -6.132e-10  1.000e+00]]\n",
       "     nfev: 75\n",
       "     njev: 5\n"
      ]
diff --git a/tutorials/index.html b/tutorials/index.html
index a02cc07d4..8fffce7f6 100644
--- a/tutorials/index.html
+++ b/tutorials/index.html
@@ -109,7 +109,7 @@ <h3 id="searchlabel">Quick search</h3>
       &copy;2023, IBM.
       
       |
-      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.5</a>
+      Powered by <a href="http://sphinx-doc.org/">Sphinx 7.2.6</a>
       &amp; <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.13</a>
       
       |