Update all guides to calculate integrals using pyscf (#109)

* Update all guides

* style

(cherry picked from commit 40b276c)

docs/how_tos/integrate_dice_solver.ipynb

@@ -21,10 +21,11 @@
    "source": [
     "%%capture\n",
     "\n",
-    "import os\n",
     "\n",
     "import numpy as np\n",
-    "from pyscf import ao2mo, tools\n",
+    "import pyscf\n",
+    "import pyscf.cc\n",
+    "import pyscf.mcscf\n",
     "from qiskit_addon_dice_solver import solve_fermion\n",
     "from qiskit_addon_sqd.configuration_recovery import recover_configurations\n",
     "from qiskit_addon_sqd.counts import counts_to_arrays, generate_counts_uniform\n",
@@ -39,12 +40,35 @@
     "open_shell = False\n",
     "spin_sq = 0\n",
     "\n",
-    "# Read in molecule from disk\n",
-    "active_space_path = os.path.abspath(os.path.join(\"..\", \"molecules\", \"n2_fci.txt\"))\n",
-    "mf_as = tools.fcidump.to_scf(active_space_path)\n",
-    "hcore = mf_as.get_hcore()\n",
-    "eri = ao2mo.restore(1, mf_as._eri, num_orbitals)\n",
-    "nuclear_repulsion_energy = mf_as.mol.energy_nuc()\n",
+    "# Specify molecule properties\n",
+    "open_shell = False\n",
+    "spin_sq = 0\n",
+    "\n",
+    "# Build N2 molecule\n",
+    "mol = pyscf.gto.Mole()\n",
+    "mol.build(\n",
+    "    atom=[[\"N\", (0, 0, 0)], [\"N\", (1.0, 0, 0)]],\n",
+    "    basis=\"6-31g\",\n",
+    "    symmetry=\"Dooh\",\n",
+    ")\n",
+    "\n",
+    "# Define active space\n",
+    "n_frozen = 2\n",
+    "active_space = range(n_frozen, mol.nao_nr())\n",
+    "\n",
+    "# Get molecular integrals\n",
+    "scf = pyscf.scf.RHF(mol).run()\n",
+    "num_orbitals = len(active_space)\n",
+    "n_electrons = int(sum(scf.mo_occ[active_space]))\n",
+    "num_elec_a = (n_electrons + mol.spin) // 2\n",
+    "num_elec_b = (n_electrons - mol.spin) // 2\n",
+    "cas = pyscf.mcscf.CASCI(scf, num_orbitals, (num_elec_a, num_elec_b))\n",
+    "mo = cas.sort_mo(active_space, base=0)\n",
+    "hcore, nuclear_repulsion_energy = cas.get_h1cas(mo)\n",
+    "eri = pyscf.ao2mo.restore(1, cas.get_h2cas(mo), num_orbitals)\n",
+    "\n",
+    "# Compute exact energy\n",
+    "exact_energy = cas.run().e_tot\n",
     "\n",
     "# Create a seed to control randomness throughout this workflow\n",
     "rng = np.random.default_rng(24)\n",
@@ -133,7 +157,7 @@
     }
    ],
    "source": [
-    "print(\"Exact energy: -109.10288938\")\n",
+    "print(\"Exact energy: {exact_energy}\")\n",
     "print(f\"Estimated energy: {np.min(e_hist[-1])}\")"
    ]
   }

docs/tutorials/01_chemistry_hamiltonian.ipynb

@@ -38,7 +38,7 @@
     "\\hat{a}_{r\\sigma}\n",
     "$$\n",
     "\n",
-    "$\\hat{a}^\\dagger_{p\\sigma}$/$\\hat{a}_{p\\sigma}$ are the fermionic creation/annihalation operators associated to the $p$-th basis set element and the spin $\\sigma$. $h_{pr}$ and $(pr|qs)$ are the one- and two-body electronic integrals. These are loaded from an ``fcidump`` file with standard chemistry software.\n",
+    "$\\hat{a}^\\dagger_{p\\sigma}$/$\\hat{a}_{p\\sigma}$ are the fermionic creation/annihalation operators associated to the $p$-th basis set element and the spin $\\sigma$. $h_{pr}$ and $(pr|qs)$ are the one- and two-body electronic integrals.\n",
     "\n",
     "The SQD workflow with  self-consistent configuration recovery is depicted in the following diagram.\n",
     "\n",
@@ -60,7 +60,7 @@
     "\n",
     "In this tutorial, we will approximate the ground state energy of an $N_2$ molecule. First, we will specify the molecule and its properties. Next, we will create a [local unitary cluster Jastrow (LUCJ)](https://pubs.rsc.org/en/content/articlelanding/2023/sc/d3sc02516k) ansatz (quantum circuit) to generate samples from a quantum computer for ground state energy estimation.\n",
     "\n",
-    "First, we will specify the molecule and its properties"
+    "First, we will specify the molecule and its properties."
    ]
   },
   {