experiments.ipynb

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   "source": [
    "# VQE experiments\n",
    "Runs VQE experiments on both the ideal QASM simulator and IBM Quantum Computers for different bond distances in the H2 molecule\n",
    "IBM-Q implementation trough Qiskit runtime so that error mitigation techniques can be easily activated (see `resilience_level` and documentation <https://qiskit.org/documentation/partners/qiskit_ibm_runtime/how_to/error-mitigation.html>)\n",
    "\n",
    "Additionally, for comparison, the exact solution for the ground state energy is computed through diagonalization of the Hamiltonian.\n",
    "\n",
    "Notebook created by **Jonas Jaeger** <jojaeger@cs.ubc.ca>"
   ],
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   "source": [
    "from hamiltonian import MolecularFermionicHamiltonian\n",
    "from mapping import JordanWigner\n",
    "from pyscf import gto\n",
    "from solver import ExactSolver\n",
    "from solver import VQESolver\n",
    "from estimator import BasicEstimator\n",
    "import csv\n",
    "from scipy.optimize import minimize\n",
    "from qiskit import Aer\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator, Session, Options\n",
    "from qiskit.circuit import Parameter, QuantumCircuit\n",
    "\n",
    "\n",
    "options = Options()\n",
    "options.resilience_level = 0\n",
    "options.optimization_level = 0\n",
    "service = QiskitRuntimeService(instance=\"ibm-q-qida/pinq2/winter-school\")\n",
    "session_backend = service.backends(\"ibmq_lima\")[0]\n",
    "\n",
    "# Define ansatz:\n",
    "varform_4qubits_1param = QuantumCircuit(4)\n",
    "a = Parameter('a')\n",
    "varform_4qubits_1param.ry(a,0)\n",
    "varform_4qubits_1param.cnot(0, 1)\n",
    "varform_4qubits_1param.cnot(1, 2)\n",
    "varform_4qubits_1param.cnot(2, 3)\n",
    "varform_4qubits_1param.x([1, 3])\n",
    "\n",
    "with open(\"dissociation_vals.csv\", \"a\") as csv_file:\n",
    "    writer = csv.writer(csv_file, delimiter=',')\n",
    "\n",
    "    with Session(service=service, backend=session_backend) as session:\n",
    "        runtime_estimator = Estimator(session=session, options=options)\n",
    "\n",
    "        # distance unit in AA\n",
    "        for distance in [0.735, 0.3, 0.5, 1., 1.5, 2.]: # or use: np.linspace(start=0.2, stop=2.5, num=100).tolist():\n",
    "            mol = gto.M(\n",
    "                atom = [['H', (0,0,-distance/2)], ['H', (0,0,distance/2)]],\n",
    "                basis = 'sto-3g'\n",
    "                )\n",
    "            energy_nuc = mol.energy_nuc()\n",
    "            print(distance)\n",
    "            molecular_hamiltonian_no_spin = MolecularFermionicHamiltonian.from_pyscf_mol(mol)\n",
    "            print(molecular_hamiltonian_no_spin)\n",
    "            print(*molecular_hamiltonian_no_spin.get_integrals(), sep=\"\\n\\n\")\n",
    "\n",
    "            molecular_hamiltonian = molecular_hamiltonian_no_spin.include_spin()\n",
    "\n",
    "            mapping = JordanWigner()\n",
    "            qubit_hamiltonian = mapping.fermionic_hamiltonian_to_qubit_hamiltonian(molecular_hamiltonian).sort()\n",
    "            print(qubit_hamiltonian)\n",
    "\n",
    "            # Exact\n",
    "            exact_solver = ExactSolver()\n",
    "            ground_state_value = exact_solver.lowest_eig_value(qubit_hamiltonian)\n",
    "            print('Ground state energy (electronic, exact) : ', ground_state_value)\n",
    "            print('Ground state energy (molecular, exact) : ', ground_state_value + energy_nuc)\n",
    "            exact_energy = ground_state_value + energy_nuc\n",
    "\n",
    "            # VQE Sim\n",
    "            backend = Aer.get_backend('qasm_simulator')\n",
    "            minimizer = lambda fct, start_param_values: minimize(\n",
    "                fct,\n",
    "                start_param_values,\n",
    "                method='SLSQP',\n",
    "                options={'maxiter': 20, 'eps': 1e-1, 'ftol': 1e-4, 'disp': True, 'iprint': 2})\n",
    "            varform = varform_4qubits_1param\n",
    "            execute_opts = {'shots': 8192}\n",
    "            estimator = BasicEstimator(varform, backend, execute_opts=execute_opts)\n",
    "            estimator.set_observable(qubit_hamiltonian)\n",
    "            vqe_solver = VQESolver(estimator, minimizer, [0, ], name='vqe_solver')\n",
    "            opt_value = vqe_solver.lowest_eig_value(qubit_hamiltonian)\n",
    "            print('Ground state position estimate (vqe) : ', vqe_solver.last_opt_params)\n",
    "            print('Ground state energy estimate (electronic, vqe) : ', opt_value)\n",
    "            print('Ground state energy estimate (molecular, vqe) : ', opt_value + energy_nuc)\n",
    "            vqe_energy_sim = opt_value + energy_nuc\n",
    "\n",
    "            # VQE IBMQ\n",
    "            minimizer = lambda fct, start_param_values: minimize(\n",
    "                fct,\n",
    "                start_param_values,\n",
    "                method='SLSQP',\n",
    "                options={'maxiter': 20, 'eps': 1e-1, 'ftol': 1e-4, 'disp': True, 'iprint': 2})\n",
    "            varform = varform_4qubits_1param\n",
    "            execute_opts = {'shots': 8192}\n",
    "            estimator = BasicEstimator(varform, runtime_estimator, execute_opts=execute_opts)\n",
    "            estimator.set_observable(qubit_hamiltonian)\n",
    "            vqe_solver = VQESolver(estimator, minimizer, [0, ], name='vqe_solver')\n",
    "            opt_value = vqe_solver.lowest_eig_value(qubit_hamiltonian)\n",
    "            print('Ground state position estimate (vqe) : ', vqe_solver.last_opt_params)\n",
    "            print('Ground state energy estimate (electronic, vqe) : ', opt_value)\n",
    "            print('Ground state energy estimate (molecular, vqe) : ', opt_value + energy_nuc)\n",
    "            vqe_energy_ibmq = opt_value + energy_nuc\n",
    "\n",
    "            writer.writerow([distance, exact_energy, vqe_energy_sim, vqe_energy_ibmq])"
   ]
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