final_submission.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "view-in-github"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jsaroni/QHack2023_Feynmanprodigies/blob/main/final_submission.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "0ov8nlwIjxBB"
      },
      "source": [
        "QHack2022 Open Hackathon - FEYNMAN PRODIGIES TEAM\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "Project Name: Efficient ground state computation methodologies for BeH2\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "In this notebook, we describe the implementation of different methodologies to find the ground state of the molecule BeH2, each with their own merits and drawbacks. The methods used consider only single and double excitations. Some of the methodologies that we implement greatly simplify the model while sacrificing chemical accuracy while others use error mitigation more efficiently through qiskit runtime which works well with hybrid algorithms such as VQE.\n",
        "\n",
        "\n",
        "We are trying to find the ground state of BeH2, so it is worth knowing more on its physical chemistry. Beryllium has chemical formula 1s2 2s2 and the two hydrogens 1s1 in electron configuration notation. When the molecule BeH2 is formed, the s orbitals from the two hydrogens hybridize with the p orbitals from beryllium to form two sp molecular orbital bonds that want to be as far away from each other as possible due to electron repulsion and this results in a linear molecule. We use the sto3g basis to approximate slater type orbitals."
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "GKqckBHOj3ZR"
      },
      "source": [
        "The following module need installation: qiskit for testing our quantum simulations, pyscf as an open source collection of electronic structure modules, qiskit_nature, and qiskit_ibm_runtime."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ExG_XkTuXRuu"
      },
      "outputs": [],
      "source": [
        "#Install the required packages\n",
        "'''\n",
        "!pip install qiskit\n",
        "!pip install pennylane\n",
        "!pip install qiskit_nature\n",
        "!pip install scipy\n",
        "!pip install pyscf\n",
        "!pip install qiskit_ibm_runtime\n",
        "'''\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#Load the required packages\n",
        "import pennylane.numpy as np\n",
        "import pennylane as qml\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "\n",
        "from qiskit import Aer, IBMQ, QuantumCircuit\n",
        "from qiskit.primitives import Estimator, BackendEstimator\n",
        "from qiskit.providers.aer import StatevectorSimulator\n",
        "from qiskit.utils import QuantumInstance\n",
        "\n",
        "from qiskit.tools.jupyter import *\n",
        "from qiskit.visualization import *\n",
        "\n",
        "from qiskit.algorithms import MinimumEigensolverResult, VQE\n",
        "from qiskit.algorithms.optimizers import SLSQP, SPSA\n",
        "\n",
        "\n",
        "from qiskit_nature.algorithms import GroundStateEigensolver, VQEUCCFactory\n",
        "from qiskit_nature.algorithms.ground_state_solvers.minimum_eigensolver_factories import NumPyMinimumEigensolverFactory\n",
        "from qiskit_nature.circuit.library import UCC, UCCSD\n",
        "from qiskit_nature.drivers import Molecule\n",
        "from qiskit_nature.drivers.second_quantization import ElectronicStructureDriverType, ElectronicStructureMoleculeDriver\n",
        "from qiskit_nature.converters.second_quantization import QubitConverter\n",
        "from qiskit_nature.mappers.second_quantization import BravyiKitaevMapper, JordanWignerMapper, ParityMapper\n",
        "from qiskit_nature.problems.second_quantization.electronic import ElectronicStructureProblem\n",
        "from qiskit_nature.transformers.second_quantization.electronic import ActiveSpaceTransformer\n",
        "\n",
        "from qiskit_nature.settings import settings\n",
        "\n",
        "settings.dict_aux_operators = True"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "VQE"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "First we do the usual hybrid VQE algorithm using single and double excitations UCCSD strategy. We use all such excitations to come up with the ground state energy calculation. \n",
        "\n",
        "For this setup we use 4 electrons in 6 orbitals inside the molecule. The pair of electrons in the 1s orbital(core) of Be atom are stable, therefore we don't include them in our active space. We use the sto-3g basis set and two-qubit reduction method using parity mapping to reduce the system size without affecting the calculation due to symmetry. We first find the true ground state energy which we will use throughout the file for reference, as the target. Note that this is calculated using NumpyEigenSolver. \n",
        "\n",
        "We then make a circuit and find the expected value of the hamiltonian using ADAM optimizer. \n",
        "\n",
        "We calculate the time taken for this method, along with the number of CNOT gates that are in the circuit. This number is calculated using the formula 13 x double_excitations + 2 x single_excitations. This is because of the number of CNOT gates using in the ansatz for the respective excitation schemes. Finally we plot the graph of the GS Energy calculation over time."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Coordinates(val) are given in Angstrom\n",
        "val = 1.291\n",
        "Beh2 = [[\"Be\", [0.0, 0.0, 0.0]],\n",
        "        [\"H\", [-val, 0.0, 0.0]], \n",
        "        [\"H\", [val, 0.0, 0.0]]]\n",
        "#define the molecule using qiskit_nature.drivers        \n",
        "BeH2 = Molecule( \n",
        "    geometry=Beh2 , # The coordinates\n",
        "    multiplicity=1, # 2*S + 1\n",
        "    charge=0,\n",
        ")\n",
        "#define driver using qiskit_nature.drivers.second_quantization\n",
        "driver = ElectronicStructureMoleculeDriver(BeH2, basis=\"sto3g\", driver_type=ElectronicStructureDriverType.PYSCF) \n",
        "\n",
        "properties = driver.run()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "num_alpha_electrons = properties.get_property('ParticleNumber').num_alpha\n",
        "num_beta_electrons = properties.get_property('ParticleNumber').num_beta\n",
        "num_spin_orbitals = int(properties.get_property('ParticleNumber').num_spin_orbitals)\n",
        "\n",
        "nuclear_rep_energy = properties.get_property('ElectronicEnergy').nuclear_repulsion_energy\n",
        "print(\"number of alpha electrons: \" , num_alpha_electrons)\n",
        "print(\"number of beta electrons: \" , num_beta_electrons)\n",
        "print(\"number of spin orbitals: \" , num_spin_orbitals)\n",
        "print(\"nuclear repulsion energy: \" , nuclear_rep_energy)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Check the occupation of the spin orbitals\n",
        "PN_property = properties.get_property(\"ParticleNumber\")\n",
        "\n",
        "\n",
        "#Now we remove/freeze the core orbital 1s of Be for the calculations\n",
        "# Define the active space around the Fermi level \n",
        "transformer = ActiveSpaceTransformer(\n",
        "    num_electrons=4, # Number of electrons in our active space\n",
        "    num_molecular_orbitals=6, # Number of orbitals in our active space\n",
        ")\n",
        "\n",
        "# Now we can get the reduced electronic structure problem\n",
        "problem_reduced = ElectronicStructureProblem(driver, transformers=[transformer]) \n",
        "\n",
        "# The second quantized Hamiltonian of the reduce problem\n",
        "second_q_ops_reduced = problem_reduced.second_q_ops()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#Using paritymapper to take advantage of the Z2 symmetry of the system\n",
        "mapper = ParityMapper()\n",
        "\n",
        "converter = QubitConverter(mapper)\n",
        "\n",
        "qubit_op = converter.convert(second_q_ops_reduced[\"ElectronicEnergy\"])\n",
        "#reduces the qubit number by 2\n",
        "parity_converter = QubitConverter(mapper, two_qubit_reduction=True)    \n",
        "\n",
        "# Compute the Hamitonian in qubit form\n",
        "qubit_op_parity = parity_converter.convert(second_q_ops_reduced.get('ElectronicEnergy'), num_particles=problem_reduced.num_particles)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#Use UCCSD ansatz to look for single and double excitation on noiseless simulator\n",
        "vqe_factory = VQEUCCFactory( \n",
        "    quantum_instance=Aer.get_backend(\"aer_simulator_statevector\"),\n",
        "    optimizer=SLSQP(maxiter=6,ftol = 1e-4),\n",
        "    ansatz=UCC(excitations='sd')\n",
        ") \n",
        "\n",
        "from qiskit.algorithms import NumPyMinimumEigensolver\n",
        "\n",
        "numpy_solver = NumPyMinimumEigensolver()\n",
        "\n",
        "#Find the real solution using classical method\n",
        "solver = GroundStateEigensolver(parity_converter, vqe_factory) \n",
        "real_solution_t = solver.solve(problem_reduced).total_energies[0]    \n",
        "print('Reference energy : ', real_solution_t)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "symbols = [\"H\",\"Be\",\"H\"]\n",
        "geometry = np.array([ -1.291/0.529, 0.0, 0.0,0.0, 0.0, 0.0, 1.291/0.529, 0.0, 0.0])\n",
        "#define the hamiltonian of the system\n",
        "hamil = qml.qchem.molecular_hamiltonian(symbols,geometry,charge = 0,basis = 'sto-3g', active_electrons=4, active_orbitals=6)[0]\n",
        "#number of qubits\n",
        "n_qubits = len(hamil.wires)\n",
        "\n",
        "#define the hf state\n",
        "hf_state = qml.qchem.hf_state(electrons=4, orbitals=n_qubits)\n",
        "# singles and doubles are used to make the AllSinglesDoubles template\n",
        "singles, doubles = qml.qchem.excitations(4, n_qubits)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "%%time\n",
        "from qiskit.utils import algorithm_globals\n",
        "algorithm_globals.random_seed = 10\n",
        "\n",
        "\n",
        "\n",
        "dev = qml.device(\"default.qubit\", wires=n_qubits)\n",
        "@qml.qnode(dev)\n",
        "\n",
        "\n",
        "def cost(weights):\n",
        "    qml.BasisState(hf_state, wires=list(range(n_qubits)))\n",
        "    for i in range(len(singles)):            \n",
        "        qml.SingleExcitation(weights[i+len(doubles)], wires=singles[i])\n",
        "    for i in range(len(doubles)):\n",
        "        qml.DoubleExcitation(weights[i], wires=doubles[i])        \n",
        "    return qml.expval(hamil)\n",
        "\n",
        "weights =np.zeros(len(doubles + singles), requires_grad=True)\n",
        "opt = qml.AdamOptimizer(stepsize=0.05)\n",
        "i=0\n",
        "iter=[]\n",
        "cost_val=[]\n",
        "Lowest_E=0\n",
        "best_weights=0\n",
        "for _ in range(30):\n",
        "    weights = opt.step(cost, weights)\n",
        "    iter.append(i)\n",
        "    cost_fn=cost(weights)\n",
        "    if Lowest_E>cost_fn:\n",
        "        Lowest_E=cost_fn\n",
        "        best_weights=weights\n",
        "    cost_val.append(cost_fn)\n",
        "    print('iter:',i,' cost_fn:',cost_fn)\n",
        "    i=i+1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#Total number of 2-qubit (CNOT) gates\n",
        "print(\"Total number of CNOT gates used = \", 13*len(doubles) + 2*len(singles)) "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# The following plot is of full VQE\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(cost_val, label=\"Estimator VQE BeH2 IDEAL\")\n",
        "plt.axhline(y=real_solution_t.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "ADAPT_VQE"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "In the previous calculation, we used all the single and double excitations, however, one can reduce their number by looking at the gradient w.r.t. parameters for those schemes. The idea is that if the parameters remain constant, then we can train the schemes where parameters need to change in order to reduce the time as well as the number of gates required.\n",
        "\n",
        "The same is demonstrated using ADAPT_VQE, where we 'ADAPT' to non-vanishing gradients and using a similar ansatz with restricted number of schemes, we get much faster and better results. This is basically due to the classical preprocessing of data.\n",
        "\n",
        "The convergence can be seen after merely 10 iterations and the time taken is less than a minute for optimization. The number of CNOT gates already reduce by a factor of 10."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#We use pennylane for faster computation\n",
        "\n",
        "#Define the symbol and geometry\n",
        "symbols = [\"H\",\"Be\",\"H\"]\n",
        "#Geometry in atomic distance for pennylane\n",
        "geometry = np.array([ -1.291/0.529, 0.0, 0.0,0.0, 0.0, 0.0, 1.291/0.529, 0.0, 0.0])\n",
        "active_electrons = 4\n",
        "H, qubits = qml.qchem.molecular_hamiltonian(\n",
        "    symbols,\n",
        "    geometry,\n",
        "    active_electrons=active_electrons,\n",
        "    active_orbitals=6\n",
        ")\n",
        "\n",
        "print(f\"Total number of excitations = {len(singles) + len(doubles)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "\n",
        "\n",
        "def circuit_1(params, excitations):\n",
        "    qml.BasisState(hf_state, wires=range(qubits))\n",
        "\n",
        "    for i, excitation in enumerate(excitations):\n",
        "        if len(excitation) == 4:\n",
        "            qml.DoubleExcitation(params[i], wires=excitation)\n",
        "        else:\n",
        "            qml.SingleExcitation(params[i], wires=excitation)\n",
        "    return qml.expval(H)\n",
        "dev = qml.device(\"default.qubit\", wires=qubits)\n",
        "cost_fn = qml.QNode(circuit_1, dev)\n",
        "\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0)\n",
        "\n",
        "params = [0.0] * len(doubles)\n",
        "grads = circuit_gradient(params, excitations=doubles)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "doubles_select = [doubles[i] for i in range(len(doubles)) if abs(grads[i]) > 1.0e-5]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "opt = qml.GradientDescentOptimizer(stepsize=0.5)\n",
        "\n",
        "params_doubles = np.zeros(len(doubles_select), requires_grad=True)\n",
        "\n",
        "for n in range(20):\n",
        "    params_doubles = opt.step(cost_fn, params_doubles, excitations=doubles_select)\n",
        "def circuit_2(params, excitations, gates_select, params_select):\n",
        "    qml.BasisState(hf_state, wires=range(qubits))\n",
        "\n",
        "    for i, gate in enumerate(gates_select):\n",
        "        if len(gate) == 4:\n",
        "            qml.DoubleExcitation(params_select[i], wires=gate)\n",
        "        elif len(gate) == 2:\n",
        "            qml.SingleExcitation(params_select[i], wires=gate)\n",
        "\n",
        "    for i, gate in enumerate(excitations):\n",
        "        if len(gate) == 4:\n",
        "            qml.DoubleExcitation(params[i], wires=gate)\n",
        "        elif len(gate) == 2:\n",
        "            qml.SingleExcitation(params[i], wires=gate)\n",
        "    return qml.expval(H)\n",
        "cost_fn = qml.QNode(circuit_2, dev)\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0)\n",
        "params = [0.0] * len(singles)\n",
        "\n",
        "grads = circuit_gradient(\n",
        "    params,\n",
        "    excitations=singles,\n",
        "    gates_select=doubles_select,\n",
        "    params_select=params_doubles\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "singles_select = [singles[i] for i in range(len(singles)) if abs(grads[i]) > 1.0e-5 ]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "cost_fn = qml.QNode(circuit_1, dev)\n",
        "\n",
        "params = np.zeros(len(doubles_select + singles_select), requires_grad=True)\n",
        "\n",
        "gates_select = doubles_select + singles_select\n",
        "energy_vals = []\n",
        "import time\n",
        "for n in range(20):\n",
        "    t1 = time.time()\n",
        "    params, energy = opt.step_and_cost(cost_fn, params, excitations=gates_select)\n",
        "    t2 = time.time()\n",
        "    energy_vals.append(energy)\n",
        "    print(\"n = {:},  E = {:.8f} H, t = {:.2f} s\".format(n, energy, t2 - t1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#Total number of 2 qubit gates used\n",
        "print('Total number of CNOT qubit gates used =', 13*len(doubles_select) + 2*len(singles_select))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# The following plot is of ADAPT_VQE\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(energy_vals, label=\"ADAPT VQE BeH2 IDEAL\")\n",
        "plt.axhline(y=real_solution_t.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "TETRIS_VQE"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "TETRIS_VQE is a dynamic circuit design based on the idea of ADAPT VQE. \n",
        "\n",
        "Instead of using the same number of gates to begin with, the idea is to keep adding gates until we converge. We start with some scheme with non-zero gradient sorted in an order. We run the optimization method for that fixed circuit and calulcate the GS Energy. After each iteration, we add more schemes from the bigger pool in a constrained manner.\n",
        "\n",
        "In this work, we look at the closeness to the actual solution. By this, we mean that we stop if the GS Energy we get after dynamic addition of schemes to circuits is close to the real energy calculated above. Another method could be to use the different in the energy values and decide convergence on that. \n",
        "\n",
        "This method could be useful for large circuits where the number of schemes is large so that a step by step addition results in a better convergence. \n",
        "\n",
        "In our code, we get the convergence we want, with time and CNOT gates in between VQE and ADAPT VQE."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "\n",
        "#Define the symbol and geometry\n",
        "symbols = [\"H\",\"Be\",\"H\"]\n",
        "#Geometry in atomic distance for pennylane\n",
        "geometry = np.array([ -1.291/0.529, 0.0, 0.0,0.0, 0.0, 0.0, 1.291/0.529, 0.0, 0.0])\n",
        "active_electrons = 4\n",
        "H, qubits = qml.qchem.molecular_hamiltonian(\n",
        "    symbols,\n",
        "    geometry,\n",
        "    charge = 0,\n",
        "    active_electrons=active_electrons,\n",
        "    basis = 'sto-3g',\n",
        "    active_orbitals=6\n",
        ")\n",
        "n_qubits = qubits\n",
        "#HF State\n",
        "hf_state= qml.qchem.hf_state(electrons=active_electrons, orbitals=n_qubits)\n",
        "\n",
        "\n",
        "#all the operators together\n",
        "all_operators=singles+doubles\n",
        "\n",
        "params = [0.0] * len(doubles+singles)\n",
        "params=np.array(params )\n",
        "\n",
        "#define the circuit again\n",
        "def circuit_1(params, excitations):\n",
        "        qml.BasisState(hf_state, wires=range(n_qubits))\n",
        "\n",
        "        for i, excitation in enumerate(excitations):\n",
        "            if len(excitation) == 4:\n",
        "                qml.DoubleExcitation(params[i], wires=excitation)\n",
        "            else:\n",
        "                qml.SingleExcitation(params[i], wires=excitation)\n",
        "        return qml.expval(H )\n",
        "\n",
        "    \n",
        "    \n",
        "dev = qml.device(\"default.qubit\", wires=n_qubits)\n",
        "cost_fn = qml.QNode(circuit_1, dev)\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0)\n",
        "grads = circuit_gradient(params, excitations=doubles+singles)\n",
        "\n",
        "#operators in the opposite manner\n",
        "opposite_pool=doubles+singles\n",
        "\n",
        "#Thresholding the excitations\n",
        "new_opposite_pool=[opposite_pool[idx] for idx in range(len(grads)) if abs(grads[idx]) >1e-5]\n",
        "#gradients for the excitations thresholded\n",
        "new_grads=[grads[idx] for idx in range(len(grads)) if abs(grads[idx]) > 1e-5]\n",
        "   \n",
        "#Now we sort these gradients and we will apply it sequentially\n",
        "indx=np.argsort(np.abs(new_grads))\n",
        "sorted_opposite_pool=[new_opposite_pool[idx] for idx in indx]\n",
        "\n",
        "#For the shallower circuit, we will use this\n",
        "shallow_circuits=[]    \n",
        "while len(sorted_opposite_pool) !=0:\n",
        "    q_layer=[]     \n",
        "    ind_left=[]  \n",
        "    for idx, op in enumerate(sorted_opposite_pool):\n",
        "        if shallow_circuits==[]:\n",
        "            shallow_circuits.append(op)\n",
        "            q_layer=q_layer+op\n",
        "        else:\n",
        "            Stack=True\n",
        "            for k in op:\n",
        "                if k in q_layer:\n",
        "                    Stack=False\n",
        "                    ind_left.append(idx)\n",
        "                    break\n",
        "            if Stack:\n",
        "                shallow_circuits.append(op)\n",
        "                q_layer=q_layer+op\n",
        "    sorted_opposite_pool=[sorted_opposite_pool[idx] for idx in ind_left]\n",
        "\n",
        "params = [0.0] * len(doubles_select+singles_select)\n",
        "params=np.array(params )\n",
        "\n",
        "q_layer=[]\n",
        "time_iterations=20\n",
        "conv_tol=1e-4\n",
        "energy=[]\n",
        "\n",
        "opt = qml.GradientDescentOptimizer(stepsize=0.3) \n",
        "dev = qml.device(\"default.qubit\", wires=n_qubits)\n",
        "\n",
        "cost_fn = qml.QNode(circuit_1, dev, expansion_strategy=\"device\")\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0) # step 2.\n",
        "\n",
        "energy = [cost_fn(params, shallow_circuits)] # step 2.\n",
        "print(f\"time_iteration = 0,  Energy = {energy[-1]:.8f} Ha\")\n",
        "print(\"Number of gates = {}\\n\".format(len(shallow_circuits)))\n",
        "configs=qml.specs(cost_fn)(params, excitations=shallow_circuits)\n",
        "print(\"Circuit Depth = {}\\n\".format(configs['depth'],))\n",
        "t1 = time.time()\n",
        "for n in range(time_iterations):\n",
        "\n",
        "    Test_set=shallow_circuits+all_operators\n",
        "    Test_parameters=list(params)+[0.0]*len(all_operators)\n",
        "    Test_parameters=np.array(Test_parameters)\n",
        "        \n",
        "    test_grads = circuit_gradient(Test_parameters,Test_set)\n",
        "    test_grads = test_grads[len(params):]\n",
        "\n",
        "    test_sorted_indx=np.argsort(np.abs(test_grads))[::-1]\n",
        "    maxpos=test_sorted_indx[0]\n",
        "    Larger_sorted_indx=[]\n",
        "    for ind in test_sorted_indx:\n",
        "        Larger_sorted_indx.append(ind)\n",
        "\n",
        "    for k,ind in enumerate(Larger_sorted_indx):\n",
        "        op_set=set(all_operators[ind])\n",
        "        q_layer_set=set(q_layer)\n",
        "        if not bool(op_set & q_layer_set):\n",
        "            q_layer=q_layer+all_operators[ind]\n",
        "            shallow_circuits.append(all_operators[ind])\n",
        "            params=np.append(params, 0.0)\n",
        "        if (len(q_layer)>=n_qubits-4): # It is hard to find the operators with non-zero gradient fill all qubit layers.\n",
        "            q_layer=[]                                 # We leave at maximum 4 idle qubits\n",
        "            break\n",
        "\n",
        "\n",
        "    params,_ = opt.step(cost_fn, params, shallow_circuits) # Step 5.\n",
        "    E_val=cost_fn(params, shallow_circuits)\n",
        "    energy.append(E_val)\n",
        "    conv = np.abs(real_solution_t.real - E_val) #step 3.\n",
        "\n",
        "    print(f\"time_iteration = {n+1}, Energy = {energy[-1]:.8f} Ha\")\n",
        "    print(\"Number of gates = {}\\n\".format(len(shallow_circuits)))\n",
        "    configs=qml.specs(cost_fn)(params, excitations=shallow_circuits)\n",
        "    print(\"Circuit Depth = {}\\n\".format(configs['depth'],))\n",
        "    if conv <= conv_tol:\n",
        "        break\n",
        "t2 = time.time()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# The following plot is of ADAPT_VQE\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(energy, label=\"TETRIS ADAPT VQE BeH2 IDEAL\")\n",
        "plt.axhline(y=real_solution_t.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"TETRIS ADAPT VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "num_two_gates = 0\n",
        "for ele in shallow_circuits:\n",
        "    if len(ele)==2:\n",
        "        num_two_gates+=2\n",
        "    else:\n",
        "        num_two_gates+=13\n",
        "print('Number of two qubit CNOT gates for TETRIS ADAPT VQE is', num_two_gates)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "print('Time taken =', t2-t1)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plotting the three different techniques overlaid on each other for comparison"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(cost_val[:20], label=\"VQE\")\n",
        "plt.plot(energy_vals, label=\"ADAPT_VQE\")\n",
        "plt.plot(energy, label=\"TETRIS_ADAPT_VQE\")\n",
        "plt.axhline(y=real_solution_t.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "So far we used hybrid algorithm VQE with different techniques to get estimates on a noiseless (simulated) quantum backend. However, on real quantum devices, the errors propagate pretty fast. Therefore, we need error mitigation techniques. \n",
        "\n",
        "Furthermore, we need to apply it to systems where the number of two qubit gates (most prone to error after toffoli) are minimized. To resolve this issue, we look at a smaller system"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now using error mitigation with qiskit runtime and just VQE. This method is based on a crude approximation, restricting the Hilbert space to an active space of unbonded electrons within the BeH2 molecule.. The circuits take longer to run depending on how available the ibm backend is but achieve error mitigated results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#Load the required packages\n",
        "import pennylane.numpy as np\n",
        "import pennylane as qml\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "\n",
        "from qiskit import Aer, IBMQ, QuantumCircuit\n",
        "from qiskit.primitives import Estimator, BackendEstimator\n",
        "from qiskit.providers.aer import StatevectorSimulator\n",
        "from qiskit.utils import QuantumInstance\n",
        "\n",
        "from qiskit.tools.jupyter import *\n",
        "from qiskit.visualization import *\n",
        "\n",
        "from qiskit.algorithms import MinimumEigensolverResult, VQE\n",
        "from qiskit.algorithms.optimizers import SLSQP, SPSA\n",
        "\n",
        "\n",
        "from qiskit_nature.algorithms import GroundStateEigensolver, VQEUCCFactory\n",
        "from qiskit_nature.algorithms.ground_state_solvers.minimum_eigensolver_factories import NumPyMinimumEigensolverFactory\n",
        "from qiskit_nature.circuit.library import UCC, UCCSD\n",
        "from qiskit_nature.drivers import Molecule\n",
        "from qiskit_nature.drivers.second_quantization import ElectronicStructureDriverType, ElectronicStructureMoleculeDriver\n",
        "from qiskit_nature.converters.second_quantization import QubitConverter\n",
        "from qiskit_nature.mappers.second_quantization import BravyiKitaevMapper, JordanWignerMapper, ParityMapper\n",
        "from qiskit_nature.problems.second_quantization.electronic import ElectronicStructureProblem\n",
        "from qiskit_nature.transformers.second_quantization.electronic import ActiveSpaceTransformer\n",
        "\n",
        "from qiskit_nature.settings import settings\n",
        "\n",
        "settings.dict_aux_operators = True"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U7CpsxQuj_gd"
      },
      "source": [
        "We use the linear geometry of the molecule and set a distance d as rougly the equilibrium distance of the two hydrogen atoms from beryllium which is 1.29 Angstroms."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JimUdlD6XzAr"
      },
      "outputs": [],
      "source": [
        "#### Fill in the values below and complete the function to define the Molecule ####\n",
        "d = 1.291\n",
        "# Coordinates are given in Angstrom\n",
        "# Replace BeH2 with appropriate molecule\n",
        "beh2 = [[\"Be\", [0, 0.0, 0.0]], \n",
        "              [\"H\", [-d, 0.0, 0.0]],\n",
        "              [\"H\", [d, 0.0, 0.0]]]\n",
        "                  \n",
        "BeH2 = Molecule( \n",
        "    geometry= beh2,  \n",
        "    multiplicity= 1, \n",
        "    charge= 0, \n",
        ")\n",
        "\n",
        "driver = ElectronicStructureMoleculeDriver(BeH2, basis=\"sto3g\", driver_type=ElectronicStructureDriverType.PYSCF) \n",
        "\n",
        "properties = driver.run()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "num_alpha_electrons = properties.get_property('ParticleNumber').num_alpha\n",
        "num_beta_electrons = properties.get_property('ParticleNumber').num_beta\n",
        "num_spin_orbitals = int(properties.get_property('ParticleNumber').num_spin_orbitals)\n",
        "\n",
        "nuclear_rep_energy = properties.get_property('ElectronicEnergy').nuclear_repulsion_energy\n",
        "print(\"number of alpha electrons: \" , num_alpha_electrons)\n",
        "print(\"number of beta electrons: \" , num_beta_electrons)\n",
        "print(\"number of spin orbitals: \" , num_spin_orbitals)\n",
        "print(\"nuclear repulsion energy: \" , nuclear_rep_energy)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Check the occupation of the spin orbitals\n",
        "PN_property = properties.get_property(\"ParticleNumber\")\n",
        "\n",
        "# Define the active space around the Fermi level \n",
        "# (selected automatically around the HOMO and LUMO, ordered by energy)\n",
        "transformer = ActiveSpaceTransformer(\n",
        "    num_electrons=2, # Number of electrons in our active space\n",
        "    num_molecular_orbitals=2, # Number of orbitals in our active space\n",
        ")\n",
        "\n",
        "# Now you can get the reduced electronic structure problem\n",
        "problem_reduced = ElectronicStructureProblem(driver, transformers=[transformer]) \n",
        "\n",
        "# The second quantized Hamiltonian of the reduce problem\n",
        "second_q_ops_reduced = problem_reduced.second_q_ops()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Setup the mapper and qubit converter\n",
        "mapper_type = 'ParityMapper'\n",
        "\n",
        "if mapper_type == 'ParityMapper':\n",
        "    mapper = ParityMapper()\n",
        "elif mapper_type == 'JordanWignerMapper':\n",
        "    mapper = JordanWignerMapper()\n",
        "elif mapper_type == 'BravyiKitaevMapper':\n",
        "    mapper = BravyiKitaevMapper()\n",
        "\n",
        "\n",
        "converter = QubitConverter(mapper)\n",
        "\n",
        "qubit_op = converter.convert(second_q_ops_reduced[\"ElectronicEnergy\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Set the mapper to qubits\n",
        "parity_mapper = ParityMapper() \n",
        "\n",
        "# Set the qubit converter with two qubit reduction to reduce the computational cost \n",
        "parity_converter = QubitConverter(parity_mapper, two_qubit_reduction=True)    \n",
        "\n",
        "# Compute the Hamitonian in qubit form\n",
        "qubit_op_parity = parity_converter.convert(second_q_ops_reduced.get('ElectronicEnergy'), num_particles=problem_reduced.num_particles)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "vqe_factory = VQEUCCFactory( # This is an example of UCC\"SD\" ansatz\n",
        "    quantum_instance=Aer.get_backend(\"aer_simulator_statevector\"),\n",
        "    optimizer=SLSQP(),\n",
        "    ansatz=UCC(excitations='sd')\n",
        ") \n",
        "\n",
        "from qiskit.algorithms import NumPyMinimumEigensolver\n",
        "\n",
        "numpy_solver = NumPyMinimumEigensolver()\n",
        "\n",
        "solver = GroundStateEigensolver(parity_converter, vqe_factory)  # Define Numpy\n",
        "real_solution_t = solver.solve(problem_reduced).total_energies[0]    \n",
        "print('Reference energy : ', real_solution_t)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Define our 'ansatz' for the problem\n",
        "ansatz = UCC(\n",
        "    qubit_converter=parity_converter,\n",
        "    num_particles=problem_reduced.num_particles, \n",
        "    num_spin_orbitals=problem_reduced.num_spin_orbitals,\n",
        "    excitations='sd'\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "token = ''\n",
        "IBMQ.save_account(token)\n",
        "service = QiskitRuntimeService()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#using qasm simulator\n",
        "backend = service.backends(simulator=True)[0]\n",
        "noisy_sim = FakeManila()\n",
        "#noisy_sim = FakeGuadalupe()\n",
        "#for running on real quantum device\n",
        "#backend = 'ibmq_lima'\n",
        "#backend = 'ibmq_guadalupe'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "service = QiskitRuntimeService(\n",
        "    channel='ibm_quantum',\n",
        "    instance='qhack-event/main/level-2-team-1',\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#for noisy simulator\n",
        "noise_model = NoiseModel.from_backend(noisy_sim)\n",
        "\n",
        "options_with_em = Options(\n",
        "    simulator={\n",
        "        \"noise_model\": noise_model,\n",
        "        \"seed_simulator\": 42,\n",
        "    },  \n",
        "    resilience_level=1 # You may change the value here. resilience_level = 1 will activate TREX\n",
        ")\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "%%time\n",
        "from qiskit.utils import algorithm_globals\n",
        "algorithm_globals.random_seed = 1024\n",
        "\n",
        "# Define convergence list\n",
        "convergence = []\n",
        "\n",
        "# Keep track of jobs \n",
        "job_list = []\n",
        "\n",
        "# Initialize estimator object\n",
        "#estimator = Estimator()\n",
        "\n",
        "# Define evaluate_expectation function\n",
        "def evaluate_expectation(x):\n",
        "    x = list(x)\n",
        "    \n",
        "    # Define estimator run parameters\n",
        "\n",
        "    with Session(service=service, backend=backend):\n",
        "      estimator = Estimator(options=options_with_em)\n",
        "      job = estimator.run(circuits=[ansatz], parameter_values=[x],observables=qubit_op_parity).result()\n",
        "      results = job.values[0]\n",
        "      job_list.append(job)\n",
        "\n",
        "\n",
        "    # Pass results back to callback function\n",
        "    return np.real(results)\n",
        "\n",
        "\n",
        "\n",
        "# Call back function\n",
        "def callback(x,fx,ax,tx,nx):\n",
        "    # Callback function to get a view on internal states and statistics of the optimizer for visualization\n",
        "    convergence.append(evaluate_expectation(fx))\n",
        "\n",
        "np.random.seed(10)\n",
        "\n",
        "# Define initial point. We shall define a random point here based on the number of parameters in our ansatz\n",
        "initial_point = np.random.random(ansatz.num_parameters)\n",
        "\n",
        "\n",
        "# Define optimizer and pass callback function\n",
        "optimizer = SPSA(maxiter = 50, callback=callback)\n",
        "\n",
        "# Define minimize function\n",
        "result =  optimizer.minimize(evaluate_expectation, x0=initial_point) "
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The energy is measured in Hartrees."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "Energy_H_t = []\n",
        "for i in range(len(convergence)):\n",
        "    sol = MinimumEigensolverResult()\n",
        "    sol.eigenvalue = convergence[i]\n",
        "    sol = problem_reduced.interpret(sol).total_energies[0]\n",
        "    Energy_H_t.append(sol)\n",
        "print(\"Computed Energy:\", Energy_H_t[-1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# The following plot compares the two Estimators - with and without noise\n",
        "\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(Energy_H_t, label=\"Estimator VQE BeH2+NOISY+TREX\")\n",
        "plt.axhline(y=real_solution_t.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()\n",
        "\n",
        "print(Energy_H_t)\n",
        "print(real_solution_t.real)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The graph below shows the use of Twirled Readout Error eXtinction (TREX) error mitgation with FakeManila. resilience_level=2 uses zero-noise extrapolation (ZNE) and resilience_level=3 probabilistic error cancellation. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#the list below is obtained from running the above code using FakeManila() backend with TREX\n",
        "\n",
        "Energy = [(-15.308589894649552+0j), (-15.376219303406794+0j), (-15.39387021095869+0j), (-15.41320988016764+0j), (-15.424979665346248+0j), (-15.43005680849908+0j), (-15.458793700847162+0j), (-15.446448283806754+0j), (-15.4898171094885+0j), (-15.476441721587053+0j), (-15.474969955813778+0j), (-15.502844077303289+0j), (-15.497264640785085+0j), (-15.50411400536762+0j), (-15.522390027528557+0j), (-15.511767919548054+0j), (-15.546447335850596+0j), (-15.507244766958324+0j), (-15.514498135878798+0j), (-15.528440541600068+0j), (-15.505466876966013+0j), (-15.534659182874288+0j), (-15.506999906756407+0j), (-15.510933484293696+0j), (-15.523721688697963+0j), (-15.510674314602634+0j), (-15.527421789425498+0j), (-15.533565249430302+0j), (-15.505068081695628+0j), (-15.52178684825123+0j), (-15.517105482753143+0j), (-15.51841838222561+0j), (-15.515969684471115+0j), (-15.52842328809817+0j), (-15.531562898320603+0j), (-15.530992698664287+0j), (-15.551054905020186+0j), (-15.519531658012843+0j), (-15.507667899741014+0j), (-15.515193693691847+0j), (-15.533802941657433+0j), (-15.528088837443674+0j), (-15.504669734193806+0j), (-15.539639668296635+0j), (-15.510747126847535+0j), (-15.513427925056904+0j), (-15.52002162186678+0j), (-15.526629340135559+0j), (-15.516375594669652+0j), (-15.505610970793215+0j)]\n",
        "\n",
        "Target_E = -15.561651427447169\n",
        "\n",
        "E = []\n",
        "for i in range(len(Energy)):\n",
        "    E.append(np.real(Energy[i]))\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0x318af68>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(E, label=\"Estimator VQE BeH2+NOISY+TREX\")\n",
        "plt.axhline(y=Target_E, color=\"tab:red\", ls=\"--\", label=\"Target, d = 1.291 Angstroms\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": []
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Additionally we have error mitigated results from the real backend ibmq_lima using TREX and ZNE. While TREX results show monotonic convergence to the ground state, we show ZNE results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "backend = 'ibmq_lima'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "service = QiskitRuntimeService(\n",
        "    channel='ibm_quantum',\n",
        "    instance='qhack-event/main/level-2-team-1',\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "options_with_em = Options(resilience_level=2 # You may change the value here. resilience_level = 1 will activate TREX\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "%%time\n",
        "from qiskit.utils import algorithm_globals\n",
        "algorithm_globals.random_seed = 1024\n",
        "\n",
        "# Define convergence list\n",
        "convergence = []\n",
        "\n",
        "# Keep track of jobs (Do-not-modify)\n",
        "job_list = []\n",
        "\n",
        "# Initialize estimator object\n",
        "#estimator = Estimator()# Enter your code here\n",
        "\n",
        "# Define evaluate_expectation function\n",
        "def evaluate_expectation(x):\n",
        "    x = list(x)\n",
        "    \n",
        "    # Define estimator run parameters\n",
        "    #### enter your code below ####\n",
        "\n",
        "\n",
        "\n",
        "    with Session(service=service, backend=backend):\n",
        "      estimator = Estimator(options=options_with_em)\n",
        "      job = estimator.run(circuits=[ansatz], parameter_values=[x],observables=qubit_op_parity).result()\n",
        "      results = job.values[0]\n",
        "      job_list.append(job)\n",
        "\n",
        "\n",
        "    # Pass results back to callback function\n",
        "    return np.real(results)\n",
        "\n",
        "\n",
        "\n",
        "# Call back function\n",
        "def callback(x,fx,ax,tx,nx):\n",
        "    # Callback function to get a view on internal states and statistics of the optimizer for visualization\n",
        "    convergence.append(evaluate_expectation(fx))\n",
        "\n",
        "np.random.seed(10)\n",
        "\n",
        "# Define initial point. We shall define a random point here based on the number of parameters in our ansatz\n",
        "initial_point = np.random.random(ansatz.num_parameters)\n",
        "\n",
        "#### enter your code below ####\n",
        "# Define optimizer and pass callback function\n",
        "optimizer = SPSA(maxiter = 50, callback=callback) # ----------- Enter your code here\n",
        "\n",
        "# Define minimize function\n",
        "result =  optimizer.minimize(evaluate_expectation, x0=initial_point) # ----------- Enter your code here"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "Energy_H_t = []\n",
        "for i in range(len(convergence)):\n",
        "    sol = MinimumEigensolverResult()\n",
        "    sol.eigenvalue = convergence[i]\n",
        "    sol = problem_reduced.interpret(sol).total_energies[0]\n",
        "    Energy_H_t.append(sol)\n",
        "print(\"Computed Energy:\", Energy_H_t[-1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "#the list below is obtained from running the above code using ibmq_lima backend with ZNE.\n",
        "\n",
        "Energy = [(-15.299725496726987+0j), (-15.404457371901044+0j), (-15.432048634488877+0j), (-15.479413567324093+0j), (-15.484154453097942+0j), (-15.498274731551897+0j), (-15.502134849652316+0j), (-15.501013354303835+0j), (-15.519383560872486+0j), (-15.525552730938573+0j), (-15.554337105185438+0j), (-15.554400483338556+0j), (-15.551891864562178+0j), (-15.545635016923596+0j), (-15.555698525879142+0j), (-15.551595355187027+0j), (-15.550354849219326+0j), (-15.551810351294685+0j), (-15.551651191275324+0j), (-15.54715839405482+0j), (-15.551579926022692+0j), (-15.549270670410346+0j), (-15.550742270040319+0j), (-15.558344780907598+0j), (-15.549046655882846+0j), (-15.554513011088916+0j), (-15.552365255003002+0j), (-15.552115439722515+0j), (-15.552561179281044+0j), (-15.548556478987896+0j), (-15.548150337736507+0j), (-15.550477227254524+0j), (-15.552545202356784+0j), (-15.549357297389344+0j), (-15.553080711408695+0j), (-15.553468837096995+0j), (-15.550786010522367+0j), (-15.550639970088818+0j), (-15.551100054992032+0j), (-15.551329759565471+0j), (-15.547600770146323+0j), (-15.5489985182846+0j), (-15.55645182159987+0j), (-15.55738365191599+0j), (-15.551482890586493+0j), (-15.551267266507073+0j), (-15.553622111797393+0j), (-15.553782805606561+0j), (-15.55176306113025+0j), (-15.550018243753359+0j)]\n",
        "\n",
        "Target_E = -15.561651427447183\n",
        "\n",
        "E = []\n",
        "for i in range(len(Energy)):\n",
        "    E.append(np.real(Energy[i]))\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<pyolite.display.Image at 0x3894850>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(E, label=\"Estimator VQE BeH2+ibmq_lima+ZNE\")\n",
        "plt.axhline(y=Target_E, color=\"tab:red\", ls=\"--\", label=\"Target d = 1.291 Angstroms\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The results show that the qiskit runtime error mitigation works quite well."
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We also use entanglement forging from circuit knitting toolbox to reduce the complexity of the problem while sacrificing chemical accuracy."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "from qiskit_nature.drivers import Molecule\n",
        "from qiskit_nature.drivers.second_quantization import PySCFDriver\n",
        "from qiskit_nature.problems.second_quantization import ElectronicStructureProblem\n",
        "from qiskit_nature.transformers.second_quantization.electronic import ActiveSpaceTransformer\n",
        "molecule = Molecule(\n",
        "    geometry=[\n",
        "        (\"Be\",[0.0,0.0,0.0]),\n",
        "        (\"H\", [0.0, 0.0, -1.3]),\n",
        "        (\"H\", [0.0, 0.0, 1.3]),\n",
        "    ],\n",
        "    charge=0,\n",
        "    multiplicity=1,\n",
        ")\n",
        "driver = PySCFDriver.from_molecule(molecule=molecule, basis=\"sto3g\")\n",
        "\n",
        "\n",
        "transformer = ActiveSpaceTransformer(\n",
        "    num_electrons=6, # Number of electrons in our active space\n",
        "    num_molecular_orbitals=2, # Number of orbitals in our active space\n",
        ")\n",
        "problem = ElectronicStructureProblem(\n",
        "        driver,\n",
        "        [transformer])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "from circuit_knitting_toolbox.entanglement_forging import EntanglementForgingAnsatz\n",
        "from qiskit.circuit.library import TwoLocal\n",
        "\n",
        "ansatz = EntanglementForgingAnsatz(\n",
        "    circuit_u=TwoLocal(2, [], \"cry\", [[0, 1], [1,0]], reps=1),\n",
        "    bitstrings_u=[(0,1),(1,0)],\n",
        ")\n",
        "\n",
        "ansatz.circuit_u.draw()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "from qiskit_ibm_runtime import QiskitRuntimeService, Options\n",
        "\n",
        "# By default, use a local simulator to implement the Qiskit Runtime Primitives\n",
        "service = None\n",
        "\n",
        "# Uncomment the following line to instead use the Qiskit Runtime Service.\n",
        "# service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
        "\n",
        "backend_names = [\"ibmq_qasm_simulator\"] * 4\n",
        "\n",
        "# If a single set of options are passed, it will be applied to all backends\n",
        "options = [Options(execution={\"shots\": 1000}), Options(execution={\"shots\": 2000}), Options(execution={\"shots\":2000}),Options(execution={\"shots\":1000})]\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from qiskit.algorithms.optimizers import COBYLA\n",
        "from circuit_knitting_toolbox.entanglement_forging import (\n",
        "    EntanglementForgingGroundStateSolver,\n",
        ")\n",
        "\n",
        "optimizer = COBYLA(maxiter=50,tol = 1e-5)\n",
        "\n",
        "solver = EntanglementForgingGroundStateSolver(\n",
        "    ansatz=ansatz,\n",
        "    optimizer=optimizer,\n",
        "    service=service,\n",
        "    backend_names=backend_names,\n",
        "    options=options,\n",
        "    initial_point=[0.0, np.pi / 2],\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "%%capture\n",
        "\n",
        "results = solver.solve(problem)"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The following results are obtained from running the above code. We also explored applying entanglement forging differently by a different choice of used bitstrings. The procedure is explained here. https://github.com/qiskit-community/prototype-entanglement-forging/blob/main/docs/3-explanatory_material/explanatory_material.md#picking-the-bitstrings"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "eigenvalue = [-15.067677961867169, -14.43349358705019, -16.850469941463, -17.35366210680921, -15.923394623984477, -17.39183988919921, -15.819941135220622, -17.66749851343628, -16.604922689851417, -17.666004725250048, -16.603020233190847, -17.29859516235202, -17.72566408267279, -17.69888982692018, -17.725690220806747, -17.69877309532289, -17.707285219181852, -17.72692685156067, -17.72285154687804, -17.72692548497306, -17.722851428629223, -17.725553090234015, -17.727115720551243, -17.726972567291043, -17.72711573111239, -17.72697242358583, -17.72706287631097, -17.727111031352962, -17.727110299209098, -17.7271157340197, -17.72711597275354, -17.727114147285853, -17.72711598580272, -17.72711650046225, -17.727115718768687, -17.72711627160566, -17.727116501379225, -17.727116401603, -17.72711642982655, -17.727116506819804, -17.72711649203592, -17.727116506782636, -17.727116492007838, -17.727116501944796, -17.72711650735905, -17.72711650663199, -17.727116507358662, -17.727116506631813, -17.727116507025464]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Energy:\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0xc289e0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "print(\"Energy:\")\n",
        "plt.plot(eigenvalue)\n",
        "plt.xlabel(\"Iterations\")\n",
        "plt.ylabel(\"Energy (Hartrees)\")\n",
        "plt.show()\n"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We also used orbital freezing through the following from IBM, problem = ElectronicStructureProblem(driver,[FreezeCoreTransformer(freeze_core=True, remove_orbitals=[-3,-2, -1])]) where we checked that excluding the orbitals we listed did not influence the chemical accuracy as much as excluding more orbitals. \n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "authorship_tag": "ABX9TyPHeZH/b2HZwQ7RmG5OBwB/",
      "include_colab_link": true,
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}