3_pioneer/11_vqe.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Differentiable ZNE: Error-mitigated VQE\n",
    "\n",
    "At this point, you've been exposed to modelling noise in a quantum circuit and how to amplify a circuit's noise via global circuit folding. In this challenge, you will pioneer a way to perform an error-mitigated version of a quintessential quantum algorithm on noisy hardware!\n",
    "\n",
    "The variational quantum eigensolver (VQE) algorithm is an elegant optimization algorithm that estimates the ground state and ground state energy of a Hamiltonian. The Hamiltonian could describe anything, so long as there's an efficient map to mapping the degrees of freedom to binary variables. Here, we'll use the qubit representation of the molecular hydrogen Hamiltonian. Go check out [our popular demo](https://pennylane.ai/qml/demos/tutorial_quantum_chemistry.html) on performing VQE with this Hamiltonian!\n",
    "\n",
    "Here, you will perform:\n",
    "- an \"ideal\" VQE routine (no noise present at all)\n",
    "- three error-ridden VQE routines\n",
    "- an extrapolation to zero-noise given the three error-ridden VQE routines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The three error-ridden VQE routines must be constructed from a noisy device, where a depolarizing channel is present on _all_ gates. There, you will employ PennyLane's builtin global circuit folding protocol that can be implemented via transforming a noisy QNode: [`qml.transforms.fold_global`](https://docs.pennylane.ai/en/stable/code/api/pennylane.transforms.fold_global.html?highlight=qml.transforms.fold_global).\n",
    "\n",
    "\n",
    "## Challenge code\n",
    "\n",
    "The provided code below contains a few functions:\n",
    "- `hydrogen_hamiltonian`: this function creates the Hamiltonian describing the H molecule given a hydrogen-to-hydrogen distance `d`.\n",
    "- `ansatz_template`: this is a quantum function that defines the ansatz for all VQE routines that you will perform.\n",
    "- `VQE`: this function performs a VQE routine given a QNode that you created with `qnode_ansatzes`.\n",
    "- `qnode_ansatzes`: employs `ansatz_template` to create QNodes given different devices: an ideal device (no noise) and \"mitigated\" devices that are global-circuit-folding transformed devices. **You must complete this function**.\n",
    "- `extrapolation`: this is where the magic happens; all VQE routines run, and then the zero-noise extrapolation takes place. **You must complete this function**.\n",
    "\n",
    "The three error-ridden VQE routines that you perform are tied to three different _scale factors_. The scale factors define the global circuit folding procedure, and more information can be found in the documentation for [`qml.transforms.fold_global`](https://docs.pennylane.ai/en/stable/code/api/pennylane.transforms.fold_global.html?highlight=qml.transforms.fold_global). When you perform the extrapolation, you will be fitting a second-degree polynomial function (a quadratic function) to VQE energies versus scale factors.\n",
    "\n",
    "### Input\n",
    "\n",
    "As input to this problem, you will be given `d`, the hydrogen-to-hydrogen distance that defines its molecular Hamiltonian.\n",
    "\n",
    "### Output\n",
    "\n",
    "This code will output two energies corresponding to the noise-free VQE routine and the extrapolated energy from the ZNE routine: `[ideal_energy, zne_energy]` (`list(float)`).\n",
    "\n",
    "If your solution matches the correct one within the given tolerance specified in `check` (in this case it's a `0.01` relative error tolerance), the output will be `\"Correct!\"`. Otherwise, you will receive a `\"Wrong answer\"` prompt.\n",
    "\n",
    "Good luck!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "import pennylane as qml\n",
    "import pennylane.numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hydrogen_hamiltonian(d):\n",
    "    \"\"\"Creates the H_2 Hamiltonian from a separation distance.\n",
    "\n",
    "    Args:\n",
    "        d (float): The distance between a hydrogen atom and the hydrogen molecule's centre of mass.\n",
    "\n",
    "    Returns:\n",
    "        H (qml.Hamiltonian): The H_2 Hamiltonian.\n",
    "        qubits (int): The number of qubits needed to simulate the H_2 Hamiltonian.\n",
    "    \"\"\"\n",
    "\n",
    "    symbols = symbols = [\"H\", \"H\"]\n",
    "    coordinates = np.array([0.0, 0.0, -d, 0.0, 0.0, d])\n",
    "    H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "\n",
    "    return H, qubits\n",
    "\n",
    "def ansatz_template(param, wires):\n",
    "    \"\"\"The unitaries used for creating an ansatz for subsequent VQE calculations.\n",
    "\n",
    "    Args:\n",
    "        param (np.array): A single differentiable parameter\n",
    "        wires (list(int)): A list of wires that the unitaries are applied to.\n",
    "    \"\"\"\n",
    "    qml.BasisState([1, 1, 0, 0], wires=wires)\n",
    "    qml.DoubleExcitation(param, wires=wires)\n",
    "\n",
    "def VQE(qnode):\n",
    "    \"\"\"Performs a VQE routine given a QNode.\n",
    "\n",
    "    Args:\n",
    "        qnode (qml.QNode):\n",
    "            The ansatz that will be optimized in order to find the ground state\n",
    "            of molecular hydrogen.\n",
    "\n",
    "    Retuns:\n",
    "        final_energy (float): The final energy from the VQE routine.\n",
    "    \"\"\"\n",
    "    param = np.array(0.0, requires_grad=True)\n",
    "    num_iters = 20\n",
    "    opt = qml.GradientDescentOptimizer(stepsize=0.4)\n",
    "\n",
    "    for _ in range(num_iters):\n",
    "        param = opt.step(qnode, param)\n",
    "\n",
    "    final_energy = qnode(param)\n",
    "\n",
    "    return final_energy\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qnode_ansatzes(d, scale_factors):\n",
    "    \"\"\"Generates ideal and mitigated qnodes.\n",
    "\n",
    "    Args:\n",
    "        d (float): The distance between a hydrogen atom and the hydrogen molecule's centre of mass.\n",
    "        scale_factors (list(int)): A list of scale factors used for ZNE.\n",
    "\n",
    "    Returns:\n",
    "       qnode_ideal (qml.QNode): The ideal QNode (no noise).\n",
    "       qnodies_mitgated (list(qml.QNode)): A list of QNodes that are mitigated. len(qnodes_mitigated) = len(scale_factors).\n",
    "    \"\"\"\n",
    "    H, qubits = hydrogen_hamiltonian(d)\n",
    "\n",
    "    def cost_fn(param):\n",
    "        ansatz_template(param, wires=range(qubits))\n",
    "        return qml.expval(H)\n",
    "\n",
    "    noise_gate = qml.DepolarizingChannel\n",
    "    noise_strength = 0.05\n",
    "\n",
    "    dev_ideal = qml.device(\"default.mixed\", wires=qubits)\n",
    "    dev_noisy = qml.transforms.insert(noise_gate, noise_strength)(dev_ideal)\n",
    "\n",
    "    qnode_ideal = qml.QNode(cost_fn, dev_ideal)\n",
    "    qnode_noisy = qml.QNode(cost_fn, dev_noisy)\n",
    "    \n",
    "    qnodes_mitigated = [qml.transforms.fold_global(qnode_noisy, scale_factor) for scale_factor in scale_factors]\n",
    "\n",
    "    return qnode_ideal, qnodes_mitigated\n",
    "\n",
    "def extrapolation(d, scale_factors):\n",
    "    \"\"\"Performs ZNE to obtain a zero-noise estimate on the ground state energy of H_2.\n",
    "\n",
    "    Args:\n",
    "        d (float): The distance between a hydrogen atom and the hydrogen molecule's centre of mass.\n",
    "        scale_factors (list(int)): A list of scale factors used for ZNE.\n",
    "\n",
    "    Returns:\n",
    "        ideal_energy (float): The ideal energy from a noise-less VQE routine.\n",
    "        zne_energy (float): The zero-noise estimate of the ground state energy of H_2.\n",
    "\n",
    "        These two energies are returned in that order within a numpy array.\n",
    "    \"\"\"\n",
    "\n",
    "    qnode_ideal, qnodes_mitigated = qnode_ansatzes(d, scale_factors)\n",
    "\n",
    "    ideal_energy = np.round_(VQE(qnode_ideal), decimals=6)\n",
    "    mitigated_energies = [VQE(qnode) for qnode in qnodes_mitigated]\n",
    "\n",
    "    # Put your code here #\n",
    "    coeffs = np.polyfit(scale_factors, mitigated_energies, 2)\n",
    "    zne_energy = coeffs[-1]\n",
    "\n",
    "    return np.array([ideal_energy, zne_energy]).tolist()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# These functions are responsible for testing the solution.\n",
    "\n",
    "def run(test_case_input: str) -> str:\n",
    "    d = json.loads(test_case_input)\n",
    "    scale_factors = [1, 2, 3]\n",
    "    energies = extrapolation(d, scale_factors)\n",
    "    return str(energies)\n",
    "\n",
    "\n",
    "def check(solution_output: str, expected_output: str) -> None:\n",
    "    solution_output = json.loads(solution_output)\n",
    "    expected_output = json.loads(expected_output)\n",
    "    assert np.allclose(\n",
    "        solution_output, expected_output, rtol=1e-2\n",
    "    ), \"Your extrapolation isn't quite right!\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_cases = [['0.6614', '[-1.13619, -0.41168]']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running test case 0 with input '0.6614'...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/saverio/xanadu-codecamp-22/codecamp/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:156: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return A.astype(dtype, order, casting, subok, copy)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct!\n"
     ]
    }
   ],
   "source": [
    "for i, (input_, expected_output) in enumerate(test_cases):\n",
    "    print(f\"Running test case {i} with input '{input_}'...\")\n",
    "\n",
    "    try:\n",
    "        output = run(input_)\n",
    "\n",
    "    except Exception as exc:\n",
    "        print(f\"Runtime Error. {exc}\")\n",
    "\n",
    "    else:\n",
    "        if message := check(output, expected_output):\n",
    "            print(f\"Wrong Answer. Have: '{output}'. Want: '{expected_output}'.\")\n",
    "\n",
    "        else:\n",
    "            print(\"Correct!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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