obp_mpf_tutorial_L12.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reducing the Trotter error of Hamiltonian dynamics with <span style=\"color:black\"> multi-product formulas</span> and <span style=\"color:#black\">operator backpropagation</span>\n",
    "\n",
    "In this notebook, you will learn how to use a  **Multi-Product Formula (MPF)** to achieve a lower Trotter error on our observable compared to the one incurred by the deepest Trotter circuit that we will actually execute.\n",
    "You will do so by working through the steps of a **Qiskit pattern**:\n",
    "\n",
    "- **Step 1: Map to quantum circuits**\n",
    "    - Initialize our problem's Hamiltonian\n",
    "    - <font color=\"blue\">**Use a MPF to generate the Trotterized time-evolution circuits**</font>\n",
    "- **Step 2: Optimize the problem**\n",
    "    - <font color=\"#4589FF\">**Slice the longest circuit**</font>\n",
    "    - <font color=\"#4589FF\">**Backpropagate slices from the longest circuit onto a Pauli observable**</font>\n",
    "    - <font color=\"#4589FF\">**Combine the remaining slices into a circuit with reduced depth**</font>\n",
    "    - Here we transpile our circuits for `ibm_torino`\n",
    "- **Step 3: Execute experiments**\n",
    "    - Use the `Estimator` primitive from qiskit runtime to compute our circuits' expectation values\n",
    "        - Run local simulation\n",
    "        - Execute experiments on `ibm_torino`\n",
    "- **Step 4: Reconstruct results**\n",
    "    - <font color=\"blue\">**Compute the MPF expectation value**</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Map to quantum problem\n",
    "\n",
    "### 1a: Setting up our Hamiltonian\n",
    "\n",
    "We use the XXZ model on a line of 12 sites:\n",
    "\n",
    "$$\n",
    "\\hat{\\mathcal{H}}_{XXZ} = \\sum_{i=1}^{L-1} J_{i,(i+1)}\\left(X_i X_{(i+1)}+Y_i Y_{(i+1)}+ 2\\cdot Z_i Z_{(i+1)} \\right) \\, ,\n",
    "$$\n",
    "\n",
    "where $J_{i,(i+1)}$ is a random coefficient corresponding to edge $(i, i+1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGBA size=1931x59>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.transpiler import CouplingMap\n",
    "from rustworkx.visualization import graphviz_draw\n",
    "\n",
    "# L = length of our 1D spin chain\n",
    "L = 12\n",
    "\n",
    "# Generate the edge-list for this spin-chain\n",
    "elist = [(i-1,i) for i in range(1, L)]\n",
    "# Generate an edge-coloring so we can make hw-efficient circuits\n",
    "even_edges  = elist[::2] \n",
    "odd_edges = elist[1::2]\n",
    "\n",
    "# Instantiate a CouplingMap object\n",
    "coupling_map = CouplingMap(elist)\n",
    "graphviz_draw(coupling_map.graph, method=\"circo\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate the hamiltonian we will evolve by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SparsePauliOp(['IIIIIIIIIIII', 'IIIIIIIIIIXX', 'IIIIIIIIIIYY', 'IIIIIIIIIIZZ', 'IIIIIIIIXXII', 'IIIIIIIIYYII', 'IIIIIIIIZZII', 'IIIIIIXXIIII', 'IIIIIIYYIIII', 'IIIIIIZZIIII', 'IIIIXXIIIIII', 'IIIIYYIIIIII', 'IIIIZZIIIIII', 'IIXXIIIIIIII', 'IIYYIIIIIIII', 'IIZZIIIIIIII', 'XXIIIIIIIIII', 'YYIIIIIIIIII', 'ZZIIIIIIIIII', 'IIIIIIIIIXXI', 'IIIIIIIIIYYI', 'IIIIIIIIIZZI', 'IIIIIIIXXIII', 'IIIIIIIYYIII', 'IIIIIIIZZIII', 'IIIIIXXIIIII', 'IIIIIYYIIIII', 'IIIIIZZIIIII', 'IIIXXIIIIIII', 'IIIYYIIIIIII', 'IIIZZIIIIIII', 'IXXIIIIIIIII', 'IYYIIIIIIIII', 'IZZIIIIIIIII'],\n",
      "              coeffs=[1.        +0.j, 0.52440675+0.j, 0.52440675+0.j, 1.0488135 +0.j,\n",
      " 0.60759468+0.j, 0.60759468+0.j, 1.21518937+0.j, 0.55138169+0.j,\n",
      " 0.55138169+0.j, 1.10276338+0.j, 0.52244159+0.j, 0.52244159+0.j,\n",
      " 1.04488318+0.j, 0.4618274 +0.j, 0.4618274 +0.j, 0.9236548 +0.j,\n",
      " 0.57294706+0.j, 0.57294706+0.j, 1.14589411+0.j, 0.46879361+0.j,\n",
      " 0.46879361+0.j, 0.93758721+0.j, 0.6958865 +0.j, 0.6958865 +0.j,\n",
      " 1.391773  +0.j, 0.73183138+0.j, 0.73183138+0.j, 1.46366276+0.j,\n",
      " 0.44172076+0.j, 0.44172076+0.j, 0.88344152+0.j, 0.64586252+0.j,\n",
      " 0.64586252+0.j, 1.29172504+0.j])\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit.quantum_info import SparsePauliOp, Pauli\n",
    "\n",
    "# Genereate random coefficients for our XXZ Hamiltonian\n",
    "np.random.seed(0)\n",
    "Js = np.random.rand(L-1) + 0.5*np.ones(L-1)\n",
    "\n",
    "hamiltonian = SparsePauliOp(Pauli('I'*L))\n",
    "for i, edge in enumerate(even_edges + odd_edges):\n",
    "    hamiltonian += SparsePauliOp.from_sparse_list(\n",
    "    [(\"XX\", (edge), Js[i] /2),\n",
    "     (\"YY\", (edge), Js[i] /2),\n",
    "     (\"ZZ\", (edge), Js[i] )], \n",
    "    num_qubits=L)\n",
    "\n",
    "print(hamiltonian)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define the observable we want to estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SparsePauliOp(['IIIIIZZIIIII'],\n",
      "              coeffs=[1.+0.j])\n"
     ]
    }
   ],
   "source": [
    "observable = SparsePauliOp.from_sparse_list(\n",
    "    [(\"ZZ\", (L//2 - 1, L//2), 1.0)], num_qubits=L\n",
    ")\n",
    "print(observable)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1b: Multi-Product Formulas\n",
    "\n",
    "MPFs reduce the Trotter error of Hamiltonian dynamics through a weighted combination of several circuit executions.\n",
    "\n",
    "To make this more concrete, we define an MPF as:\n",
    "\n",
    "$$\n",
    "\\mu(t) = \\sum_{j} x_j \\rho^{k_j}_{j}\\left(\\frac{t}{k_j}\\right) + \\text{some remaining Trotter error} \\, ,\n",
    "$$\n",
    "\n",
    "where $x_j$ are our weighting coefficients, $\\rho^{k_j}_j$ is the density matrix corresponding to the pure state obtained by evolving the initial state with the product formula, $S^{k_j}$, involving $k_j$ Trotter steps, and $j$ indexes the number of PFs that make up the MPF.\n",
    "\n",
    "The key here is, that the remaining Trotter error is smaller than the Trotter error that one would obtain by simply using the largest $k_j$ value!\n",
    "\n",
    "You can view the usefulness of this from two perspectives:\n",
    "\n",
    "1. For a fixed budget of Trotter steps that you are able to execute, you can obtain results with a Trotter error that is smaller in total.\n",
    "2. Given some target number of Trotter steps that is too large to execute, you can use the MPF to find a shorter-depth circuit to run which results in a similar Trotter error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing our Trotter steps, $k_j$\n",
    "\n",
    "The choice of $k_j$ is up to the end-user.\n",
    "In principle, any values can be chosen but some $k_j$'s will lead to a larger noise amplification on real devices than other choices.\n",
    "Thus, it is important that one tries to find _\"good\"_ values of $k_j$.\n",
    "\n",
    "Here, we will simply pick some fixed values for $k_j$. The rule of thumb is that $t/k_{\\text{min}} \\lt 1$. In our case $0.6/3 = 0.2$, so we are well-within the MPF technique's limits. If you want to learn more about this and how to choose your other $k_j$ values, refer to the respective guide: [How to choose the Trotter steps for an MPF](https://qiskit.github.io/qiskit-addon-mpf/how_tos/choose_trotter_steps.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_time = 0.6\n",
    "mpf_trotter_steps = [3,4,7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Setting up the LSE\n",
    "\n",
    "Now that we have chosen our $k_j$s, we must first construct the LSE, $Ax=b$ as explained above.\n",
    "The matrix $A$ depends not only on $k_j$ but also our choice of PF, in particular its _order_.\n",
    "Additionally, one may take into account whether the PF is symmetric or not (see [Carrera Vazquez et al., 2023]), by setting `symmetric=True`.\n",
    "However, this is not required as shown by [Zhuk et al., 2023]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The static coefficients associated with the ansatze are: [ 2.25       -5.33333333  4.08333333]\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_mpf.static import setup_lse\n",
    "\n",
    "lse = setup_lse(mpf_trotter_steps, order=1, symmetric=False)\n",
    "mpf_coeffs = lse.solve()\n",
    "print(f\"The static coefficients associated with the ansatze are: {mpf_coeffs}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1c: Construct each of the Trotter circuits in our MPF decomposition\n",
    "\n",
    "At this point, we have found our expansion coefficients, $x$, and all that is left to do, is to generate the Trotterized quantum circuits.\n",
    "The [qiskit_addon_utils.problem_generators](https://qiskit.github.io/qiskit-addon-utils/stubs/qiskit_addon_utils.problem_generators.html) module with a handy function do just that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We are also going to add an extra circuit with 100 steps\n",
    "trotter_steps_total = mpf_trotter_steps + [100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 980.827x207.356 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "from qiskit.synthesis import LieTrotter\n",
    "from qiskit_addon_utils.problem_generators import generate_time_evolution_circuit\n",
    "\n",
    "# Generate an initial state\n",
    "initial_state = QuantumCircuit(L)\n",
    "for i in range(L):\n",
    "    if i%2:\n",
    "        initial_state.x(i)\n",
    "\n",
    "trotter_circuits = [\n",
    "    initial_state.compose(\n",
    "        generate_time_evolution_circuit(\n",
    "            hamiltonian,\n",
    "            time=total_time,\n",
    "            synthesis=LieTrotter(reps=num_steps),\n",
    "        ) \n",
    "    )\n",
    "    for num_steps in trotter_steps_total]\n",
    "\n",
    "mpf_circuits = trotter_circuits[:3]\n",
    "ref_circuit = trotter_circuits[-1]\n",
    "\n",
    "fig = mpf_circuits[2].draw(\"mpl\", fold = -1, scale = 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2a: Optimize the problem with OBP\n",
    "### Create circuit slices to backpropagate\n",
    "\n",
    "The ``backpropagate`` function will backpropagate entire circuit slices at a time, so the choice of how to slice can have an impact on how well backpropagation performs for a given problem. Here, we will group gates of the same type into slices using the [slice_by_gate_types](https://qiskit.github.io/qiskit-addon-utils/stubs/qiskit_addon_utils.slicing.slice_by_gate_types.html) function.\n",
    "\n",
    "For a more detailed discussion on circuit slicing, check out this [how-to guide](https://qiskit.github.io/qiskit-addon-utils/how_tos/create_circuit_slices.html) of the [qiskit-addon-utils](https://qiskit.github.io/qiskit-addon-utils/index.html) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Separated the circuit into 43 slices.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1683.16x207.356 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit_addon_utils.slicing import slice_by_gate_types, combine_slices\n",
    "\n",
    "slices = slice_by_gate_types(mpf_circuits[-1])\n",
    "print(f\"Separated the circuit into {len(slices)} slices.\")\n",
    "fig = combine_slices(slices, include_barriers=True).draw(\"mpl\", fold = -1, scale = 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constrain how large the operator may grow during backpropagation\n",
    "\n",
    "During backpropagation, the number of terms in the operator will generally approach $4^N$, where $N$ is the number of qubits. The size of the operator can be bounded by specifying the ``operator_budget`` kwarg of the ``backpropagate`` function, which accepts an [OperatorBudget](https://qiskit.github.io/qiskit-addon-obp/stubs/qiskit_addon_obp.utils.simplify.OperatorBudget.html) instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_obp.utils.simplify import OperatorBudget\n",
    "\n",
    "op_budget = OperatorBudget(max_paulis = None,\n",
    "                           max_qwc_groups = None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specify your OBP error tolerance to optimize classical and quantum overhead\n",
    "\n",
    "As our operators are back-propagated, some terms in the decomposition will have small coefficients and can be truncated without incurring much error. By allowing some amount of error budget we can reduce both the overhead of performing OBP, while also reducing the size of the observable which we obtain in the end.\n",
    "\n",
    "Relevant parameters in this procedure are\n",
    "- `max_error_total`: The total amount of error you are willing to incur\n",
    "- `num_slices`: The number of slices over which to distribute the error budget\n",
    "- `p_norm`: The $p$-norm in which the error is measured\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_obp.utils.truncating import setup_budget\n",
    "\n",
    "num_obp_slices = 10\n",
    "\n",
    "max_error_total = 0.05\n",
    "error_budget = setup_budget(max_error_total = max_error_total,\n",
    "                            num_slices=num_obp_slices,\n",
    "                            p_norm=2)\n",
    "\n",
    "error_budget.per_slice_budget = [0]*(num_obp_slices-1) + [max_error_total]\n",
    "# print(error_budget.per_slice_budget)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backpropagate slices from the circuit\n",
    "\n",
    "First, we will specify the Pauli-Z observable on qubit 0, and we will backpropagate slices from the time-evolution circuit until the terms in the observable can no longer be combined into 8 or fewer qubit-wise commuting Pauli groups.\n",
    "\n",
    "Below you will see that we backpropagated 7 slices but only used 6 of the 8 allotted Pauli groups. This implies that backpropagating one more slice would cause the number of Pauli groups to exceed 8. We can verify that this is the case by inspecting the returned metadata."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Back-propagated 10 slices with 0.0409 accumulated error.\n",
      "New observable has 11 terms, which can be combined into 9 qwc groups.\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_obp import backpropagate\n",
    "\n",
    "# Back-propagate slices onto the observable\n",
    "bp_obs, remaining_slices, metadata = backpropagate(observable, \n",
    "                                                   slices[-num_obp_slices:], \n",
    "                                                   operator_budget=op_budget,\n",
    "                                                   truncation_error_budget = error_budget)\n",
    "\n",
    "# Recombine the slices remaining after back-propagation\n",
    "bp_circuit = combine_slices(slices[:-num_obp_slices] + remaining_slices, include_barriers=False)\n",
    "\n",
    "print(f\"Back-propagated {metadata.num_backpropagated_slices} slices with {metadata.accumulated_error(0):.4f} accumulated error.\")\n",
    "print(f\"New observable has {len(bp_obs.paulis)} terms, which can be combined into {len(bp_obs.group_commuting(qubit_wise=True))} qwc groups.\")\n",
    "#print(f\"Note that back-propagating one more slice would result in {metadata.backpropagation_history[-1].num_paulis[0]} terms \"\n",
    "#      f\"across {metadata.backpropagation_history[-1].num_qwc_groups} groups.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We can inspect OBP metadata to get more information about how the computation went\n",
    "This can be useful when determining OBP input parameters, such as the desired error budget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from qiskit_addon_obp.utils.visualization import (\n",
    "    plot_accumulated_error,\n",
    "    plot_left_over_error_budget,\n",
    "    plot_num_qwc_groups,\n",
    "    plot_num_truncated_paulis,\n",
    "    plot_slice_errors,\n",
    "    plot_num_paulis,\n",
    "    plot_sum_paulis\n",
    ")\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, figsize=(20, 10))\n",
    "plot_slice_errors(metadata, axes[(0, 0)])\n",
    "plot_accumulated_error(metadata, axes[(1, 0)])\n",
    "plot_num_paulis(metadata, axes[(1, 1)])\n",
    "plot_num_truncated_paulis(metadata, axes[(0, 1)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Before and after OBP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 980.827x207.356 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 746.716x207.356 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "long_fig = combine_slices(slices, include_barriers=False).draw(\"mpl\", fold = -1, scale = 0.2)\n",
    "short_fig = bp_circuit.draw(\"mpl\", fold=-1, scale=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Execute quantum experiments using `AerSimulator` backend\n",
    "\n",
    "We can simulate our various Trotter circuits, including the back-propagated one using the ``Estimator`` primitive from ``qiskit-ibm-runtime`` and we will compare the results we get with a Trotter circuit of 100 steps. \n",
    "These simulations do not have any sources of noise apart from statistical uncertainty due to drawing finitely many shots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create PUBs (Primitives Unified Blocs) which specify our experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "pub_circuits    =    mpf_circuits    + [bp_circuit] + [ref_circuit]\n",
    "pub_observables = ([observable] * 3) +   [bp_obs]   + [observable]\n",
    "pubs = list(zip(pub_circuits, pub_observables))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Noiseless local simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Qiskit Runtime service and Estimator\n",
    "# V2 is the default version in qiskit-ibm-runtime>=0.28.0, no need to import EstimatorV2 as Estimator\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator\n",
    "\n",
    "num_shots = 2**20\n",
    "\n",
    "# Instantiate a local Estimator using a Simulator\n",
    "local_service = QiskitRuntimeService(channel=\"local\")\n",
    "simulator = local_service.backend(\"aer_simulator\")\n",
    "simulator_estimator = Estimator(simulator)\n",
    "\n",
    "# Simulate experiments, retrieve epxectation values\n",
    "noiseless_result = simulator_estimator.run(pubs, precision=1/np.sqrt(num_shots)).result()\n",
    "noiseless_expvals = [pub_result.data.evs.tolist() for pub_result in noiseless_result]\n",
    "\n",
    "# Re-organize expectation values\n",
    "mpf_expvals = noiseless_expvals[:3]\n",
    "mpf_obp_expvals = noiseless_expvals[:2] + [noiseless_expvals[3]]\n",
    "ref_expval = noiseless_expvals[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Reconstruct MPF expectation values\n",
    "\n",
    "Now that we have obtained the results for our different Trotter circuits, we can reconstruct the MPF and MPF + OBP expectation values to compare them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "mpf_expval     =     mpf_expvals @ mpf_coeffs\n",
    "mpf_obp_expval = mpf_obp_expvals @ mpf_coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ground Truth:\t-0.6948\n",
      "––––––––––––––––––––––––––––––––––––––\n",
      "3 steps:\t-0.6124, |∆| = 0.0824\n",
      "4 steps:\t-0.6425, |∆| = 0.0522\n",
      "7 steps:\t-0.6717, |∆| = 0.0230\n",
      "7 steps + OBP:\t-0.6569, |∆| = 0.0379\n",
      "––––––––––––––––––––––––––––––––––––––\n",
      "MPF:\t\t-0.6941, |∆| = 0.0007\n",
      "MPF + OBP:\t-0.6335, |∆| = 0.0613\n"
     ]
    }
   ],
   "source": [
    "print(f\"Ground Truth:\\t{ref_expval:.4f}\")\n",
    "print('––'*19)\n",
    "print(f\"{mpf_trotter_steps[0]} steps:\\t{mpf_expvals[0]:.4f}, |∆| = {np.abs(ref_expval - mpf_expvals[0]):.4f}\")\n",
    "print(f\"{mpf_trotter_steps[1]} steps:\\t{mpf_expvals[1]:.4f}, |∆| = {np.abs(ref_expval - mpf_expvals[1]):.4f}\")\n",
    "print(f\"{mpf_trotter_steps[2]} steps:\\t{mpf_expvals[2]:.4f}, |∆| = {np.abs(ref_expval - mpf_expvals[2]):.4f}\")\n",
    "print(f\"{mpf_trotter_steps[2]} steps + OBP:\\t{mpf_obp_expvals[2]:.4f}, |∆| = {np.abs(ref_expval - mpf_obp_expvals[2]):.4f}\")\n",
    "print('––'*19)\n",
    "print(f\"MPF:\\t\\t{mpf_expval:.4f}, |∆| = {np.abs(ref_expval - mpf_expval):.4f}\")\n",
    "print(f\"MPF + OBP:\\t{mpf_obp_expval:.4f}, |∆| = {np.abs(ref_expval - mpf_obp_expval):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Redo Steps 2-4 for a hardware experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2b: Transpile circuits into ISA Circuits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create PUBs (Primitives Unified Blocs) which specify our experiment\n",
    "Note that this time we will not be submitting the 100 Trotter step circuit. On real hardware this will not return useful results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "pub_circuits = mpf_circuits + [bp_circuit] \n",
    "pub_observables = ([observable] * 3) + [bp_obs]\n",
    "pubs = list(zip(pub_circuits, pub_observables))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transpile PUBs (circuits and observables) to match the backend ISA (Instruction Set Architecture)\n",
    "By selecting `optimization_level=3`, the transpiler will choose a 1D chain of qubits which minimizes the noise affecting our circuit. Once we have converted our circuits into the format that the backend is prepared to accept, we will apply a complimentary transformation to our observables as well. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "\n",
    "# need to create a service that's not local\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\", instance='ibm-q-internal/dev-services/middleware')\n",
    "backend = service.backend(\"ibm_torino\")\n",
    "\n",
    "# Transpile pubs (circuits and observables) to match ISA\n",
    "pass_manager = generate_preset_pass_manager(backend=backend, optimization_level=3)\n",
    "isa_circuits = [pass_manager.run(circuit) for circuit in pub_circuits]\n",
    "isa_observables = [obs.apply_layout(isa_circuit.layout) \n",
    "                                if isinstance(obs, SparsePauliOp) \n",
    "                                else [sub_obs.apply_layout(isa_circuit.layout) for sub_obs in obs]\n",
    "                                for (isa_circuit, obs) in zip(isa_circuits, pub_observables)]\n",
    "isa_pubs = zip(isa_circuits, isa_observables)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Execute quantum experiments on `ibm_torino`\n",
    "\n",
    "Now we will repeat the same experiments on real quantum hardware"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Configure ``EstimatorOptions``, to control the parameters of our hardware experiment\n",
    "For more information about the available execution options, see the [qiskit-ibm-runtime documentation](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.EstimatorOptions). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "twirling_options = {'enable_gates' : True,\n",
    "                    'enable_measure':True,\n",
    "                    'num_randomizations':300,\n",
    "                    'shots_per_randomization':100,\n",
    "                    'strategy':'active'}\n",
    "\n",
    "zne_options = {'amplifier': 'gate_folding',\n",
    "               'noise_factors': [1, 2, 3],\n",
    "               'extrapolated_noise_factors': list(np.linspace(0,3, 31)),\n",
    "               'extrapolator': [\"exponential\", \"linear\", \"fallback\"]}\n",
    "\n",
    "meas_learning_options = {'num_randomizations': 512,\n",
    "                        'shots_per_randomization': 512}\n",
    "\n",
    "resilience_options = {'measure_mitigation': True,\n",
    "                      'zne_mitigation': True,\n",
    "                      'zne': zne_options,\n",
    "                      'measure_noise_learning': meas_learning_options}\n",
    "\n",
    "estimator_options = {'resilience': resilience_options,\n",
    "                     'twirling': twirling_options}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Execute experiments / load previous results from disk\n",
    "Here is where we would initiate our experiments through runtime, however, for the purposes of this demo, we will instead be loading previously run results from disk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from demo_utils import dill_dump, dill_load\n",
    "from qiskit_ibm_runtime import Estimator\n",
    "\n",
    "hw_results_save_path = f\"L{L}/{'_'.join([str(k) for k in mpf_trotter_steps])}/hw_results.pkl\"\n",
    "\n",
    "estimator = Estimator(backend, options = estimator_options)\n",
    "\n",
    "# # ========== Execute Experiments =================\n",
    "# hw_results = estimator.run(isa_pubs).result()\n",
    "# hw_results_dicts = [pub_result.data.__dict__ for pub_result in hw_results]\n",
    "#\n",
    "# # ========== Save Results to Disk =================\n",
    "# dill_dump([hw_results_dicts, estimator_options], hw_results_save_path, make_dirs=True)\n",
    "\n",
    "# ========== Load Results to Disk =================\n",
    "hw_results_dicts, estimator_options = dill_load(hw_results_save_path)\n",
    "\n",
    "\n",
    "# Re-organize expectation values\n",
    "hw_expvals = [pub_result_data['evs'].tolist() for pub_result_data in hw_results_dicts]\n",
    "mpf_expvals_hw = hw_expvals[:3]\n",
    "mpf_obp_expvals_hw = hw_expvals[:2] + [hw_expvals[3]]\n",
    "ref_expval = noiseless_expvals[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Reconstruct MPF expectation values\n",
    "\n",
    "Now that we have obtained the results for our different Trotter circuits, we can reconstruct the MPF and MPF + OBP expectation values to compare them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "mpf_expval_hw     =     mpf_expvals_hw @ mpf_coeffs\n",
    "mpf_obp_expval_hw = mpf_obp_expvals_hw @ mpf_coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ideal:\t\t-0.6948\n",
      "––––––––––––––––––––––––––––––––––––––\n",
      "3 steps:\t-0.4863, |∆| = 0.2085\n",
      "4 steps:\t-0.5316, |∆| = 0.1632\n",
      "7 steps:\t-0.5410, |∆| = 0.1538\n",
      "7 steps + OBP:\t-0.5889, |∆| = 0.1059\n",
      "––––––––––––––––––––––––––––––––––––––\n",
      "MPF:\t\t-0.4683, |∆| = 0.2265\n",
      "MPF + OBP:\t-0.6639, |∆| = 0.0309\n"
     ]
    }
   ],
   "source": [
    "print(f\"Ideal:\\t\\t{ref_expval:.4f}\")\n",
    "print('––'*19)\n",
    "print(f\"{mpf_trotter_steps[0]} steps:\\t{mpf_expvals_hw[0]:.4f}, |∆| = {np.abs(ref_expval - mpf_expvals_hw[0]):.4f}\")\n",
    "print(f\"{mpf_trotter_steps[1]} steps:\\t{mpf_expvals_hw[1]:.4f}, |∆| = {np.abs(ref_expval - mpf_expvals_hw[1]):.4f}\")\n",
    "print(f\"{mpf_trotter_steps[2]} steps:\\t{mpf_expvals_hw[2]:.4f}, |∆| = {np.abs(ref_expval - mpf_expvals_hw[2]):.4f}\")\n",
    "print(f\"{mpf_trotter_steps[2]} steps + OBP:\\t{mpf_obp_expvals_hw[2]:.4f}, |∆| = {np.abs(ref_expval - mpf_obp_expvals_hw[2]):.4f}\")\n",
    "print('––'*19)\n",
    "print(f\"MPF:\\t\\t{mpf_expval_hw:.4f}, |∆| = {np.abs(ref_expval - mpf_expval_hw):.4f}\")\n",
    "print(f\"MPF + OBP:\\t{mpf_obp_expval_hw:.4f}, |∆| = {np.abs(ref_expval - mpf_obp_expval_hw):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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