{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8a7c9df5-d836-4ecb-8aec-8a1f2faa017a",
   "metadata": {},
   "source": [
    "# Using different Lp-norms for Pauli term truncation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5958e635-64c1-4599-82ca-225b83312906",
   "metadata": {},
   "source": [
    "**Note:** If you have not yet read the how-to guide on [truncating Pauli terms](https://qiskit.github.io/qiskit-addon-obp/how_tos/truncate_operator_terms.html) you should do so before reading this guide."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2780c587-cd2a-4398-8faa-de5e0c661a10",
   "metadata": {},
   "source": [
    "You are already familiar with the truncation of low-weight Pauli terms that is built into the [backpropagate](https://qiskit.github.io/qiskit-addon-obp/stubs/qiskit_addon_obp.backpropagate.html) method based on a specified [TruncationErrorBudget](https://qiskit.github.io/qiskit-addon-obp/stubs/qiskit_addon_obp.utils.truncating.TruncationErrorBudget.html).\n",
    "In this guide, you will learn about its additional keyword argument `p_norm`, which can be used to change the Lp-norm used to estimate the error incurred by the truncated Pauli terms."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "872aeae7-0312-41db-8ebb-f7b02838b54d",
   "metadata": {},
   "source": [
    "## Constructing an example circuit\n",
    "\n",
    "For the purposes of this guide, we will use the same example circuit as in the [Pauli term truncation guide](https://qiskit.github.io/qiskit-addon-obp/how_tos/truncate_operator_terms.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d6f281d4-706e-41ad-b7b5-bc7ebe106996",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1828x521.733 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import rustworkx.generators\n",
    "from qiskit.synthesis import LieTrotter\n",
    "from qiskit_addon_utils.problem_generators import (\n",
    "    PauliOrderStrategy,\n",
    "    generate_time_evolution_circuit,\n",
    "    generate_xyz_hamiltonian,\n",
    ")\n",
    "from qiskit_addon_utils.slicing import combine_slices, slice_by_gate_types\n",
    "\n",
    "# we generate a linear chain of 10 qubits\n",
    "num_qubits = 10\n",
    "linear_chain = rustworkx.generators.path_graph(num_qubits)\n",
    "\n",
    "# we use an arbitrary XY model\n",
    "hamiltonian = generate_xyz_hamiltonian(\n",
    "    linear_chain,\n",
    "    coupling_constants=(0.05, 0.02, 0.0),\n",
    "    ext_magnetic_field=(0.02, 0.08, 0.0),\n",
    "    pauli_order_strategy=PauliOrderStrategy.InteractionThenColor,\n",
    ")\n",
    "# we evolve for some time\n",
    "circuit = generate_time_evolution_circuit(hamiltonian, synthesis=LieTrotter(reps=3), time=2.0)\n",
    "# slice the circuit by gate type\n",
    "slices = slice_by_gate_types(circuit)\n",
    "\n",
    "# for visualization purposes only, we recombine the slices with barriers between them and draw the resulting circuit\n",
    "combine_slices(slices, include_barriers=True).draw(\"mpl\", fold=50, scale=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a7c7299-0c82-4279-b3dc-4f39e8dddd7e",
   "metadata": {},
   "source": [
    "The observable that we will look at is the total magnetization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ea9e7adc-b003-4762-a889-10e8d84a63d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "obs = SparsePauliOp.from_sparse_list(\n",
    "    [(\"Z\", [i], 1.0) for i in range(num_qubits)], num_qubits=num_qubits\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "423150d8-80d2-4b80-9665-033808d30272",
   "metadata": {},
   "source": [
    "For reference, we compute the exact expectation value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4dc72426-2eb5-4f8d-8bba-79650da06b54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.318197859862146\n"
     ]
    }
   ],
   "source": [
    "from qiskit.primitives import StatevectorEstimator\n",
    "\n",
    "estimator = StatevectorEstimator()\n",
    "job = estimator.run([(circuit, obs)])\n",
    "res = job.result()\n",
    "exact_exp = res[0].data.evs\n",
    "print(exact_exp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d21490c0-e86c-4fe0-af90-c9625813e0c0",
   "metadata": {},
   "source": [
    "## Using the L1 norm\n",
    "\n",
    "By default, and as you have already seen in the [other how-to guide](https://qiskit.github.io/qiskit-addon-obp/how_tos/truncate_operator_terms.html), `p_norm=1` which means that the error is estimated as:\n",
    "$$\n",
    "|\\langle\\psi|\\Delta|\\psi\\rangle| \\leq \\sum_{P\\in\\mathcal{T}} |c_P|\n",
    "$$\n",
    "where $\\psi$ is the quantum state, $\\Delta$ is the real difference between the exact and truncated observable (which is unknown), $\\mathcal{T}$ is the set of Pauli terms that were truncated and $c_P$ is the Pauli terms coefficient.\n",
    "This inequality is rigorous but a very loose upper bound for most scenarios."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "425293ce-49fb-4bd0-8d2f-44a3a43db967",
   "metadata": {},
   "source": [
    "For this simple guide, we will backpropagate 6 slices of our example circuit.\n",
    "We will use a constant error per slice of `0.001`. This value is to be understood as the budget within the given `p_norm`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b46531b3-055b-4112-903a-11f2dd52a9ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TruncationErrorBudget(per_slice_budget=[0.001], max_error_total=inf, p_norm=1)\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_obp.utils.truncating import setup_budget\n",
    "\n",
    "l1_truncation_error_budget = setup_budget(max_error_per_slice=0.001, p_norm=1)\n",
    "print(l1_truncation_error_budget)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bc252678-58a0-407e-91fe-b7c545d57ae8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Backpropagated 6 circuit slices.\n",
      "New observable contains 116 terms and 10 commuting groups.\n"
     ]
    }
   ],
   "source": [
    "from qiskit_addon_obp import backpropagate\n",
    "\n",
    "max_slices = 6\n",
    "l1_bp_obs, l1_remaining_slices, l1_metadata = backpropagate(\n",
    "    obs, slices[-max_slices:], truncation_error_budget=l1_truncation_error_budget\n",
    ")\n",
    "l1_reduced_circuit = combine_slices(slices[:-max_slices] + l1_remaining_slices)\n",
    "print(f\"Backpropagated {max_slices - len(l1_remaining_slices)} circuit slices.\")\n",
    "print(\n",
    "    f\"New observable contains {len(l1_bp_obs)} terms and {len(l1_bp_obs.group_commuting(qubit_wise=True))} commuting groups.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f2782f8-1e93-4319-af26-dc467d7ed459",
   "metadata": {},
   "source": [
    "We can now compute the expectation value of the backpropagated observable, as well as the error with respect to the exact reference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5be8c457-6569-452d-8502-0fc5e39bf918",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.317869899338842 0.00032796052330397174\n"
     ]
    }
   ],
   "source": [
    "estimator = StatevectorEstimator()\n",
    "job = estimator.run([(l1_reduced_circuit, l1_bp_obs)])\n",
    "res = job.result()\n",
    "l1_exp = res[0].data.evs\n",
    "l1_error = exact_exp - l1_exp\n",
    "print(l1_exp, l1_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0eccc5b-dc71-45b3-ad79-3d3dcb491f2d",
   "metadata": {},
   "source": [
    "Finally, we can plot the error incurred during the backpropagation of each slice, as well as the accumulated error.\n",
    "The accumulated error is simply the accumulated sum of the slice errors. We can see clearly that the accumulated error is a very loose upper bound to the actual error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ff72e77f-e2c0-4cce-8575-c5aa587f78fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x500 with 2 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_slice_errors,\n",
    ")\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "axes[1].plot([6], [l1_error], \"x\", color=\"red\", label=\"actual error\")\n",
    "plot_slice_errors(l1_metadata, axes[0])\n",
    "plot_accumulated_error(l1_metadata, axes[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10dd1139-c597-43c2-9f58-0a0988de768f",
   "metadata": {},
   "source": [
    "## Using the L2 norm\n",
    "\n",
    "One can argue that the L2 norm is a better approximation of the incurred error than the L1 norm.\n",
    "That is because we can assume the quantum state $|\\psi\\rangle$ to be drawn from a Haar random ensemble in which case the incurred error follows a distribution with a vanishing mean and a variance that can be approximately bound by the L2 norm:\n",
    "$$\n",
    "|\\langle\\psi|\\Delta|\\psi\\rangle| \\lesssim \\left( \\sum_{P\\in\\mathcal{T}} |c_P|^2 \\right)^{1/2}\n",
    "$$\n",
    "While the bound is not rigorous, it will only be violated in pathological cases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f302d808-b341-49cb-8bbd-b03f2bfc6dd6",
   "metadata": {},
   "source": [
    "Once again, we will backpropagate 6 slices of our example circuit using a maximum error per slice of `0.001` (this time, interpreted on the L2 norm)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c7b7e21f-22e4-479d-954c-39400974f8c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TruncationErrorBudget(per_slice_budget=[0.001], max_error_total=inf, p_norm=2)\n"
     ]
    }
   ],
   "source": [
    "l2_truncation_error_budget = setup_budget(max_error_per_slice=0.001, p_norm=2)\n",
    "print(l2_truncation_error_budget)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e92680c5-497e-47e0-ae0f-69465028dd66",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Backpropagated 6 circuit slices.\n",
      "New observable contains 84 terms and 6 commuting groups.\n"
     ]
    }
   ],
   "source": [
    "max_slices = 6\n",
    "l2_bp_obs, l2_remaining_slices, l2_metadata = backpropagate(\n",
    "    obs, slices[-max_slices:], truncation_error_budget=l2_truncation_error_budget\n",
    ")\n",
    "l2_reduced_circuit = combine_slices(slices[:-max_slices] + l2_remaining_slices)\n",
    "print(f\"Backpropagated {max_slices - len(l2_remaining_slices)} circuit slices.\")\n",
    "print(\n",
    "    f\"New observable contains {len(l2_bp_obs)} terms and {len(l2_bp_obs.group_commuting(qubit_wise=True))} commuting groups.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a05f992a-3a38-4912-9e1b-bcd40463c35e",
   "metadata": {},
   "source": [
    "Once again, we can compute the expectation value of the backpropagated observable, as well as the error with respect to the exact reference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "73fe737a-c3b0-4639-83dc-d614521dd77a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.317829770853422 0.00036808900872387085\n"
     ]
    }
   ],
   "source": [
    "estimator = StatevectorEstimator()\n",
    "job = estimator.run([(l2_reduced_circuit, l2_bp_obs)])\n",
    "res = job.result()\n",
    "l2_exp = res[0].data.evs\n",
    "l2_error = exact_exp - l2_exp\n",
    "print(l2_exp, l2_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81fd099c-f144-4c59-9b76-72fd8b06d8ad",
   "metadata": {},
   "source": [
    "Plotting the incurred errors per slice and the accumulated error yields a similar picture to before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fe7f454c-7d79-4c61-b1dd-6a98564fb5f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "axes[1].plot([6], [l2_error], \"x\", color=\"red\", label=\"actual error\")\n",
    "plot_slice_errors(l2_metadata, axes[0])\n",
    "plot_accumulated_error(l2_metadata, axes[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ef23a93-5c3b-48be-a02a-e666179c8c65",
   "metadata": {},
   "source": [
    "Note, that the accumulated error is once again simply the sum of the single slice errors. This is yet another loose bound due to the Minkowski inequality since we have to compute this bound recursively:\n",
    "$$\n",
    "|\\langle\\psi|\\Delta_{i}|\\psi\\rangle| \\leq |\\langle\\psi|\\tilde{\\Delta}_{i-1}|\\psi\\rangle| + \\left( \\sum_{P\\in\\mathcal{T_i}} |c_P|^2 \\right)^{1/2} = |\\langle\\psi|\\tilde{\\Delta}_{i}|\\psi\\rangle|\n",
    "$$\n",
    "where the new subscript $i$ indicates the current slice iteration making $\\Delta_i$ the actual error at backpropagation iteration $i$, $\\tilde{\\Delta}_{i-1}$ the approximated truncation error from iteration $i-1$ and $\\mathcal{T}_i$ the set of Pauli terms truncated at iteration $i$."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}