{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "26d926db-2e2f-41ff-947e-9757a9f426d8",
   "metadata": {},
   "source": [
    "# Classically simulating circuits with OBP"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7642d6db-fe6d-4506-8e49-6c840f166e2b",
   "metadata": {},
   "source": [
    "In this guide, you will learn how to classically simulate `QuantumCircuit` instances to estimate expectation values entirely through the means of OBP.\n",
    "\n",
    "Since OBP will take an observable and backpropagate it through a given circuit, the \"simulation\" of a circuit amounts to computing the expectation value of the target observable with respect to this circuit.\n",
    "As you will see later, the `qiskit-addon-obp` package is even capable of handling simple noise models, allowing you to compute noisy expectation values, too!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e996d79-36fd-4a71-bd6b-737fc8e44987",
   "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": "b7946767-904b-422e-b076-7f956f3fdb70",
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63bcf4d0-7abe-4467-bc2b-f95d8d66dee5",
   "metadata": {},
   "source": [
    "However, the above is purely the circuit describing the time evolution under a chosen Hamiltonian.\n",
    "We also need an initial state to start from, with respect to which we compute the expectation values of our observable.\n",
    "\n",
    "Of course, we could choose the all-zero (or vacuum) state as our initial state, but to show how one would insert their own initial state, we choose a different one below.\n",
    "\n",
    "One possibility, would be to prepend the initial state to our time-evolution circuit above: `circuit.compose(initial_state, front=True)`.\n",
    "But since we have already sliced our `circuit`, it is easier to simply insert the initial state as the first slice, which we do below.\n",
    "\n",
    "In this way, we can simply replace the first slice with another initial state, if we want to exchange that in the future, without having to recompute our slices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ffaa07e2-af75-4424-9e7b-61c81b3bb9ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.circuit import QuantumCircuit\n",
    "\n",
    "initial_state = QuantumCircuit(num_qubits)\n",
    "for i in range(0, num_qubits, 2):\n",
    "    initial_state.x(i)\n",
    "\n",
    "slices.insert(0, initial_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8758f393-8691-4116-94ca-1185c6188bb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1928.33x521.733 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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": "bc9d51da-0a4e-46e2-8a5a-3501456aeb81",
   "metadata": {},
   "source": [
    "## Simulating a noiseless expectation value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1125cb39-4eda-4928-86b2-24e1872ed87e",
   "metadata": {},
   "source": [
    "As our target observable, we choose the `ZZ` observable on the central qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ee438fc3-8196-43d9-bcdb-956fd9ec4cf4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import SparsePauliOp\n",
    "\n",
    "obs = SparsePauliOp(\"IIIIZZIIII\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d06f10b0-683e-476e-9ac3-5c110364a0c8",
   "metadata": {},
   "source": [
    "At this point, we are already set to classically simulate the expectation value using OBP.\n",
    "To do so, we simply provide the _all_ the slices to the `backpropagate` method, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6402f5f5-08e0-4d05-ab2b-0c8863e9f966",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_obp import backpropagate\n",
    "\n",
    "vacuum_state_obs, _, metadata = backpropagate(obs, slices)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b2d555e-7fab-49f1-82d4-74a770f1be75",
   "metadata": {},
   "source": [
    "We have now backpropagated our target observable `obs` through the _entire_ circuit (**including** the `initial_state` which we placed on `slices[0]`) resulting in a new `SparsePauliOp` whose expectation value we obtain by projecting it on the _vacuum state_ (`|00...00>`).\n",
    "\n",
    "This can be achieved in a straight forward manner by summing up the coefficients of all Pauli terms defined in the computational basis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "63ae0edc-e8f6-467b-896a-ddd451d40a9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.complex128(-0.8285688012239535+4.9487770271457865e-20j)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vacuum_state_obs.coeffs[~vacuum_state_obs.paulis.x.any(axis=1)].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "107a0d89-323c-469b-8442-5e3f48169cd4",
   "metadata": {},
   "source": [
    "As a sanity check (and to prove that this works) we can compare our result against Qiskit's `Statevector`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f3cb999d-688a-4e82-bf12-d958ef0e2ec0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.complex128(-0.8285687255430366+0j)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "Statevector(combine_slices(slices)).expectation_value(obs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02207cde-e89e-4cf6-8b3e-727a750d245c",
   "metadata": {},
   "source": [
    "### Some notes on performance\n",
    "\n",
    "The computational efficiency of the `backpropagate` call above will heavily depend on many things, including:\n",
    "- the structure of the `circuit`\n",
    "- the method of slicing the circuit\n",
    "- the target observable\n",
    "- the truncation parameters\n",
    "\n",
    "Since the `backpropagate` method simplifies the observable after every _slice_ has been applied, the number of gates in a slice can dramatically influence the computational burden.\n",
    "The most aggressive strategy in terms of operator simplification can be achieved by slicing your circuit into slices of individual gates.\n",
    "\n",
    "Additionally, you can leverage all of the truncation mechanism built into the `backpropagate` method.\n",
    "We did not do so above, effectively resulting in an exact expectation value, but you can learn how to in the [Pauli term truncation guide](https://qiskit.github.io/qiskit-addon-obp/how_tos/truncate_operator_terms.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ba37abf-0f78-4053-8995-2ab8340237ab",
   "metadata": {},
   "source": [
    "## Simulating a noisy expectation value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a5e753b-c479-42d9-84d0-5ce4860ec091",
   "metadata": {},
   "source": [
    "The `qiskit-addon-obp` package also supports handling of noise models in the form of `PauliLindbladError`s.\n",
    "This is especially useful when you have characterized the noise model of the 2-qubit layers in your circuit, for example using the [`NoiseLearner`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/noise-learner-noise-learner).\n",
    "\n",
    "In this section, you will see how you can use the `LayerError` objects returned by the `NoiseLearner` to compute noisy expectation values using OBP."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d50dbf1-3abd-4945-bed9-1ed49758e9cc",
   "metadata": {},
   "source": [
    "### Obtaining a noise model\n",
    "\n",
    "Normally, you would execute the `NoiseLearner` to obtain a noise model of your specific circuit.\n",
    "To avoid complexity (and randomness) in this tutorial, we will refrain from doing so, and instead hard-code some noise model for our circuit below.\n",
    "\n",
    "However, we make sure that the structure of our data matches that of the [`NoiseLearnerResult`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/noise-learner-result)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54a7aba1-a7ee-4d0f-b95b-095158511ce0",
   "metadata": {},
   "source": [
    "In its current (non-transpiled) form, our circuit contains 4 unique layers of 2-qubit gates:\n",
    "- `slices[1]`: which has `Rxx` gates acting on all odd pairs of qubits\n",
    "- `slices[2]`: which has `Rxx` gates acting on all even pairs of qubits\n",
    "- `slices[3]`: which has `Ryy` gates acting on all odd pairs of qubits\n",
    "- `slices[4]`: which has `Ryy` gates acting on all even pairs of qubits\n",
    "\n",
    "In the cell below, we manually construct 4 `LayerError` instances for each one of these layers with some randomized error rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e7a3b1f9-b60c-4735-8d6b-5151a7c5b92b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit.quantum_info import PauliList\n",
    "from qiskit_ibm_runtime.utils.noise_learner_result import LayerError, PauliLindbladError\n",
    "\n",
    "# fmt: off\n",
    "pauli_errors_even = ['IIIIIIIIIX', 'IIIIIIIIIY', 'IIIIIIIIIZ', 'IIIIIIIIXI', 'IIIIIIIIXX', 'IIIIIIIIXY', 'IIIIIIIIXZ', 'IIIIIIIIYI', 'IIIIIIIIYX', 'IIIIIIIIYY', 'IIIIIIIIYZ', 'IIIIIIIIZI', 'IIIIIIIIZX', 'IIIIIIIIZY', 'IIIIIIIIZZ', 'IIIIIIIXII', 'IIIIIIIXXI', 'IIIIIIIXYI', 'IIIIIIIXZI', 'IIIIIIIYII', 'IIIIIIIYXI', 'IIIIIIIYYI', 'IIIIIIIYZI', 'IIIIIIIZII', 'IIIIIIIZXI', 'IIIIIIIZYI', 'IIIIIIIZZI', 'IIIIIIXIII', 'IIIIIIXXII', 'IIIIIIXYII', 'IIIIIIXZII', 'IIIIIIYIII', 'IIIIIIYXII', 'IIIIIIYYII', 'IIIIIIYZII', 'IIIIIIZIII', 'IIIIIIZXII', 'IIIIIIZYII', 'IIIIIIZZII', 'IIIIIXIIII', 'IIIIIXXIII', 'IIIIIXYIII', 'IIIIIXZIII', 'IIIIIYIIII', 'IIIIIYXIII', 'IIIIIYYIII', 'IIIIIYZIII', 'IIIIIZIIII', 'IIIIIZXIII', 'IIIIIZYIII', 'IIIIIZZIII', 'IIIIXIIIII', 'IIIIXXIIII', 'IIIIXYIIII', 'IIIIXZIIII', 'IIIIYIIIII', 'IIIIYXIIII', 'IIIIYYIIII', 'IIIIYZIIII', 'IIIIZIIIII', 'IIIIZXIIII', 'IIIIZYIIII', 'IIIIZZIIII', 'IIIXIIIIII', 'IIIXXIIIII', 'IIIXYIIIII', 'IIIXZIIIII', 'IIIYIIIIII', 'IIIYXIIIII', 'IIIYYIIIII', 'IIIYZIIIII', 'IIIZIIIIII', 'IIIZXIIIII', 'IIIZYIIIII', 'IIIZZIIIII', 'IIXIIIIIII', 'IIXXIIIIII', 'IIXYIIIIII', 'IIXZIIIIII', 'IIYIIIIIII', 'IIYXIIIIII', 'IIYYIIIIII', 'IIYZIIIIII', 'IIZIIIIIII', 'IIZXIIIIII', 'IIZYIIIIII', 'IIZZIIIIII', 'IXIIIIIIII', 'IXXIIIIIII', 'IXYIIIIIII', 'IXZIIIIIII', 'IYIIIIIIII', 'IYXIIIIIII', 'IYYIIIIIII', 'IYZIIIIIII', 'IZIIIIIIII', 'IZXIIIIIII', 'IZYIIIIIII', 'IZZIIIIIII', 'XIIIIIIIII', 'XXIIIIIIII', 'XYIIIIIIII', 'XZIIIIIIII', 'YIIIIIIIII', 'YXIIIIIIII', 'YYIIIIIIII', 'YZIIIIIIII', 'ZIIIIIIIII', 'ZXIIIIIIII', 'ZYIIIIIIII', 'ZZIIIIIIII']\n",
    "pauli_errors_odd = ['IIIIIIIIXI', 'IIIIIIIIYI', 'IIIIIIIIZI', 'IIIIIIIXII', 'IIIIIIIXXI', 'IIIIIIIXYI', 'IIIIIIIXZI', 'IIIIIIIYII', 'IIIIIIIYXI', 'IIIIIIIYYI', 'IIIIIIIYZI', 'IIIIIIIZII', 'IIIIIIIZXI', 'IIIIIIIZYI', 'IIIIIIIZZI', 'IIIIIIXIII', 'IIIIIIXXII', 'IIIIIIXYII', 'IIIIIIXZII', 'IIIIIIYIII', 'IIIIIIYXII', 'IIIIIIYYII', 'IIIIIIYZII', 'IIIIIIZIII', 'IIIIIIZXII', 'IIIIIIZYII', 'IIIIIIZZII', 'IIIIIXIIII', 'IIIIIXXIII', 'IIIIIXYIII', 'IIIIIXZIII', 'IIIIIYIIII', 'IIIIIYXIII', 'IIIIIYYIII', 'IIIIIYZIII', 'IIIIIZIIII', 'IIIIIZXIII', 'IIIIIZYIII', 'IIIIIZZIII', 'IIIIXIIIII', 'IIIIXXIIII', 'IIIIXYIIII', 'IIIIXZIIII', 'IIIIYIIIII', 'IIIIYXIIII', 'IIIIYYIIII', 'IIIIYZIIII', 'IIIIZIIIII', 'IIIIZXIIII', 'IIIIZYIIII', 'IIIIZZIIII', 'IIIXIIIIII', 'IIIXXIIIII', 'IIIXYIIIII', 'IIIXZIIIII', 'IIIYIIIIII', 'IIIYXIIIII', 'IIIYYIIIII', 'IIIYZIIIII', 'IIIZIIIIII', 'IIIZXIIIII', 'IIIZYIIIII', 'IIIZZIIIII', 'IIXIIIIIII', 'IIXXIIIIII', 'IIXYIIIIII', 'IIXZIIIIII', 'IIYIIIIIII', 'IIYXIIIIII', 'IIYYIIIIII', 'IIYZIIIIII', 'IIZIIIIIII', 'IIZXIIIIII', 'IIZYIIIIII', 'IIZZIIIIII', 'IXIIIIIIII', 'IXXIIIIIII', 'IXYIIIIIII', 'IXZIIIIIII', 'IYIIIIIIII', 'IYXIIIIIII', 'IYYIIIIIII', 'IYZIIIIIII', 'IZIIIIIIII', 'IZXIIIIIII', 'IZYIIIIIII', 'IZZIIIIIII']\n",
    "# fmt: on\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "layer_error_odd_xx = LayerError(\n",
    "    circuit=slices[1],\n",
    "    qubits=list(range(num_qubits)),\n",
    "    error=PauliLindbladError(\n",
    "        PauliList(pauli_errors_odd),\n",
    "        0.0001 + 0.0004 * np.random.rand(len(pauli_errors_odd)),\n",
    "    ),\n",
    ")\n",
    "\n",
    "layer_error_even_xx = LayerError(\n",
    "    circuit=slices[2],\n",
    "    qubits=list(range(num_qubits)),\n",
    "    error=PauliLindbladError(\n",
    "        PauliList(pauli_errors_even),\n",
    "        0.0001 + 0.0004 * np.random.rand(len(pauli_errors_even)),\n",
    "    ),\n",
    ")\n",
    "\n",
    "layer_error_odd_yy = LayerError(\n",
    "    circuit=slices[3],\n",
    "    qubits=list(range(num_qubits)),\n",
    "    error=PauliLindbladError(\n",
    "        PauliList(pauli_errors_odd),\n",
    "        0.0001 + 0.0004 * np.random.rand(len(pauli_errors_odd)),\n",
    "    ),\n",
    ")\n",
    "\n",
    "layer_error_even_yy = LayerError(\n",
    "    circuit=slices[4],\n",
    "    qubits=list(range(num_qubits)),\n",
    "    error=PauliLindbladError(\n",
    "        PauliList(pauli_errors_even),\n",
    "        0.0001 + 0.0004 * np.random.rand(len(pauli_errors_even)),\n",
    "    ),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9dff7ad-2c7a-4fc2-b7b5-5aa1a0e9b9db",
   "metadata": {},
   "source": [
    "If you would have used the `NoiseLearner` to identify the unique 2-qubit gate layers of your circuit and characterize their noise, you would obtain a `NoiseLearnerResult` object.\n",
    "This result would contain a list of `LayerError` objects, just like the ones we have manually constructed above.\n",
    "\n",
    "For each unique 2-qubit layer, the `LayerError` contains:\n",
    "- the `QuantumCircuit` representing that 2-qubit gate layer\n",
    "- the qubit indices which this circuit is acting upon\n",
    "- the `PauliLindbladError` which represents the characterized noise model of this layer\n",
    "\n",
    "The `PauliLindbladError` will contain two objects:\n",
    "- the list of Pauli errors that have been characterized\n",
    "- the error rates corresponding to each one of those Pauli errors\n",
    "\n",
    "Normally, the list of Pauli errors will be sparse. More specifically, it will contain the single-qubit Pauli errors on all qubits that have gates acting upon them as well as the two-qubit Pauli errors on all those qubits that are connected."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c3a1a9d-6fcb-4345-b9ba-e86e2e362a7e",
   "metadata": {},
   "source": [
    "### Inserting the noisy layers into our circuit\n",
    "\n",
    "In the previous section, we have specifically constructed one `LayerError` for each of our known unique 2-qubit gate layers.\n",
    "This means, we know which `LayerError` matches a specific one of our slices exactly.\n",
    "\n",
    "Normally, when using the `LayerError`, you will need to figure out what the unique 2-qubit gate layer is, and where it occurs inside of your circuit.\n",
    "You will then need to adjust your `circuit` and/or `slices` to insert the `LayerError` accordingly.\n",
    "How to do this in the general case, is beyond the scope of this how-to guide.\n",
    "**TODO: link to external documentation, once it exists!**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcb5937e-83d8-41ab-a526-d6677201c8f4",
   "metadata": {},
   "source": [
    "Here, our life is simpler because we know which slice a `LayerError` corresponds to.\n",
    "Therefore, it is now just a matter of inserting new slices to represent the noise.\n",
    "\n",
    "Note, that we must wrap each `PauliLindbladError` from `LayerError.error` in a `PauliLindbladErrorInstruction` for it to be a valid `QuantumCircuit` instruction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1f5c4655-f6af-439f-8475-0ecf0c673de5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_addon_obp.utils.noise import PauliLindbladErrorInstruction\n",
    "\n",
    "noisy_slices = []\n",
    "for slice_ in slices:\n",
    "    if slice_ == layer_error_even_xx.circuit:\n",
    "        noisy_slices.append(\n",
    "            QuantumCircuit.from_instructions(\n",
    "                [(PauliLindbladErrorInstruction(layer_error_even_xx.error), slice_.qubits)]\n",
    "            )\n",
    "        )\n",
    "    elif slice_ == layer_error_odd_xx.circuit:\n",
    "        noisy_slices.append(\n",
    "            QuantumCircuit.from_instructions(\n",
    "                [(PauliLindbladErrorInstruction(layer_error_odd_xx.error), slice_.qubits)]\n",
    "            )\n",
    "        )\n",
    "    elif slice_ == layer_error_even_yy.circuit:\n",
    "        noisy_slices.append(\n",
    "            QuantumCircuit.from_instructions(\n",
    "                [(PauliLindbladErrorInstruction(layer_error_even_yy.error), slice_.qubits)]\n",
    "            )\n",
    "        )\n",
    "    elif slice_ == layer_error_odd_yy.circuit:\n",
    "        noisy_slices.append(\n",
    "            QuantumCircuit.from_instructions(\n",
    "                [(PauliLindbladErrorInstruction(layer_error_odd_yy.error), slice_.qubits)]\n",
    "            )\n",
    "        )\n",
    "    noisy_slices.append(slice_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3778d94-4d04-4094-990d-a354f2062932",
   "metadata": {},
   "source": [
    "We can check our work and draw the circuit below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dadc314d-452f-465c-a382-d54685ce3f2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 4979.11x695.644 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combine_slices(noisy_slices, include_barriers=True).draw(\"mpl\", fold=100, scale=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10b88555-0263-4cdb-a4c1-6895d7e55a5b",
   "metadata": {},
   "source": [
    "### Simulating a noisy expectation value\n",
    "\n",
    "At this point, classically simulating the expectation value works exactly the same as before, just"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0e3ecb85-08c4-4fda-85e2-1000983c8842",
   "metadata": {},
   "outputs": [],
   "source": [
    "vacuum_state_noisy_obs, _, metadata = backpropagate(obs, noisy_slices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a74e9e88-2f1c-4d40-873d-bf4524e2b7fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.complex128(-0.7230801696448901+7.082755280463563e-19j)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vacuum_state_noisy_obs.coeffs[~vacuum_state_noisy_obs.paulis.x.any(axis=1)].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a4d2ff5-7c49-463e-8515-6fc9daa951ad",
   "metadata": {},
   "source": [
    "We point out again, that multiple performance concerns should be considered.\n",
    "Please go back to the [corresponding section above](#some-notes-on-performance)."
   ]
  }
 ],
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