{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4f546a10",
   "metadata": {},
   "source": [
    "(samplex-io)="
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2997d421",
   "metadata": {},
   "source": [
    "# Samplex Inputs and Outputs\n",
    "\n",
    "## Introduction\n",
    "\n",
    "{class}`~.Samplex` is the core type of the samplomatic library.\n",
    "A samplex represents a parametric probability distribution over the\n",
    "parameters of some template circuit, as well as other array-valued fields to use in\n",
    "post-processing data collected from executing the bound template circuit. Its central interface \n",
    "is the {meth}`~.Samplex.sample` method that draws from this distribution to produce a\n",
    "collection of arrays.\n",
    "\n",
    "This guide is about using the {meth}`~.Samplex.sample` interface, how to query and specify required inputs, and how to inspect expected outputs.\n",
    "The arrays supplied to and returned from {meth}`~.Samplex.sample` are strongly typed, in the\n",
    "sense that for any particular instance of a samplex, their names, types, and shapes are fixed and queryable before any sampling is performed.\n",
    "The various inputs and outputs present in a samplex depend on many factors, for example, whether measurement twirling is present or whether noise\n",
    "injection is required.\n",
    "For this reason, we can't generally expect two samplex instances to have the same inputs and outputs as each other.\n",
    "\n",
    "## Setup\n",
    "\n",
    "To begin, we construct a boxed-up circuit and build it into a samplex and template pair to use in the examples that follow.\n",
    "Note that while manually boxing up the circuit, we use the names `alpha`, `beta`, `ref1`, `ref2`, `mod_ref1`, `mod_ref2`, `mod_ref3`, and `conclude`, and moreover the circuit has four `Parameter`s.\n",
    "This guide shows how each of these play a role in the samplex inputs and outputs.\n",
    "See [the transpiler guide](./transpiler) for information about boxing up circuits automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07d0b65e",
   "metadata": {
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "# Without this cell, plotly outputs do not appear in the docs. We hide this cell from itself being\n",
    "# rendered in the docs by editing its metadata to contain the tags [\"remove-input\", \"remove-output\"]\n",
    "import plotly.io as pio\n",
    "\n",
    "pio.renderers.default = \"sphinx_gallery\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0176921d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1334.69x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from qiskit.circuit import ClassicalRegister, Parameter, QuantumCircuit, QuantumRegister\n",
    "from qiskit.quantum_info import Operator, Pauli, PauliLindbladMap\n",
    "\n",
    "from samplomatic import ChangeBasis, InjectNoise, Twirl, build\n",
    "\n",
    "# our circuit has two classical registers named alpha and beta\n",
    "circuit = QuantumCircuit(\n",
    "    QuantumRegister(4), alpha := ClassicalRegister(3, \"alpha\"), beta := ClassicalRegister(1, \"beta\")\n",
    ")\n",
    "\n",
    "# the first box is only twirled\n",
    "with circuit.box([Twirl()]):\n",
    "    for idx in range(4):\n",
    "        circuit.rx(Parameter(f\"a{idx}\"), idx)\n",
    "    circuit.cz(0, 1)\n",
    "    circuit.cz(1, 2)\n",
    "\n",
    "# the second box is twirled, and has noise injected\n",
    "with circuit.box([Twirl(), InjectNoise(ref=\"ref1\", modifier_ref=\"mod_ref1\")]):\n",
    "    circuit.h(1)\n",
    "    circuit.cz(1, 2)\n",
    "\n",
    "# the third box is twirled, and has different noise injected\n",
    "with circuit.box([Twirl(), InjectNoise(ref=\"ref2\", modifier_ref=\"mod_ref2\")]):\n",
    "    circuit.rx(0.1, range(4))\n",
    "    circuit.cz(0, 1)\n",
    "    circuit.cz(1, 2)\n",
    "\n",
    "# the fourth box is the same as the second, but with a different modifer ref\n",
    "with circuit.box([Twirl(), InjectNoise(ref=\"ref1\", modifier_ref=\"mod_ref3\")]):\n",
    "    circuit.h(1)\n",
    "    circuit.cz(1, 2)\n",
    "\n",
    "circuit.barrier()\n",
    "\n",
    "# the final two boxes twirl, and add a basis change in one case\n",
    "with circuit.box([Twirl(), ChangeBasis(ref=\"conclude\")]):\n",
    "    circuit.measure(range(3), alpha)\n",
    "\n",
    "with circuit.box([Twirl()]):\n",
    "    circuit.measure([3], beta)\n",
    "\n",
    "circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f8a3aa7",
   "metadata": {},
   "source": [
    "Next, we call {func}`~.build` on the boxed-up circuit to construct a template and samplex pair, and we see how each of the boxes is turned into a barrier-sandwich including `rz-sx-rz-sx-rz` fragments to implement dressing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "daf30300",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4428.31x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "template, samplex = build(circuit)\n",
    "\n",
    "template.draw(\"mpl\", fold=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3540a34",
   "metadata": {},
   "source": [
    "Plotting the samplex DAG and hovering over the nodes we see that \n",
    " - All of the sampling nodes (stars) are responsible for generating randomizations for twirling, sampling from noise models, or injecting basis changes.\n",
    " - All of the collection nodes (bow ties) are responsible for rendering slices of outputs, which are either measurement flips or parameter angles.\n",
    " - All of the intermediate nodes (circles) are responsible for various kinds of data manipulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f9febfb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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New Roman\"}},\"hovertext\":[\"\\u003cb\\u003eTwirlSamplingNode(\\u003c+lhs_0, +rhs_0\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {lhs_0: (1, 'VirtualType.PAULI'), rhs_0: (1, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eLHS Register\\u003c\\u002fb\\u003e: 'lhs_0'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRHS Register\\u003c\\u002fb\\u003e: 'rhs_0'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eDistribution\\u003c\\u002fb\\u003e: UniformPauli(\\u003cnum_subsystems=1, register_type=VirtualType.PAULI\\u003e)\",\"\\u003cb\\u003eSliceRegisterNode(\\u003crhs_0(r), +z2_collect_1\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {rhs_0: ([0], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {z2_collect_1: (1, 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eCollectZ2ToOutputNode(\\u003cz2_collect_1(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {z2_collect_1: ([0], 'VirtualType.Z2')}\\u003cbr\\u003e\\n• \\u003cb\\u003eoutputs_to\\u003c\\u002fb\\u003e: {measurement_flips.beta: ([0], 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'z2_collect_1'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: measurement_flips.beta\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [0]\",\"\\u003cb\\u003eTwirlSamplingNode(\\u003c+lhs_2, +rhs_2\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {lhs_2: (3, 'VirtualType.PAULI'), rhs_2: (3, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eLHS Register\\u003c\\u002fb\\u003e: 'lhs_2'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRHS Register\\u003c\\u002fb\\u003e: 'rhs_2'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eDistribution\\u003c\\u002fb\\u003e: UniformPauli(\\u003cnum_subsystems=3, register_type=VirtualType.PAULI\\u003e)\",\"\\u003cb\\u003eSliceRegisterNode(\\u003crhs_2(r), +z2_collect_3\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {rhs_2: ([0, 1, 2], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {z2_collect_3: (3, 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eCollectZ2ToOutputNode(\\u003cz2_collect_3(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {z2_collect_3: ([0, 1, 2], 'VirtualType.Z2')}\\u003cbr\\u003e\\n• \\u003cb\\u003eoutputs_to\\u003c\\u002fb\\u003e: {measurement_flips.alpha: ([0, 1, 2], 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'z2_collect_3'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: measurement_flips.alpha\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [0 1 2]\",\"\\u003cb\\u003eChangeBasisNode(\\u003c+basis_change_4\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {basis_change_4: (3, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'basis_change_4'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystems\\u003c\\u002fb\\u003e: 3\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eBasis Reference\\u003c\\u002fb\\u003e: 'basis_changes.conclude'\",\"\\u003cb\\u003eTwirlSamplingNode(\\u003c+lhs_5, +rhs_5\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {lhs_5: (2, 'VirtualType.PAULI'), rhs_5: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eLHS Register\\u003c\\u002fb\\u003e: 'lhs_5'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRHS Register\\u003c\\u002fb\\u003e: 'rhs_5'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eDistribution\\u003c\\u002fb\\u003e: UniformPauli(\\u003cnum_subsystems=2, register_type=VirtualType.PAULI\\u003e)\",\"\\u003cb\\u003eInjectNoiseNode(\\u003c+inject_noise_6, +sign_6\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {inject_noise_6: (2, 'VirtualType.PAULI'), sign_6: (1, 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'inject_noise_6'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eNoise Reference\\u003c\\u002fb\\u003e: 'ref1'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eModifier Reference\\u003c\\u002fb\\u003e: 'mod_ref3'\",\"\\u003cb\\u003eCollectZ2ToOutputNode(\\u003csign_6(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {sign_6: ([0], 'VirtualType.Z2')}\\u003cbr\\u003e\\n• \\u003cb\\u003eoutputs_to\\u003c\\u002fb\\u003e: {pauli_signs: ([2], 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'sign_6'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: pauli_signs\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [0]\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cinject_noise_6(r), lhs_5(r), +leftwards_7\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {inject_noise_6: ([0, 1], 'VirtualType.PAULI'), lhs_5: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_7: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: PAULI\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_5': ([0, 1], [0, 1], 'VirtualType.PAULI'), 'inject_noise_6': ([0, 1], [0, 1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003ePauliPastCliffordNode(\\u003cleftwards_7(r), leftwards_7(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_7: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_7: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperation\\u003c\\u002fb\\u003e: 'cz'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'leftwards_7'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [[0, 1]]\",\"\\u003cb\\u003eSliceRegisterNode(\\u003cleftwards_7(r), +leftwards_8\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_7: ([0], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_8: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightMultiplicationNode(\\u003cleftwards_8(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_8: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eFixed Operand\\u003c\\u002fb\\u003e: U2Register(\\u003c1, 1\\u003e)\",\"\\u003cb\\u003eTwirlSamplingNode(\\u003c+lhs_9, +rhs_9\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {lhs_9: (4, 'VirtualType.PAULI'), rhs_9: (4, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eLHS Register\\u003c\\u002fb\\u003e: 'lhs_9'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRHS Register\\u003c\\u002fb\\u003e: 'rhs_9'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eDistribution\\u003c\\u002fb\\u003e: UniformPauli(\\u003cnum_subsystems=4, register_type=VirtualType.PAULI\\u003e)\",\"\\u003cb\\u003eCombineRegistersNode(\\u003clhs_0(r), rhs_9(r), +collect_10\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {lhs_0: ([0], 'VirtualType.PAULI'), rhs_9: ([3], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {collect_10: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 1\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_0': ([0], [0], 'VirtualType.PAULI'), 'rhs_9': ([3], [0], 'VirtualType.PAULI')}\",\"\\u003cb\\u003eCollectTemplateValues(\\u003ccollect_10(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {collect_10: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: 'parameter_values'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eTemplate Indices\\u003c\\u002fb\\u003e: [[45, 46, 47]]\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'collect_10'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003e\\u003cclass 'samplomatic.synths.synth.Synth'\\u003e\\u003c\\u002fb\\u003e: RzSxSynth(\\u003cnum_qubits_per_subsystem=1, num_params_per_subsystem=3\\u003e)\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cbasis_change_4(r), lhs_2(r), rhs_5(r), rhs_9(r), +collect_11\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• basis_change_4: ([0, 1, 2], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• lhs_2: ([0, 1, 2], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• rhs_5: ([0, 1], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• rhs_9: ([0], 'VirtualType.PAULI')\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {collect_11: (3, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 3\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_2': ([0, 1, 2], [0, 1, 2], 'VirtualType.PAULI'), 'basis_change_4': ([0, 1, 2], [0, 1, 2], 'VirtualType.U2'), 'rhs_5': ([0, 1], [1, 2], 'VirtualType.PAULI'), 'rhs_9': ([0], [0], 'VirtualType.PAULI')}\",\"\\u003cb\\u003eCollectTemplateValues(\\u003ccollect_11(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {collect_11: ([0, 1, 2], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: 'parameter_values'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eTemplate Indices\\u003c\\u002fb\\u003e: [[36, 37, 38], [39, 40, 41], [42, 43, 44]]\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'collect_11'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003e\\u003cclass 'samplomatic.synths.synth.Synth'\\u003e\\u003c\\u002fb\\u003e: RzSxSynth(\\u003cnum_qubits_per_subsystem=1, num_params_per_subsystem=3\\u003e)\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cleftwards_7(r), leftwards_8(r), rhs_9(r), +collect_12\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_7: ([1], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_8: ([0], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• rhs_9: ([1, 2], 'VirtualType.PAULI')\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {collect_12: (2, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'leftwards_7': ([1], [1], 'VirtualType.PAULI'), 'leftwards_8': ([0], [0], 'VirtualType.U2'), 'rhs_9': ([1, 2], [0, 1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003eCollectTemplateValues(\\u003ccollect_12(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {collect_12: ([0, 1], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: 'parameter_values'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eTemplate Indices\\u003c\\u002fb\\u003e: [[30, 31, 32], [33, 34, 35]]\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'collect_12'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003e\\u003cclass 'samplomatic.synths.synth.Synth'\\u003e\\u003c\\u002fb\\u003e: RzSxSynth(\\u003cnum_qubits_per_subsystem=1, num_params_per_subsystem=3\\u003e)\",\"\\u003cb\\u003eInjectNoiseNode(\\u003c+inject_noise_13, +sign_13\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {inject_noise_13: (4, 'VirtualType.PAULI'), sign_13: (1, 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'inject_noise_13'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystems\\u003c\\u002fb\\u003e: 4\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eNoise Reference\\u003c\\u002fb\\u003e: 'ref2'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eModifier Reference\\u003c\\u002fb\\u003e: 'mod_ref2'\",\"\\u003cb\\u003eCollectZ2ToOutputNode(\\u003csign_13(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {sign_13: ([0], 'VirtualType.Z2')}\\u003cbr\\u003e\\n• \\u003cb\\u003eoutputs_to\\u003c\\u002fb\\u003e: {pauli_signs: ([1], 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'sign_13'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: pauli_signs\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [0]\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cinject_noise_13(r), lhs_9(r), +leftwards_14\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {inject_noise_13: ([1, 2], 'VirtualType.PAULI'), lhs_9: ([1, 2], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_14: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: PAULI\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_9': ([1, 2], [0, 1], 'VirtualType.PAULI'), 'inject_noise_13': ([1, 2], [0, 1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003ePauliPastCliffordNode(\\u003cleftwards_14(r), leftwards_14(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_14: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_14: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperation\\u003c\\u002fb\\u003e: 'cz'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'leftwards_14'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [[0, 1]]\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cinject_noise_13(r), leftwards_14(r), lhs_9(r), +leftwards_15\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• inject_noise_13: ([0], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_14: ([0], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• lhs_9: ([0], 'VirtualType.PAULI')\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_15: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: PAULI\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_9': ([0], [0], 'VirtualType.PAULI'), 'inject_noise_13': ([0], [0], 'VirtualType.PAULI'), 'leftwards_14': ([0], [1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003ePauliPastCliffordNode(\\u003cleftwards_15(r), leftwards_15(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_15: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_15: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperation\\u003c\\u002fb\\u003e: 'cz'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'leftwards_15'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [[0, 1]]\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cinject_noise_13(r), lhs_9(r), +leftwards_16\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {inject_noise_13: ([3], 'VirtualType.PAULI'), lhs_9: ([3], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_16: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 1\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_9': ([3], [0], 'VirtualType.PAULI'), 'inject_noise_13': ([3], [0], 'VirtualType.PAULI')}\",\"\\u003cb\\u003eRightMultiplicationNode(\\u003cleftwards_16(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_16: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eFixed Operand\\u003c\\u002fb\\u003e: U2Register(\\u003c1, 1\\u003e)\",\"\\u003cb\\u003eSliceRegisterNode(\\u003cleftwards_14(r), +leftwards_17\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_14: ([1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_17: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightMultiplicationNode(\\u003cleftwards_17(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_17: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eFixed Operand\\u003c\\u002fb\\u003e: U2Register(\\u003c1, 1\\u003e)\",\"\\u003cb\\u003eTwirlSamplingNode(\\u003c+lhs_18, +rhs_18\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {lhs_18: (2, 'VirtualType.PAULI'), rhs_18: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eLHS Register\\u003c\\u002fb\\u003e: 'lhs_18'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRHS Register\\u003c\\u002fb\\u003e: 'rhs_18'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eDistribution\\u003c\\u002fb\\u003e: UniformPauli(\\u003cnum_subsystems=2, register_type=VirtualType.PAULI\\u003e)\",\"\\u003cb\\u003eInjectNoiseNode(\\u003c+inject_noise_19, +sign_19\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {inject_noise_19: (2, 'VirtualType.PAULI'), sign_19: (1, 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'inject_noise_19'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eNoise Reference\\u003c\\u002fb\\u003e: 'ref1'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eModifier Reference\\u003c\\u002fb\\u003e: 'mod_ref1'\",\"\\u003cb\\u003eCollectZ2ToOutputNode(\\u003csign_19(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {sign_19: ([0], 'VirtualType.Z2')}\\u003cbr\\u003e\\n• \\u003cb\\u003eoutputs_to\\u003c\\u002fb\\u003e: {pauli_signs: ([0], 'VirtualType.Z2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'sign_19'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: pauli_signs\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [0]\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cinject_noise_19(r), lhs_18(r), +leftwards_20\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {inject_noise_19: ([0, 1], 'VirtualType.PAULI'), lhs_18: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_20: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: PAULI\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_18': ([0, 1], [0, 1], 'VirtualType.PAULI'), 'inject_noise_19': ([0, 1], [0, 1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003ePauliPastCliffordNode(\\u003cleftwards_20(r), leftwards_20(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_20: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_20: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperation\\u003c\\u002fb\\u003e: 'cz'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'leftwards_20'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [[0, 1]]\",\"\\u003cb\\u003eSliceRegisterNode(\\u003cleftwards_20(r), +leftwards_21\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_20: ([0], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_21: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightMultiplicationNode(\\u003cleftwards_21(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_21: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eFixed Operand\\u003c\\u002fb\\u003e: U2Register(\\u003c1, 1\\u003e)\",\"\\u003cb\\u003eTwirlSamplingNode(\\u003c+lhs_22, +rhs_22\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {lhs_22: (4, 'VirtualType.PAULI'), rhs_22: (4, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eLHS Register\\u003c\\u002fb\\u003e: 'lhs_22'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRHS Register\\u003c\\u002fb\\u003e: 'rhs_22'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eDistribution\\u003c\\u002fb\\u003e: UniformPauli(\\u003cnum_subsystems=4, register_type=VirtualType.PAULI\\u003e)\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cleftwards_20(r), leftwards_21(r), rhs_22(r), +collect_23\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_20: ([1], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_21: ([0], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• rhs_22: ([1, 2], 'VirtualType.PAULI')\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {collect_23: (2, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'leftwards_20': ([1], [1], 'VirtualType.PAULI'), 'leftwards_21': ([0], [0], 'VirtualType.U2'), 'rhs_22': ([1, 2], [0, 1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003eCollectTemplateValues(\\u003ccollect_23(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {collect_23: ([0, 1], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: 'parameter_values'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eTemplate Indices\\u003c\\u002fb\\u003e: [[12, 13, 14], [15, 16, 17]]\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'collect_23'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003e\\u003cclass 'samplomatic.synths.synth.Synth'\\u003e\\u003c\\u002fb\\u003e: RzSxSynth(\\u003cnum_qubits_per_subsystem=1, num_params_per_subsystem=3\\u003e)\",\"\\u003cb\\u003eSliceRegisterNode(\\u003clhs_22(r), +leftwards_24\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {lhs_22: ([1, 2], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_24: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003ePauliPastCliffordNode(\\u003cleftwards_24(r), leftwards_24(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_24: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_24: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperation\\u003c\\u002fb\\u003e: 'cz'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'leftwards_24'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [[0, 1]]\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cleftwards_24(r), lhs_22(r), +leftwards_25\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_24: ([0], 'VirtualType.PAULI'), lhs_22: ([0], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_25: (2, 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: PAULI\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'lhs_22': ([0], [0], 'VirtualType.PAULI'), 'leftwards_24': ([0], [1], 'VirtualType.PAULI')}\",\"\\u003cb\\u003ePauliPastCliffordNode(\\u003cleftwards_25(r), leftwards_25(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_25: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_25: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperation\\u003c\\u002fb\\u003e: 'cz'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'leftwards_25'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eSubsystem Indices\\u003c\\u002fb\\u003e: [[0, 1]]\",\"\\u003cb\\u003eSliceRegisterNode(\\u003cleftwards_25(r), +leftwards_26\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_25: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_26: (2, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightU2ParametricMultiplicationNode(\\u003cleftwards_26(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_26: ([0, 1], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperand\\u003c\\u002fb\\u003e: 'rx'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eParameter Indices\\u003c\\u002fb\\u003e: [0, 1]\",\"\\u003cb\\u003eSliceRegisterNode(\\u003clhs_22(r), +leftwards_27\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {lhs_22: ([3], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_27: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightU2ParametricMultiplicationNode(\\u003cleftwards_27(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_27: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperand\\u003c\\u002fb\\u003e: 'rx'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eParameter Indices\\u003c\\u002fb\\u003e: [2]\",\"\\u003cb\\u003eSliceRegisterNode(\\u003cleftwards_24(r), +leftwards_28\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_24: ([1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_28: (1, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightU2ParametricMultiplicationNode(\\u003cleftwards_28(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_28: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperand\\u003c\\u002fb\\u003e: 'rx'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eParameter Indices\\u003c\\u002fb\\u003e: [3]\",\"\\u003cb\\u003eSliceRegisterNode(\\u003cleftwards_15(r), +leftwards_29\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {leftwards_15: ([0, 1], 'VirtualType.PAULI')}\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {leftwards_29: (2, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\",\"\\u003cb\\u003eRightMultiplicationNode(\\u003cleftwards_29(w)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ewrites_to\\u003c\\u002fb\\u003e: {leftwards_29: ([0], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eFixed Operand\\u003c\\u002fb\\u003e: U2Register(\\u003c1, 1\\u003e)\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cleftwards_16(r), leftwards_17(r), leftwards_29(r), rhs_18(r), rhs_22(r), +collect_30\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_16: ([0], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_17: ([0], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_29: ([0, 1], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• rhs_18: ([0, 1], 'VirtualType.PAULI')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• rhs_22: ([0, 3], 'VirtualType.PAULI')\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {collect_30: (4, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 4\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'leftwards_16': ([0], [3], 'VirtualType.U2'), 'leftwards_17': ([0], [2], 'VirtualType.U2'), 'leftwards_29': ([1, 0], [0, 1], 'VirtualType.U2'), 'rhs_18': ([0, 1], [1, 2], 'VirtualType.PAULI'), 'rhs_22': ([0, 3], [0, 3], 'VirtualType.PAULI')}\",\"\\u003cb\\u003eCollectTemplateValues(\\u003ccollect_30(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {collect_30: ([0, 1, 2, 3], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: 'parameter_values'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eTemplate Indices\\u003c\\u002fb\\u003e: [[18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'collect_30'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003e\\u003cclass 'samplomatic.synths.synth.Synth'\\u003e\\u003c\\u002fb\\u003e: RzSxSynth(\\u003cnum_qubits_per_subsystem=1, num_params_per_subsystem=3\\u003e)\",\"\\u003cb\\u003eCombineRegistersNode(\\u003cleftwards_26(r), leftwards_27(r), leftwards_28(r), +collect_31\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_26: ([0, 1], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_27: ([0], 'VirtualType.U2')\\n\\u003c\\u002fbr\\u003e&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;• leftwards_28: ([0], 'VirtualType.U2')\\u003cbr\\u003e\\n• \\u003cb\\u003einstantiates\\u003c\\u002fb\\u003e: {collect_31: (4, 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Type\\u003c\\u002fb\\u003e: U2\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Num Subsystems\\u003c\\u002fb\\u003e: 4\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOperands\\u003c\\u002fb\\u003e: {'leftwards_26': ([1, 0], [0, 1], 'VirtualType.U2'), 'leftwards_27': ([0], [3], 'VirtualType.U2'), 'leftwards_28': ([0], [2], 'VirtualType.U2')}\",\"\\u003cb\\u003eCollectTemplateValues(\\u003ccollect_31(r)\\u003e)\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n• \\u003cb\\u003ereads_from\\u003c\\u002fb\\u003e: {collect_31: ([0, 1, 2, 3], 'VirtualType.U2')}\\u003cbr\\u003e\\n────────────────────────────\\u003cb\\u003e\\u003c\\u002fb\\u003e\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eOutput Name\\u003c\\u002fb\\u003e: 'parameter_values'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eTemplate Indices\\u003c\\u002fb\\u003e: [[0, 1, 2], [3, 4, 5], [6, 7, 8], [9, 10, 11]]\\u003cbr\\u003e\\n ▸ \\u003cb\\u003eRegister Name\\u003c\\u002fb\\u003e: 'collect_31'\\u003cbr\\u003e\\n ▸ \\u003cb\\u003e\\u003cclass 'samplomatic.synths.synth.Synth'\\u003e\\u003c\\u002fb\\u003e: RzSxSynth(\\u003cnum_qubits_per_subsystem=1, 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                       {\"responsive\": true}                    )                };            </script>        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samplex.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50e7afc6",
   "metadata": {},
   "source": [
    "## Querying the required inputs and expected outputs\n",
    "\n",
    "The easiest way to see the required inputs and expected outputs is to print the {class}`~.Samplex` object. Array items are formatted as `'{name}' <{type}[{shape}...]>`, and the required inputs precede the optional inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b438811f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Samplex(<57 nodes>)\n",
      "  Inputs:\n",
      "  - 'basis_changes.conclude' <uint8[3]>: Basis changing gates, in the symplectic ordering\n",
      "      I=0, Z=1, X=2, and Y=3.\n",
      "  - 'parameter_values' <float64[4]>: Input parameter values to use during sampling.\n",
      "  - 'pauli_lindblad_maps.ref1' <PauliLindbladMap>: A PauliLindblad map acting on 2 qubits,\n",
      "      with 'num_terms_ref1' terms.\n",
      "  - 'pauli_lindblad_maps.ref2' <PauliLindbladMap>: A PauliLindblad map acting on 4 qubits,\n",
      "      with 'num_terms_ref2' terms.\n",
      "\n",
      "  - 'local_scales.mod_ref1' <float64['num_terms_ref1']>: (Optional) An array of factors by\n",
      "      which to scale individual rates of a Pauli Lindblad map, where the order should match the\n",
      "      corresponding list of terms.\n",
      "  - 'local_scales.mod_ref2' <float64['num_terms_ref2']>: (Optional) An array of factors by\n",
      "      which to scale individual rates of a Pauli Lindblad map, where the order should match the\n",
      "      corresponding list of terms.\n",
      "  - 'local_scales.mod_ref3' <float64['num_terms_ref1']>: (Optional) An array of factors by\n",
      "      which to scale individual rates of a Pauli Lindblad map, where the order should match the\n",
      "      corresponding list of terms.\n",
      "  - 'noise_scales.mod_ref1' <float64[]>: (Optional) A scalar factor by which to scale rates\n",
      "      of a Pauli Lindblad map.\n",
      "  - 'noise_scales.mod_ref2' <float64[]>: (Optional) A scalar factor by which to scale rates\n",
      "      of a Pauli Lindblad map.\n",
      "  - 'noise_scales.mod_ref3' <float64[]>: (Optional) A scalar factor by which to scale rates\n",
      "      of a Pauli Lindblad map.\n",
      "  Outputs:\n",
      "    * 'measurement_flips.alpha' <bool['num_randomizations', 1, 3]>: Bit-flip corrections\n",
      "        for measurement twirling.\n",
      "    * 'measurement_flips.beta' <bool['num_randomizations', 1, 1]>: Bit-flip corrections for\n",
      "        measurement twirling.\n",
      "    * 'parameter_values' <float32['num_randomizations', 48]>: Parameter values valid for an\n",
      "        associated template circuit.\n",
      "    * 'pauli_signs' <bool['num_randomizations', 3]>: Signs from sampled Pauli Lindblad\n",
      "        maps. The order matches the iteration order of injected noise in the circuit.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(samplex)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a45dbea",
   "metadata": {},
   "source": [
    "The {meth}`~.Samplex.inputs` and {meth}`~.Samplex.outputs` of the samplex, as well as more detailed information like their names, shapes, types, and descriptions, can also be queried programatically. The return type of both of these methods is a {class}`~.TensorInterface`. For example, we list here all specifications of the input interface:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "11348b44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[TensorSpecification('basis_changes.conclude', (3,), dtype('uint8'), 'Basis changing gates, in the symplectic ordering I=0, Z=1, X=2, and Y=3. '),\n",
       " TensorSpecification('local_scales.mod_ref1', ('num_terms_ref1',), dtype('float64'), 'An array of factors by which to scale individual rates of a Pauli Lindblad map, where the order should match the corresponding list of terms.', optional=True),\n",
       " TensorSpecification('local_scales.mod_ref2', ('num_terms_ref2',), dtype('float64'), 'An array of factors by which to scale individual rates of a Pauli Lindblad map, where the order should match the corresponding list of terms.', optional=True),\n",
       " TensorSpecification('local_scales.mod_ref3', ('num_terms_ref1',), dtype('float64'), 'An array of factors by which to scale individual rates of a Pauli Lindblad map, where the order should match the corresponding list of terms.', optional=True),\n",
       " TensorSpecification('noise_scales.mod_ref1', (), dtype('float64'), 'A scalar factor by which to scale rates of a Pauli Lindblad map.', optional=True),\n",
       " TensorSpecification('noise_scales.mod_ref2', (), dtype('float64'), 'A scalar factor by which to scale rates of a Pauli Lindblad map.', optional=True),\n",
       " TensorSpecification('noise_scales.mod_ref3', (), dtype('float64'), 'A scalar factor by which to scale rates of a Pauli Lindblad map.', optional=True),\n",
       " TensorSpecification('parameter_values', (4,), dtype('float64'), 'Input parameter values to use during sampling.'),\n",
       " PauliLindbladMapSpecification('pauli_lindblad_maps.ref1', num_qubits=2, num_terms=num_terms_ref1),\n",
       " PauliLindbladMapSpecification('pauli_lindblad_maps.ref2', num_qubits=4, num_terms=num_terms_ref2)]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samplex.inputs().specs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a95cda",
   "metadata": {},
   "source": [
    "Next, as an example, we choose to print some information about those output specifiers whose names contain the string `\"flips\"`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d764761d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "measurement_flips.alpha ('num_randomizations', 1, 3) bool\n",
      "measurement_flips.beta ('num_randomizations', 1, 1) bool\n"
     ]
    }
   ],
   "source": [
    "for spec in samplex.outputs().get_specs(\"flips\"):\n",
    "    print(spec.name, spec.shape, spec.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6da925d5",
   "metadata": {},
   "source": [
    "## Binding input values and sampling\n",
    "\n",
    "In order to {meth}`~.Samplex.sample`, the samplex needs to be provided with values for at least those {meth}`~.Samplex.inputs` that are marked as required.\n",
    "These values are first bound to an input interface so that it can perform all necessary type checking (or type coercion in some cases) and shape analysis. \n",
    "If anything is wrong with the types or shapes, or if a required value is missing, a verbose error is raised.\n",
    "\n",
    "### Binding input\n",
    "\n",
    "In the following example, we pass the {meth}`~.Samplex.sample` method its bare minimum requirements, and use it to draw 3 randomizations from the samplex.\n",
    "The required bindings arising from the dressings are the Pauli Lindblad maps for noise injection and the basis change array. In addition to these, values for the four parameters in the original boxed-up circuit are required, which in this case we set to `np.linspace(0, 1, 4)`. The samplex will compose these parameters into the dressings, so that they effectively end up as modifications to the output parameter values of the samplex.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "674498e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SamplexOutput(<\n",
      "  - Dimension constraints: num_randomizations=3\n",
      "\n",
      "  * 'measurement_flips.alpha' <bool['num_randomizations', 1, 3]>: Bit-flip corrections for\n",
      "      measurement twirling.\n",
      "  * 'measurement_flips.beta' <bool['num_randomizations', 1, 1]>: Bit-flip corrections for\n",
      "      measurement twirling.\n",
      "  * 'parameter_values' <float32['num_randomizations', 48]>: Parameter values valid for an\n",
      "      associated template circuit.\n",
      "  * 'pauli_signs' <bool['num_randomizations', 3]>: Signs from sampled Pauli Lindblad maps.\n",
      "      The order matches the iteration order of injected noise in the circuit.\n",
      ">)\n"
     ]
    }
   ],
   "source": [
    "inputs = samplex.inputs().bind(\n",
    "    # bind() concatenates nested dicts with a '.' so that we can\n",
    "    # set 'pauli_lindblad_maps.noise0/1' as follows. note that the\n",
    "    # names 'ref1' and 'ref2' derive from the names in the InjectNoise\n",
    "    # annotation.\n",
    "    pauli_lindblad_maps={\n",
    "        \"ref1\": PauliLindbladMap.identity(2),\n",
    "        \"ref2\": PauliLindbladMap.identity(4),\n",
    "    },\n",
    "    # likewise, we can set all basis changes as follows, where\n",
    "    # the name 'conclude' comes from our basis change annotation\n",
    "    basis_changes={\"conclude\": [0, 1, 2]},\n",
    "    # we must provide values for all parameters in the original circuit\n",
    "    parameter_values=np.linspace(0, 1, 4),\n",
    ")\n",
    "\n",
    "outputs = samplex.sample(inputs, num_randomizations=3)\n",
    "print(outputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a212742",
   "metadata": {},
   "source": [
    "Inputs can be bound to the interface through multiple calls to {meth}`~.TensorInterface.bind` or by direct item assignment.\n",
    "Despite the nested dictionary format that {meth}`~.TensorInterface.bind` allows for convenience, it is a flat mapping object, and supports all of the usual mapping syntax.\n",
    "Once all required inputs have been found, {attr}`~.TensorInterface.fully_bound` becomes true."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "898d2d00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fully bound? False\n",
      "Fully bound? True\n",
      "Fully bound? True\n"
     ]
    }
   ],
   "source": [
    "inputs = (\n",
    "    samplex.inputs()\n",
    "    .bind(\n",
    "        pauli_lindblad_maps={\n",
    "            \"ref1\": PauliLindbladMap.identity(2),\n",
    "            \"ref2\": PauliLindbladMap.identity(4),\n",
    "        }\n",
    "    )\n",
    "    .bind(parameter_values=np.linspace(0, 1, 4))\n",
    ")\n",
    "\n",
    "# once the final requirement is bound, fully_bound becomes True\n",
    "print(\"Fully bound?\", inputs.fully_bound)\n",
    "inputs[\"basis_changes.conclude\"] = [0, 2, 3]\n",
    "print(\"Fully bound?\", inputs.fully_bound)\n",
    "\n",
    "# setting optional values does not affect whether the interface is fully bound\n",
    "inputs[\"noise_scales.mod_ref1\"] = 3\n",
    "print(\"Fully bound?\", inputs.fully_bound)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af2782a0",
   "metadata": {},
   "source": [
    "All {class}`~.TensorInterface` objects, including the {class}`~.SamplexOutput` subclass, are mapping objects against data that has been bound to them.\n",
    "This means that we can get, for example, the template parameter values as follows, which in this case has shape `(3, 48)` since we asked for 3 randomizations and the template circuit has 48 parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "de081625",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(num_randomizations, num_template_params) = (3, 48)\n",
      "[ 3.1415927   3.1415927   0.          1.5707964   0.33333334 -1.5707964\n",
      "  1.5707964   0.6666667   1.5707964  -1.5707964   2.1415927  -1.5707964\n",
      "  0.          1.5707964   3.1415927   3.1415927   3.1415927   0.\n",
      " -1.5707964   0.1         1.5707964  -1.5707964   0.1         1.5707964\n",
      " -1.5707964   0.1         1.5707964   1.5707964   0.1         1.5707964\n",
      "  3.1415927   1.5707964   0.          3.1415927   3.1415927   0.\n",
      " -1.5707964   3.1415927   1.5707964  -1.5707964   3.1415927   1.5707964\n",
      "  0.          1.5707964   0.          3.1415927   3.1415927   0.        ]\n"
     ]
    }
   ],
   "source": [
    "print(\"(num_randomizations, num_template_params) =\", outputs[\"parameter_values\"].shape)\n",
    "print(outputs[\"parameter_values\"][0, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "611cbea9",
   "metadata": {},
   "source": [
    "### Specifying input as a dictionary\n",
    "\n",
    "Instead of providing a fully-bound {class}`~.TensorInterface`, we can specify the inputs as a standard dictionary, as is shown in the cell below. In this case, the {meth}`~.Samplex.sample` method internally binds the items of the dictionary to the samplex' input interface to validate all required inputs are present and compatible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba9ac951",
   "metadata": {},
   "outputs": [],
   "source": [
    "inputs = {\n",
    "    \"pauli_lindblad_maps\": {\n",
    "        \"ref1\": PauliLindbladMap.identity(2),\n",
    "        \"ref2\": PauliLindbladMap.identity(4),\n",
    "    },\n",
    "    \"basis_changes\": {\"conclude\": [0, 1, 2]},\n",
    "    \"parameter_values\": np.linspace(0, 1, 4),\n",
    "}\n",
    "outputs = samplex.sample(inputs, num_randomizations=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aeae6d5c",
   "metadata": {},
   "source": [
    "### Input types\n",
    "\n",
    "Presently, there are two distinct interface value types, though this may grow:\n",
    " - Array-valued: These have a shape and a data type. Bound values are coerced into the data type if possible. Any dimension can be a free dimension.\n",
    " - Pauli Lindblad maps: These must be of type {class}`qiskit.quantum_info.PauliLindbladMap` and must act on the prescribed number of qubits. The number of terms in the map is a free dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "482b839f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# up to precision loss, these are equivalent via automatic type coersion of array inputs\n",
    "samplex.inputs()[\"parameter_values\"] = [1, 2, 8, 9]\n",
    "samplex.inputs()[\"parameter_values\"] = np.array([1, 2, 8, 9], dtype=np.float16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23b10694",
   "metadata": {},
   "source": [
    "### Free dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2b10f7d",
   "metadata": {},
   "source": [
    "The {class}`~.TensorInterface` class has a notion of _free dimensions_, which are named integer sizes whose values are undetermined until some data has been bound to the interface that constrains them.\n",
    "All free dimensions of the same name must resolve to a consistent size when binding data or an error will be raised.\n",
    "For example, in the {meth}`~.Samplex.outputs` of any samplex, the array axis corresponding to randomizations is a free parameter that has the name `\"num_randomizations\"` by convention.\n",
    "When {func}`~.Samplex.sample` is called, it binds values to the outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1b5588dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All free dimensions: {'num_randomizations'}\n",
      "Current constraints: {'num_randomizations': 3}\n"
     ]
    }
   ],
   "source": [
    "print(\"All free dimensions:\", outputs.free_dimensions)\n",
    "print(\"Current constraints:\", outputs.bound_dimensions)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0f4f7a3",
   "metadata": {},
   "source": [
    "Another common free-dimension scenario is the sharing of term constraints between Pauli lindblad map specifications and their modifiers.\n",
    "A {class}`qiskit.quantum_info.PauliLindbladMap` is an ordered sequence of terms, where each term contains a floating point rate and a sparse Pauli representation.\n",
    "The {func}`~.build` function adds a specifier `\"pauli_lindblad_maps.<ref>\"` for this type for each {class}`~.InjectNoise` annotation, and if it contains a {attr}`~.InjectNoise.modifier_ref`,\n",
    "then a `\"local_scales.<modifier_ref>\"` specifier is also added.\n",
    "Both of these share the free dimension called `\"num_terms_<ref>\"` that specifies how many Pauli Lindblad terms are present in the noise model, for the latter needs to zip against the rates of the former in order to scale them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b8febe7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All free dimensions: {'num_terms_ref2', 'num_terms_ref1'}\n",
      "Current constraints: {'num_terms_ref2': 2}\n"
     ]
    }
   ],
   "source": [
    "# both the PauliLindbladMap and the local scales imply 2 terms, so that the free dimension\n",
    "# 'num_terms_noise2' is satisfied\n",
    "inputs = samplex.inputs().bind(\n",
    "    pauli_lindblad_maps={\"ref2\": PauliLindbladMap.from_list([(\"XXYZ\", 0.1), (\"IIXX\", 0.2)])},\n",
    "    local_scales={\"mod_ref2\": [1, 2]},\n",
    ")\n",
    "print(\"All free dimensions:\", inputs.free_dimensions)\n",
    "print(\"Current constraints:\", inputs.bound_dimensions)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ae1cf61",
   "metadata": {},
   "source": [
    "## Qubit ordering convention\n",
    "\n",
    "Samplexes constructed from boxed-up circuits by the {func}`~.build` function can require array-valued inputs to {meth}`~.Samplex.sample` where one index corresponds to qubits of some box of the circuit.\n",
    "This section explains the ordering convention that should be used for such axes.\n",
    "In short: use the qubit order of the boxed-up circuit, restricted to the qubits of the box.\n",
    "\n",
    "As an example, suppose we are trying to figure out how to specify a Pauli Lindblad map for `\"noise1\"`.\n",
    "Then the order of qubits in the noise map is with respect to these qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ff6b8981",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<Qubit register=(4, \"q0\"), index=1>, <Qubit register=(4, \"q0\"), index=2>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "box_of_interest = circuit[1]\n",
    "qubit_ordering_convention = [qubit for qubit in circuit.qubits if qubit in box_of_interest.qubits]\n",
    "qubit_ordering_convention"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cb8cfbb",
   "metadata": {},
   "source": [
    "That is, if we want `<Qubit register=(4, \"q0\"), index=2>` to be noisy with `X` noise, then we should define a Pauli Lindblad map like this one because it is at index `1` of `qubit_ordering_convention`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a0214a6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<PauliLindbladMap with 1 term on 2 qubits: (0.12)L(X_1)>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samplex.inputs().bind(\n",
    "    pauli_lindblad_maps={\n",
    "        \"ref1\": (noise1 := PauliLindbladMap.from_sparse_list([(\"X\", [1], 0.12)], num_qubits=2))\n",
    "    }\n",
    ")\n",
    "noise1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13015694",
   "metadata": {},
   "source": [
    "The same holds true for basis changes. If we want to rotate into the +1 eigenstates of the operators X, Y, and Z for qubits 0, 1, and 2 of `circuit` respectively, then we should do so with the following array, recalling the symplectic convention {math}`I=0`, {math}`Z=1`, {math}`X=2`, and {math}`Y=3` is used in this library, as well as qiskit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e99ff659",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 1]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samplex.inputs().bind(basis_changes={\"conclude\": (basis_change := [2, 3, 1])})\n",
    "basis_change"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7db1a4ed",
   "metadata": {},
   "source": [
    "Note that the qubit ordering convention is _not_ the order defined by:\n",
    " - `box_instruction.qubits`, where `box_instruction` is a {class}`qiskit.circuit.CircuitInstruction` whose operation is a {class}`qiskit.circuit.BoxOp`, because the order of this list of qubits may depend on the order in which instructions were added to the box context, which would be a confusing convention. For example, `with box(): circuit.x([0, 1])` and `with box(): circuit.x([1, 0])` would result in different orderings.\n",
    " - `box_instruction.operation.body.qubits` because these qubits might not even appear in the outer circuit; qubits inside of the actual body of `BoxOp` instructions (or any other control flow operation like `IfElseOp`) are only promised to have a consisent meaning within that scope. This would be an ill-defined convention, and hard to use in general."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57d97f42",
   "metadata": {},
   "source": [
    "## Local testing with the template circuit\n",
    "\n",
    "If a {class}`~.Samplex` is constructed via the {func}`~.build` function, then the parameter values that it outputs should be directly compatible with the parameters of the associated template circuit.\n",
    "For example, we can bind values for one of the randomizations to the template for local inspection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "563885fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4428.31x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inputs = samplex.inputs().bind(\n",
    "    pauli_lindblad_maps={\n",
    "        \"ref1\": PauliLindbladMap.identity(2),\n",
    "        \"ref2\": PauliLindbladMap.identity(4),\n",
    "    },\n",
    "    basis_changes={\"conclude\": [0, 0, 0]},\n",
    "    parameter_values=np.linspace(0, 1, 4),\n",
    ")\n",
    "\n",
    "outputs = samplex.sample(inputs, num_randomizations=3)\n",
    "\n",
    "bound_template = template.assign_parameters(outputs[\"parameter_values\"][2])\n",
    "bound_template.draw(\"mpl\", fold=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d46c1d45",
   "metadata": {},
   "source": [
    "This enables a means to inspect that the samplex is outputing samples that are expected.\n",
    "For example, below, we cast the bound circuit to a {class}`qiskit.quantum_info.Operator` object and compose with the bitflip Paulis to visually inspect that all three randomizations are logically equivalent to the base circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "492f3c01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit.transpiler import PassManager\n",
    "\n",
    "from samplomatic.transpiler.passes import InlineBoxes\n",
    "\n",
    "# Operator requires that we unpack all of the boxes first\n",
    "unboxed = PassManager([InlineBoxes()]).run(circuit).assign_parameters(inputs[\"parameter_values\"])\n",
    "# We want to plot unitary matrix amplitudes, so we need to remove the non-unitary measurements\n",
    "unboxed.remove_final_measurements()\n",
    "unboxed_unitary = Operator(unboxed)\n",
    "\n",
    "# Plot magnitudes of the unitary matrix represenation of the circuit\n",
    "plt.subplot(1, 4, 1)\n",
    "plt.imshow(np.abs(unboxed_unitary))\n",
    "plt.title(\"Base Circuit\")\n",
    "\n",
    "# For each randomization we sampled, plot the unitary matrix representation\n",
    "for idx in range(3):\n",
    "    bound_template = template.assign_parameters(outputs[\"parameter_values\"][idx])\n",
    "    bound_template.remove_final_measurements()\n",
    "\n",
    "    # Our example does measurement twirling by compiling random bitflip gates before the\n",
    "    # measurements, so we need to undo these at the operator level for each randomization.\n",
    "    # We do this by casting them to Paulis and composing with the bound circuit's unitary\n",
    "    alpha_flips = Pauli(([0, 0, 0], outputs[\"measurement_flips.alpha\"][idx, 0]))\n",
    "    beta_flips = Pauli(([0], outputs[\"measurement_flips.beta\"][idx, 0]))\n",
    "    flips = beta_flips ^ alpha_flips\n",
    "    bound_unitary = Operator(bound_template) & flips\n",
    "\n",
    "    # Plot magnitudes of the unitary matrix represenation of the circuit\n",
    "    plt.subplot(1, 4, idx + 2)\n",
    "    plt.imshow(np.abs(bound_unitary))\n",
    "    plt.title(f\"Randomization {idx}\")\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6924386c",
   "metadata": {},
   "source": [
    "Along the same lines, here, we pass output parameter values and the template to a sampler to simulate 10,000 shots of all randomizations, and compare the resulting expectation values (only of the alpha register) to the expectation values of a simulation of the base circuit alone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9ed6e27e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  EVs from base circuit: [0.7819611  0.93553883 0.99500417]\n",
      "EVs from randomizations: [0.7816 0.932  0.995 ]\n"
     ]
    }
   ],
   "source": [
    "from qiskit.primitives import StatevectorEstimator as Estimator\n",
    "from qiskit.primitives import StatevectorSampler as Sampler\n",
    "from qiskit.primitives.containers import BitArray\n",
    "\n",
    "# simulate some expectation values direction from the base circuit\n",
    "estimator_job = Estimator().run([(unboxed, [\"IZII\", \"IIZI\", \"IIIZ\"])])\n",
    "evs = estimator_job.result()[0].data[\"evs\"]\n",
    "\n",
    "# get the sampler data from each randomization, and do bitflip correction\n",
    "sampler_job = Sampler().run([(template, outputs[\"parameter_values\"])], shots=10_000)\n",
    "alpha_data = sampler_job.result()[0].data[\"alpha\"]\n",
    "alpha_data ^= BitArray.from_bool_array(outputs[\"measurement_flips.alpha\"], \"little\")\n",
    "\n",
    "# compare the results\n",
    "print(\"  EVs from base circuit:\", evs)\n",
    "print(\"EVs from randomizations:\", alpha_data.expectation_values([\"ZII\", \"IZI\", \"IIZ\"]))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}