diff --git a/docs/qubit_mapping_guide.ipynb b/docs/notebooks/qubit_mapping_guide.ipynb similarity index 100% rename from docs/qubit_mapping_guide.ipynb rename to docs/notebooks/qubit_mapping_guide.ipynb diff --git a/docs/pulse_efficient_transpilation_qsim.ipynb b/docs/pulse_efficient_transpilation_qsim.ipynb deleted file mode 100644 index d712825..0000000 --- a/docs/pulse_efficient_transpilation_qsim.ipynb +++ /dev/null @@ -1,787 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# How to transpile circuits in a pulse-efficient way?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this notebook, we show readers how to transpile circuits in a pulse-efficient way by transpiling the two-qubit gates into the [`RZXGate`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.RZXGate.html). The 'RZXGate' is a continuous gate set native to the hardware. We show examples where this method results in shorter circuit depth and duration. Since qubits have a limited coherence time, a shorter total circuit duration is desirable. We demonstrate how to implement this technique to transpile a relevant circuit in simulating quantum dynamics. And the Runtime result from the hardware suggests that the `RZXGate` type of transpilation produces more accurate results." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Start" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "# for circuit construction\n", - "from qiskit.circuit import QuantumCircuit, QuantumRegister, Parameter\n", - "from qiskit.circuit.library import PauliEvolutionGate\n", - "from qiskit.quantum_info import SparsePauliOp\n", - "\n", - "# for transpilation\n", - "from qiskit.providers import Backend\n", - "from qiskit.compiler import transpile, schedule as build_schedule\n", - "from qiskit.transpiler import PassManager, CouplingMap\n", - "from qiskit.transpiler.passes import (Optimize1qGatesDecomposition,\n", - " RZXCalibrationBuilder, \n", - " FullAncillaAllocation, \n", - " )\n", - "\n", - "# for running circuits on backend\n", - "from qiskit_ibm_runtime import QiskitRuntimeService\n", - "\n", - "# other basic modules\n", - "import numpy as np\n", - "import random\n", - "from typing import Dict, List\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "service = QiskitRuntimeService(channel=\"ibm_quantum\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Build\n", - "When running a generic quantum circuit on the hardware, the circuits need to be transpired into a basic set of gates so that it is compatible with a target backend. This process is handled by the [`qiskit.transpiler`](https://qiskit.org/documentation/apidoc/transpiler.html), and in the how-to guide, we will introduce two ways of defining the basis gate set." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# standard way: basis gate set that includes CNOT gate\n", - "BASIS_GATES = ['cx', 'x', 'sx', 'rz']\n", - "\n", - "# pulse efficient way: basis gate set that includes the pulse RZX gate\n", - "BASIS_GATES = ['rzx', 'x', 'sx', 'rz']" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A standard way to transpile is to transpile into a basis gate set that includes a CNOT gate, which is pre-calibrated on the hardware. In practice, CNOT gates have relatively long gate times and are one of the main sources of errors. In this guide, we show a method to transpile into a `RZXGate` pulse gate. It is a continuous two-qubit entangling gate with the angle $\\theta$ as a gate parameter and has adjustable gate time accordingly. In some use cases, we show that the transpiled circuits are pulse-efficient, meaning they have fewer two-qubit gates and a shorter circuit duration. This is beneficial since the qubits have a finite coherence time. \n", - "\n", - "The recipe to transpile into `RZXGate` has two main steps:\n", - "\n", - "* First, we decompose the input circuit in terms of single-qubit gates and the `RZXGate`;\n", - "* Strech the pulse schedule according to the desired rotation angle and attach the new schedule to the 'RZXGate's." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example: Ising model\n", - "\n", - "Let's start by looking at a simple example circuit on two qubits. The circuit example we use here simulates the dynamics generated by the Hamiltonian $H = - J \\sum_{i,j}Z_i\\otimes Z_j + h\\sum_{i}X_i$. To approximate the dynamics, we implement its trotterized evolution using [`PauliEvolutionGate`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.PauliEvolutionGate.html) pametrized by $J$, $h$ and the trotterized time step $t$." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "def build_trotter_evolution(num_qubits: int, rep = 1):\n", - " Jt = Parameter('Jt')\n", - " ht = Parameter('ht')\n", - " qr = QuantumRegister(num_qubits, 'q')\n", - " qc = QuantumCircuit(qr)\n", - " even_indices = [i for i in range(0, num_qubits-1, 2)]\n", - " odd_indices = [i for i in range(1, num_qubits-1, 2)]\n", - " for _ in range(rep):\n", - " for i in odd_indices + even_indices:\n", - " ZZ_term = 'I' * (num_qubits - i - 2) + 'ZZ' + 'I' * i\n", - " UU = PauliEvolutionGate(SparsePauliOp([ZZ_term]), time=Jt)\n", - " qc.append(UU, qr)\n", - " for i in range(num_qubits):\n", - " X_term = 'I' * (num_qubits - i - 1) + 'X' + 'I' * i \n", - " UU = PauliEvolutionGate(SparsePauliOp([X_term]), time=ht)\n", - " qc.append(UU, qr)\n", - " return qc\n", - "\n", - "qc = build_trotter_evolution(num_qubits=2)\n", - "qc.draw('mpl', fold=-1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Transpile" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's compare the following two transpilation methods:\n", - "1. transpile to the standard gate set with the CNOT gate\n", - "2. transpile into a basis gate set with `RZXGate`\n", - "We will compare the two-qubit circuit depth of the transpiled circuits. We only count the two-qubit gates here since they are considered more 'costly' as they have longer gate time than single-qubit gates and have a higher error rate." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "two-qubit circuit depth = 2\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# transpile into CNOT gates\n", - "cx_circ = transpile(qc, basis_gates=['cx', 'x', 'sx', 'rz'])\n", - "print(f'two-qubit circuit depth = {cx_circ.depth(lambda x: x[0].num_qubits == 2)}')\n", - "cx_circ.draw('mpl')" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "two-qubit circuit depth = 1\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# transpile into RZX gates\n", - "rzx_circ = transpile(qc, basis_gates=['rzx', 'x', 'sx', 'rz'])\n", - "print(f'two-qubit circuit depth = {rzx_circ.depth(lambda x: x[0].num_qubits == 2)}')\n", - "rzx_circ.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The RZX transpilation results in three `RZXGate`s, which effectively shortens the two-qubit circuit depth by half compared with the CNOT transpilation! In fact, this is a general result: any 2-qubit unitary can be represented in the `RZXGate` decomposition with at most three `RZXGate` via the so-called KAK decomposition. \n", - "\n", - "Notice that in the `RZXGate` transpiled circuit, the `RZXGate`s are parameterized by the angle `Jt.` To properly implement the gate, we need to instruct the hardware on the proper pulse schedule. This is done by creating a customized [pulse gate](https://qiskit.org/documentation/tutorials/circuits_advanced/05_pulse_gates.html) by attaching a stretched pulse schedule to the `RZXGate` based on the desired entangling angle. \n", - "\n", - "To show how to do this, we first pick a backend to transpile the circuit to and assign values to the circuit paramters." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "backend = service.get_backend('ibm_auckland')" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "# TODO: assign parameters by name instead of order\n", - "J = 1\n", - "h = 1\n", - "t = random.uniform(0,np.pi)\n", - "params = rzx_circ.parameters\n", - "circ_params = {params[0]: J * t, \n", - " params[1]: h * t}\n", - "# bind the paramter to the circuit\n", - "rzx_circ.assign_parameters(circ_params, inplace=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The transpiler pass [`RZXCalibrationBuilder`](https://qiskit.org/documentation/stubs/qiskit.transpiler.passes.RZXCalibrationBuilder.html) can be used to attach the pulse schedule to the `RZXGate` by stretching the pre-calibrated pulse schedule for the CNOT gate. This calibration information is stored in a [`InstructionScheduleMap`] object and is available for each `Backend`. " - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "inst_sched_map = backend.defaults().instruction_schedule_map\n", - "channel_map = backend.configuration().qubit_channel_mapping\n", - "pass_manager = PassManager([RZXCalibrationBuilder(inst_sched_map, channel_map)])\n", - "rzx_circ = pass_manager.run(rzx_circ)\n", - "rzx_circ.draw('mpl')" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "#TODO: what about new backends with ECR gates??" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Not all 2-qubit unitary will result in shorter circuit duration. It depends on the circuit parameters. To see this explicitly, let's perform transpilation for different parameters and get the circuit duration by [building pulse schedules](https://qiskit.org/documentation/tutorials/circuits_advanced/06_building_pulse_schedules.html) of the transpiled circuit." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### estimate circuit duration" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "# transpile to CNOT and get circuit duration\n", - "def cal_cx_circ_duration(circuit: QuantumCircuit, backend: Backend, params: Dict) -> int:\n", - " # transpile circuit into cx basis gate, get duration\n", - " cx_circ = transpile(circuit, basis_gates=['cx', 'x', 'sx', 'rz'])\n", - " # assign parameters\n", - " parameters = cx_circ.parameters\n", - " params_dict = {parameters[0]: params['Jt'],\n", - " parameters[1]: params['ht']}\n", - " cx_circ.assign_parameters(params_dict, inplace=True)\n", - " # schedule\n", - " circuits_transpiled = build_schedule(cx_circ, backend)\n", - " return circuits_transpiled.duration\n", - "\n", - "# transpile to rzx and get circuit duration\n", - "def cal_rzx_circ_duration(circuit: QuantumCircuit, backend: Backend, params: Dict):\n", - " # transpile\n", - " rzx_circ = transpile(circuit, basis_gates=['rzx', 'x', 'sx', 'rz'])\n", - " # assign parameters\n", - " parameters = rzx_circ.parameters\n", - " params_dict = {parameters[0]: params['Jt'],\n", - " parameters[1]: params['ht']}\n", - " rzx_circ.assign_parameters(params_dict, inplace=True)\n", - " # attach schedule\n", - " inst_sched_map = backend.defaults().instruction_schedule_map\n", - " channel_map = backend.configuration().qubit_channel_mapping\n", - " pass_manager = PassManager([RZXCalibrationBuilder(inst_sched_map, channel_map)])\n", - " rzx_circ = pass_manager.run(rzx_circ)\n", - " # schedule\n", - " rzx_schedule = build_schedule(rzx_circ, backend)\n", - " return rzx_schedule.duration" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below, we sweep the entangling angle from $0$ to $\\pi$ and compare which transpilation gives shorter circuit duration, the standard CNOT transpilation or the `RZXGate` transpilation. " - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "angles = np.linspace(0, np.pi, 100)\n", - "cx_durations = [cal_cx_circ_duration(qc, backend, {'Jt': J*t, 'ht': h*t}) for t in angles]\n", - "rzx_durations = [cal_rzx_circ_duration(qc, backend, {'Jt': J*t, 'ht': h*t}) for t in angles]" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 73, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(angles, cx_durations,label='cx')\n", - "plt.plot(angles, rzx_durations, label='rzx')\n", - "plt.xlabel(r'entangleing angle $t$')\n", - "plt.ylabel('circuit duration in dt')\n", - "plt.legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "From the plot above, it is clear that the `RZXGate` transpilation results in shorter circuit duration for small entangling angles\n", - "\n", - "### A larger example\n", - "Let's extend our example to a 1D spin chain of $N=21$ qubits. We follow the same steps to transpile into a basis gate set that includes either a `cx` or a `rzx` gate. This is what the trotterized evolution circuit looks like." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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dqDrgLAB5cBYAnAWgbM4CgLMAlM1ZAHAWgLJ19SwQoQNQVVc7oAFQTVcbEKEDUFVXO6ABUE1XGxChA1BVVzugAVBNVxsQoQNQVVc7oAFQTVcbEKEDUNUoO7AwTYDm5PK5X5T9AJpRYgMidAAWVmIHNAB6SmxAhA7AwnRAByhbrg2IsBNAU3LtgLMANCPXBkQ4C0BTcu2AswA0I9cGRDgLQFNy7YCzADQj1wZEOAtAU3LtgLMANKfEDmgA9JTYgAgdgIWV2AENgJ4SGxChA7CwEjugAdBTYgMidAAWVmIHNAB6cmqAzz2Mnu8iB7raAQ2AarragAgdgKq62gENgGq62oAIHYCqutoBDYDqRtUBZwHIg7MA4CwAZXMWAJwFoGzOAoCzAJTNWQDQAShbVxsQoQNQVVc7oAFQTVcbEKEDUFVXO6ABUI3vIYTy5PS5X5j9AJpTYgc0AHpKbECEDsDCSuyABkBPiQ2I0AFYWIkd0ADoKbEBEToACyuxAxoAPbk2IEIHoCm5dsBOAM3ItQERzgLQlFw74CwAzci1ARHOAtCUXDvgLADNyLUBEc4C0JRcO+AsAM3ItQERzgLQlFw74CwAzSmxAxoAPSU2IEIHYGG5dMDnHvLgu8ihbF1tQIQOQFVd7YAGQDVdbUCEDkBVXe2ABkA1XW1AhA5AVV3tgAZANV1tQIQOQFVd7YAGQDVdbUCEDkBVXe2ABkB1o+qAswDkwVkAcBaAsjkLAM4CUDZnAcBZAMrW1bNAhA5AVb6HEMqTy+d+Uf57AmhGiQ2I0AFYWIkd0ADoKbEBEToACyuxAxoAPSU2IEIHYGEldkADoKfEBkToACysxA5oAPSU2IAIHYCFldgBDYCeEhsQoQOwMB3QAcqWawMi7ATQlFw74CwAzci1ARHOAtCUXDvgLADNyLUBEc4C0JRcO+AsAM3ItQERzgLQlNQdWGeddeKCCy6Y0mtn1Hwv2brmmmsiImKjjTaa8PcfeeSROO+88yIiYuutt17w69OmTav089daa61xvzZr1qyIiLjhhhuGudUFbr755im/dmHLLb38Ev+Mydx051XxL1/bKSIiDnvbD2O1FZ+U7L2g7W668cZ4+LEHR/LeqTqgAVBdFxsQoQMwjC52QANgOKPqgLMA5MFZAHAWgLI5CwDOAlA2ZwHAWQDK1sWzQIQOwDC62AENgOq62IAIHYBhdLEDGgDVdbEBEToAw+hiBzQAqutiAyJ0AIbRxQ5oAFTXxQZE6AAMY5QdWJgmQHNy+dwvyn4AzSitARE6AIsqrQMaAP1Ka0CEDsCidEAHKFuuDYiwE0BTcu2AswA0I9cGRDgLQFNy7YCzADQj1wZEOAtAU3LtgLMANCPXBkQ4C0BTcu2AswA0p7QOaAD0K60BEToAiyqtAxoA/UprQIQOwKJK64AGQL/SGhChA7Co0jqgAdAvpwb43MPo+S5yoIsd0ACorosNiNABGEYXO6ABUF0XGxChAzCMLnZAA2A4o+qAswDkwVkAcBaAsjkLAM4CUDZnAcBZAMrmLADoAJStiw2I0AEYRhc7oAFQXRcbEKEDMIwudkADoDrfQwjlyelzvzD7ATSntA5oAPQrrQEROgCLKq0DGgD9SmtAhA7AokrrgAZAv9IaEKEDsKjSOqAB0C/XBkToADQl1w7YCaAZuTYgwlkAmpJrB5wFoBm5NiDCWQCakmsHnAWgGbk2IMJZAJqSawecBaAZuTYgwlkAmpJrB5wFoDmldUADoF9pDYjQAVhULh3wuYc8+C5yKFsXGxChAzCMLnZAA6C6LjYgQgdgGF3sgAZAdV1sQIQOwDC62AENgOq62IAIHYBhdLEDGgDVdbEBEToAw+hiBzQAhjOqDjgLQB6cBQBnASibswDgLABlcxYAnAWgbF08C0ToAAzD9xBCeXL53C/Kf08AzSitARE6AIsqrQMaAP1Ka0CEDsCiSuuABkC/0hoQoQOwqNI6oAHQr7QGROgALKq0DmgA9CutARE6AIsqrQMaAP1Ka0CEDsCidEAHKFuuDYiwE0BTcu2AswA0I9cGRDgLQFNy7YCzADQj1wZEOAtAU3LtgLMANCPXBkQ4C0BTcu7AjFHfQFMeeOCBiIh4+OGHJ/z9448/Pu65555YY401Yv3116/lPX/xi19ERMRmm202pdevs846tdzHMjNm1vJzFnXznVfHgUe9NB565L74zP4/jo3X2yrJ+0BXrLveevHo4w+N5L1TdEADYDhda0CEDsCwutYBDYDhjaoDzgKQB2cBwFkAyuYsADgLQNmcBQBnAShb184CEToAw+paBzQAhtO1BkToAAyrax3QABhO1xoQoQMwrK51QANgOF1rQIQOwLC61gENgOF0rQEROgDDGmUHFqYJ0JxcPveLsh9AM0pqQIQOwERK6oAGwHglNSBCB2AiOqADlC3XBkTYCaApuXbAWQCakWsDIpwFoCm5dsBZAJqRawMinAWgKbl2wFkAmpFrAyKcBaApuXbAWQCaU1IHNADGK6kBEToAEympAxoA45XUgAgdgImU1AENgPFKakCEDsBESuqABsB4OTXA5x5Gz3eRA13rgAbAcLrWgAgdgGF1rQMaAMPpWgMidACG1bUOaAAMb1QdcBaAPDgLAM4CUDZnAcBZAMrmLAA4C0DZnAUAHYCyda0BEToAw+paBzQAhtO1BkToAAyrax3QABiO7yGE8uT0uV+Y/QCaU1IHNADGK6kBEToAEympAxoA45XUgAgdgImU1AENgPFKakCEDsBESuqABsB4uTYgQgegKbl2wE4Azci1ARHOAtCUXDvgLADNyLUBEc4C0JRcO+AsAM3ItQERzgLQlFw74CwAzci1ARHOAtCUXDvgLADNKakDGgDjldSACB2AieTSAZ97yIPvIoeyda0BEToAw+paBzQAhtO1BkToAAyrax3QABhO1xoQoQMwrK51QANgOF1rQIQOwLC61gENgOF0rQEROgDD6loHNACGN6oOOAtAHpwFAGcBKJuzAOAsAGVzFgCcBaBsXTsLROgADMv3EEJ5cvncL8p/TwDNKKkBEToAEympAxoA45XUgAgdgImU1AENgPFKakCEDsBESuqABsB4JTUgQgdgIiV1QANgvJIaEKEDMJGSOqABMF5JDYjQAZiIDugAZcu1ARF2AmhKrh1wFoBm5NqACGcBaEquHXAWgGbk2oAIZwFoSq4dcBaAZuTagAhnAWhK6g6ss846U37tjBrvI2vrrLNO3HfffXHBBRfEdttt1/d71113XRx00EEREbHVVvVE64YbbohPfOITsfPOO8ezn/3sKf2MCy64oJZ7eeLRiHO+VMuPWuCWu66JA496adz/0N1x+Dt+HM94ynaDXwSF+9tlf4vpy4zmvevugAbA8LrUgAgdgKnoUgc0AKZmVB1wFoA8OAsAzgJQNmcBwFkAyuYsADgLQNm6dBaI0AGYii51QANgeF1qQIQOwFR0qQMaAMPrUgMidACmoksd0AAYXpcaEKEDMBVd6oAGwPC61IAIHYCpGGUHFqYJ0JxcPveLsh9AM0ppQIQOwGRK6YAGwMRKaUCEDsBkdADKlmsDIuwE0JRcO+AsAM3ItQERzgLQlFw74CwAzci1ARHOAtCUXDvgLADNyLUBEc4C0JRcO+AsAM0ppQMaABMrpQEROgCTKaUDGgATK6UBEToAkymlAxoAEyulARE6AJMppQMaABPLqQE+9zB6vosc6FIHNACG16UGROgATEWXOqABMLwuNSBCB2AqutQBDYCpGVUHnAUgD84CgLMAlM1ZAHAWgLI5CwDOAlA2ZwFAB6BsXWpAhA7AVHSpAxoAw+tSAyJ0AKaiSx3QABie7yGE8uT0uV+Y/QCaU0oHNAAmVkoDInQAJlNKBzQAJlZKAyJ0ACZTSgc0ACZWSgMidAAmU0oHNAAmlmsDInQAmpJrB+wE0IxcGxDhLABNybUDzgLQjFwbEOEsAE3JtQPOAtCMXBsQ4SwATcm1A84C0IxcGxDhLABNybUDzgLQnFI6oAEwsVIaEKEDMJlcOuBzD3nwXeRQti41IEIHYCq61AENgOF1qQEROgBT0aUOaAAMr0sNiNABmIoudUADYHhdakCEDsBUdKkDGgDD61IDInQApqJLHdAAmJpRdcBZAPLgLAA4C0DZnAUAZwEom7MA4CwAZevSWSBCB2AqfA8hlCeXz/2i/PcE0IxSGhChAzCZUjqgATCxUhoQoQMwmVI6oAEwsVIaEKEDMJlSOqABMLFSGhChAzCZUjqgATCxUhoQoQMwmVI6oAEwsVIaEKEDMBkdgLLl2oAIOwE0JdcOOAtAM3JtQISzADQl1w44C0Azcm1AhLMANCXXDjgLQDNybUCEswA0JecOTBv1DTTl5S9/eUREHHbYYXHZZZct+PXf/OY3seOOO8bdd98dERFbb731Er/X/fffH6997Wtj6aWXjm9+85tL/PNyc8td18SH/uvv4r6H7orP7H9WPOMpzxn1LQEN0gBAB6BsGgDoAJRNAwAdgLJpAKADUDYNAHQA0AEomwYAOgBl0wBAB6BsGgDoAJRNAwAdABamCVA2DQB0AMqmAYAOADoAZdMAQAegbBoA6ACUTQMAHYCyaQCgA1A2DQB0AMqmAYAOQNk0ANABKJsGQHl87gEdgLJpAKADUDYNAHQAyqYBgA5A2TQA0AEomwYAOgBl0wBAB6BsGgDoAKADUDYNAHQAyqYBwMI0AdABKJsGADoAZdMAQAegbBoA6ACUTQMAHQB0AMqmAYAOQNk0ANABKJsGADoAZdMAQAegbBoA6ACUx+ceyqYBgA5A2TQA0AEomwYAOgBl0wBAB6BsGgDoAJRNAwAdgLJpAKADUDYNAHQAyqYBgA4AOgAsTBOgbBoA6ACUTQMAHYCyaQCgA1A2DQB0AMqmAYAOQNk0ANABQAegbBoA6ACUTQMAHYCyaQCgA1A2DYB2mjHqG2jKv/7rv8ZJJ50U1113XWyxxRax2WabxUMPPRR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- "text/plain": [ - "
" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "num_qubits = 21\n", - "evol = build_trotter_evolution(num_qubits=num_qubits, rep=3)\n", - "evol.draw('mpl', fold=-1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Initialize the qubit state in the `0101...01` antiferromagnetic state, then compose the evolution circuit `evol` after the state initialization. At least, we assign circuit parameters $Jt=1$ and $ht=1$." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "qr = QuantumRegister(num_qubits, 'q')\n", - "qc = QuantumCircuit(qr) \n", - "# state initialization\n", - "for i in range(0, num_qubits, 2):\n", - " qc.x(i)\n", - "\n", - "# evolve\n", - "qc.compose(evol, inplace=True)\n", - "\n", - "# assign parameters\n", - "parameters = qc.parameters\n", - "qc.assign_parameters({parameters[0]: 1, parameters[1]: 1}, inplace=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, we are ready to perform transpilation. As an example, we will transpile to run on the backend `ibm_auckland`. We define two functions: one to transpile into a basis gate set includes the `cx` gate, and the other includes the `rzx` gate." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "# TODO: package the two transpilation into funcitons for simpler display\n", - "def transpile_to_cx(circuit: QuantumCircuit, \n", - " layout: List,\n", - " backend: Backend):\n", - " BASIS_GATES = ['cx', 'x', 'sx', 'rz']\n", - " # transpile\n", - " cx_circ = transpile(circuit, basis_gates=BASIS_GATES, backend=backend, initial_layout=layout, layout_method='trivial', optimization_level=1)\n", - " print(f'CX transpile: two-qubit circuit depth = {cx_circ.depth(lambda x: x[0].num_qubits == 2)}')\n", - " return cx_circ\n", - "\n", - "def transpile_to_rzx(circuit: QuantumCircuit, \n", - " layout: List,\n", - " backend: Backend):\n", - " BASIS_GATES = ['rzx', 'x', 'sx', 'rz']\n", - " # transpile\n", - " rzx_circ = transpile(qc, basis_gates= BASIS_GATES, backend=backend, initial_layout=layout, layout_method='trivial', optimization_level=0)\n", - " # optimize 1q\n", - " pm = PassManager([Optimize1qGatesDecomposition([\"sx\", \"rz\", \"rzx\", \"cx\", \"ecr\"])])\n", - " rzx_circ = pm.run(rzx_circ)\n", - " # attach schedule\n", - " inst_sched_map = backend.defaults().instruction_schedule_map\n", - " channel_map = backend.configuration().qubit_channel_mapping\n", - "\n", - " pass_manager = PassManager([\n", - " RZXCalibrationBuilder(inst_sched_map, channel_map)],\n", - " FullAncillaAllocation(CouplingMap(backend.configuration().coupling_map)))\n", - " rzx_circ = pass_manager.run(rzx_circ)\n", - " print(f'RZX transpile: two-qubit circuit depth = {rzx_circ.depth(lambda x: x[0].num_qubits == 2)}')\n", - " return rzx_circ" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CX transpile: two-qubit circuit depth = 12\n", - "RZX transpile: two-qubit circuit depth = 6\n" - ] - } - ], - "source": [ - "# map to physical qubits that form 1D chain\n", - "layout = [0, 1, 4, 7, 10, 12, 15, 18, 21, 23, 24, 25, 22, 19, 16, 14, 11, 8, 5, 3, 2]\n", - "\n", - "# transpile into CX gates\n", - "cx_circ = transpile_to_cx(qc, layout=layout, backend=backend)\n", - "# transpile into RZX gates\n", - "rzx_circ = transpile_to_rzx(qc, layout=layout, backend=backend)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 428, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 428, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "rzx_circ.draw('mpl', fold=-1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "After transpilation, we notice:\n", - "* virtual qubits are mapped to physical qubits, and the transpiled circuits `cx_circ` and `rzx_circ` are defined over all 27 physical qubits.\n", - "* gates are parsed in the basis gates. When we use the `rzx` based transpilation, all `RZXGate`s should have calibrations attached.\n", - "Layout information of the transpiled circuit is stored, and we can visualize it by calling `plot_circuit_layout.` Below, we see our original circuit `qc` on a 1D spin chain is mapped to the backend, and the physical qubits used are marked in black." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.visualization import plot_circuit_layout" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plot_circuit_layout(cx_circ, backend, view='physical')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Verify" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Suppose we want to measure `Z` on the first (virtual) qubit Q0. To get the exact result of the expectation value, we pass the circuit and the observable to run on the simulator as a verification step." - ] - }, - { - "cell_type": "code", - "execution_count": 385, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit_ibm_runtime import Estimator\n", - "# to get a sense of good and bad, simulate the circuit to get the ideal, noiseless result\n", - "estimator = Estimator(backend='ibmq_qasm_simulator')\n", - "# define virtual observale\n", - "obs = 'Z' + 'I' * (num_qubits - 1)\n", - "# simulate the original circuit\n", - "sim_job = estimator.run(qc, obs, shots=10000)\n", - "sim_result = sim_job.result()" - ] - }, - { - "cell_type": "code", - "execution_count": 415, - "metadata": {}, - "outputs": [], - "source": [ - "# simulate the transpiled circuit\n", - "obs = 'Z' + 'I' * (backend.configuration().n_qubits - 1)\n", - "estimator = Estimator(backend='ibmq_qasm_simulator')\n", - "sim_job = estimator.run(cx_circ, obs, shots=10000)\n", - "sim_result = sim_job.result()" - ] - }, - { - "cell_type": "code", - "execution_count": 416, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "EstimatorResult(values=array([1.]), metadata=[{'variance': 0.0, 'shots': 10000}])" - ] - }, - "execution_count": 416, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sim_result" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Run" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we run the `RZX`-based transpiled circuit on the hardware using the Runtime. To compare, we also run the `CX`-based transpiled circuit. Since we already transpiled our circuits in a customized way, we set `skip_transpilation = True`. " - ] - }, - { - "cell_type": "code", - "execution_count": 322, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit_ibm_runtime import Options\n", - "\n", - "obs = 'Z' + 'I' * (rzx_circ.num_qubits - 1)\n", - "options = Options()\n", - "options.execution.shots = 10000\n", - "options.transpilation.skip_transpilation = True\n", - "options.resilience_level = 1\n", - "\n", - "estimator = Estimator(backend=backend, options=options)\n", - "rzx_job_z = estimator.run(rzx_circ, obs)\n", - "cx_job_z = estimator.run(cx_circ, obs)" - ] - }, - { - "cell_type": "code", - "execution_count": 420, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "exact_value = 1.0+/-0.0\n", - "cx_value = 0.9791081642751113+/-0.26123768997780655\n", - "rzx_value = 0.9898751427861932+/-0.2339005638671414\n" - ] - } - ], - "source": [ - "### Compare exact, unoptimized, vs optimized\n", - "print(f'exact_value = {sim_result.values[0]}' + '+/-' + f'{np.sqrt(sim_result.metadata[0][\"variance\"])}')\n", - "print(f'cx_value = {cx_job_z.result().values[0]}' + '+/-' + f'{np.sqrt(cx_job_z.result().metadata[0][\"variance\"])}')\n", - "print(f'rzx_value = {rzx_job_z.result().values[0]}' + '+/-' + f'{np.sqrt(rzx_job_z.result().metadata[0][\"variance\"])}')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this notebook, we started from a simple two-qubit example, and we see that the `RZXGate` transpilation shortens the circuit duration when the trotter step $t$ (which corresponds to the entangling angle in the `RZXGate`) is small. In the larger 21-qubit example, we have shown how to transpile and run the circuit with the `Estimator.` We have seen that the `RZXGate` transpilation produces results closer to the exact value." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To conclude, we have shown you how to transpile into `RZXGate`s. You may wonder if this method is useful for your circuit. Try it out on your own circuit using the `transpile_to_rzx()` function. To compare with the standard CNOT-based transpilation, use the `transpile_to_cx()` function. You can use the circuit duration calculator `cal_cx_circ_duration` and `cal_rzx_circ_duration` to see if `RZXGate` transpilation gives shorter circuits!" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "numpy version 1.25.2\n", - "qiskit runtime version 0.11.3\n" - ] - }, - { - "data": { - "text/html": [ - "

Version Information

SoftwareVersion
qiskit0.44.1
qiskit-terra0.25.1
qiskit_ibm_provider0.6.3
qiskit_ibm_runtime0.11.3
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 15:35:09
OSDarwin
CPUs10
Memory (Gb)64.0
Tue Nov 07 20:12:11 2023 EST
" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy\n", - "print(f\"numpy version {numpy.__version__}\")\n", - "\n", - "import qiskit_ibm_runtime\n", - "print(f\"qiskit runtime version {qiskit_ibm_runtime.version.get_version_info()}\")\n", - "\n", - "import qiskit.tools.jupyter\n", - "%qiskit_version_table" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "runtime", - "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": "3.9.17" - }, - "orig_nbformat": 4 - }, - "nbformat": 4, - "nbformat_minor": 2 -}