PaperlayerView exact revision on arXiv

Source-linked AI summary

Qiskit Pulse: Programming Quantum Computers Through the Cloud with Pulses

Thomas Alexander, Naoki Kanazawa, Daniel J. Egger, Lauren Capelluto, Christopher J. Wood, Ali Javadi-Abhari, David McKay

arXiv:2004.06755v1quant-ph

TL;DR

The circuit model hides the physical implementation needed for precise quantum-hardware control. This paper introduces Qiskit Pulse, demonstrates it by characterizing and calibrating cross-resonance gates on a cloud-accessible IBM system, and reports CNOT fidelities comparable to the standard backend gate.

  • Problem

    The circuit model abstracts away pulse-level implementation, limiting precise hardware control and access to advanced control techniques.

  • Method

    The paper implements OpenPulse within Qiskit and uses quantum process tomography to characterize echoed and un-echoed cross-resonance pulses before calibrating them into a CNOT gate.

  • Results

    Average gate fidelities are F = 0.981 and F = 0.979 for the CR1 and CR2 calibrated CNOT gates, respectively, compared with F = 0.984 for the standard CNOT gate.

  • Takeaways & Limitations

    Qiskit Pulse exposes hardware control for exploring error mitigation, dynamical decoupling, and other schemes unavailable at the circuit level.

Abstract

from arXiv · show

The quantum circuit model is an abstraction that hides the underlying physical implementation of gates and measurements on a quantum computer. For precise control of real quantum hardware, the ability to execute pulse and readout-level instructions is required. To that end, we introduce Qiskit Pulse, a pulse-level programming paradigm implemented as a module within Qiskit-Terra \cite{Qiskit}. To demonstrate the capabilities of Qiskit Pulse, we calibrate both un-echoed and echoed variants of the cross-resonance entangling gate with a pair of qubits on an IBM Quantum system accessible through the cloud. We perform Hamiltonian characterization of both single and two-pulse variants of the cross-resonance entangling gate with varying amplitudes on a cloud-based IBM Quantum system. We then transform these calibrated sequences into a high-fidelity CNOT gate by applying pre and post local-rotations to the qubits, achieving average gate fidelities of $F=0.981$ and $F=0.979$ for the un-echoed and echoed respectively. This is comparable to the standard backend CNOT fidelity of $F_{CX}=0.984$. Furthermore, to illustrate how users can access their results at different levels of the readout chain, we build a custom discriminator to investigate qubit readout correlations. Qiskit Pulse allows users to explore advanced control schemes such as optimal control theory, dynamical decoupling, and error mitigation that are not available within the circuit model.

I. INTRODUCTION

Qiskit Pulse extends circuit-level quantum programming with a pulse-level representation and compilation path, exposing hardware control that the standard circuit model abstracts away. It supports reusable, technology-independent control techniques and cloud execution while retaining integration with circuit programs.

  • Motivation: The circuit model abstracts gates and measurements from the physical dynamics and pulse-level implementation of quantum hardware.Hardware operations are enacted through classical control fields such as shaped microwave pulses.
  • Contribution: Qiskit Pulse adds pulse-level scheduling, analysis, optimization, and OpenPulse compilation to the Qiskit compilation pipeline.It represents quantum programs as time-scheduled pulse sequences and targets executable OpenPulse object code.
  • Motivation: Pulse-level programming addresses the need to craft hardware-independent instructions that can be target-compiled to diverse control instruments and architectures.Direct circuit-to-hardware compilation can hide the pulses that manipulate the hardware and remove a degree of control.
  • Contribution: Qiskit Pulse enables technology-independent quantum control techniques to be remotely retargeted to cloud-based quantum computers.The framework is embedded within Qiskit while exposing analog stimulus control.
  • Capabilities: Pulse-level timing and synchronization enable user-defined gate schedules and techniques including crosstalk correction, optimal control, and error mitigation.These capabilities are unavailable within the standard circuit abstraction.
  • Programming model: The framework provides a virtual pulse execution model that can be compiled to an underlying control-hardware ISA, while its instruction set is expected to expand.This work focuses on the virtual model and a limited pulse-coprocessor instruction set.

B. Channels

Qiskit Pulse models hardware signal paths as typed channels with queued, synchronized instructions for driving, measuring, controlling, and acquiring quantum-system signals. Channel behavior is tied to target hardware and qubit-specific calibration.

  • Channel model: Channels label signal lines that transmit or receive signals between control electronics and the quantum device.Each channel executes instructions from a first-in, first-out queue.
  • Channel constraints: Channel calibration and pulse assignments depend on the physical target qubit, so channels are not interchangeable by permutation.Target code generation constrains channels to hardware components such as arbitrary waveform generators.
  • Channel types: DriveChannels, MeasureChannels, and ControlChannels are PulseChannel subtypes, while AcquireChannels receive readout data without transmitting stimulus.AcquireChannels communicate when qubit readout data should be acquired.
  • Instruction execution: Pulse instructions use channels and instruction-specific constants as operands, with fixed deterministic durations and synchronized execution across channel queues.Instructions are loaded into per-channel FIFO queues before execution begins synchronously.
  • Pulse control: ShiftPhase changes a channel’s phase persistently, supporting phase accumulation and virtual Z-gates.Play uses the configured frequency and phase to emit a pulse on a target PulseChannel.
  • Readout: Acquire instructions specify duration, acquisition channel, and result register, and must align with measurement stimulus pulses.Readout chains may include acquisition, filtering, kerneling, and state discrimination, motivating multiple readout-data levels.
  • System integration: The channel and instruction abstraction is intended to support arbitrary quantum systems and integration with classical control flow and gate-level programs.A lowering procedure can translate higher-level instructions into pulse instructions within a shared software stack.

D. The Pulse Schedule

Qiskit Pulse represents programs as ordered pulse schedules and lowers transpiled circuits into timed hardware instructions. Users can override calibrated gate schedules and scheduling policies to control pulse-level execution.

  • Schedule representation: A pulse Schedule is an ordered collection of scheduled pulse instructions representing a pulse program.Its deterministic instruction durations make it analogous to a basic block in classical computation.
  • Schedule execution: A schedule can play a measurement pulse, acquire the resulting data into a memory slot, and return execution counts from the backend.The example constructs and runs a schedule for preparing and measuring qubit 0.
  • Compilation: The transpiler optimizes circuits using target topology, native gates, and fidelities before a scheduler compiles the native circuit into a pulse program.Scheduling requires system-dependent definitions of native gates as pulse instructions.
  • Scheduling: The default as-late-as-possible policy minimizes same-channel deadtime while placing gates as late as permitted by circuit constraints.The input circuit supplies implicit topological timing constraints, leaving free alignment parameters for the scheduler.
  • User control: Users may replace backend-native pulse programs and define scheduling policies that aggregate gates into composite pulse sequences.This provides low-level control over gate definitions used during scheduling.
  • Circuit-to-pulse mapping: Figure 2 maps a Bell-state circuit to equivalent composite pulse sequences, including waveform quadratures, phase shifts, readout triggers, and scheduler timing.Backend mappings are automatic but may be overridden by the user.

III. DEMONSTRATION OF A CROSS-RESONANCE ENTANGLING GATE

The paper uses Qiskit Pulse to characterize and calibrate cross-resonance interactions on cloud-accessible quantum hardware, then constructs entangling gates from the calibrated pulses. It examines unwanted Hamiltonian terms and compares single-pulse and echoed pulse implementations.

  • Qiskit Pulse enables quantum process tomography of echoed and un-echoed cross-resonance pulses with varying amplitudes on a cloud-based quantum computer.The tomography data are used to calculate effective cross-resonance Hamiltonian coefficients and implement a calibrated CNOT gate.
  • A. The Cross-Resonance Interaction: The cross-resonance gate drives the control qubit at the target-qubit frequency to stimulate an effective ZX interaction.The ZX rotation angle depends on the applied pulse’s strength and duration.
  • A. The Cross-Resonance Interaction: Additional Hamiltonian terms produce coherent errors, motivating multi-pulse echoes and cancellation tones to suppress them.These terms cause divergence from the ideal target unitary and must be characterized for high-fidelity entangling operations.
  • B. Constructing and Calibrating a Cross-Resonance Gate: The experiments implement single-pulse CR1 and echoed two-pulse CR2 gates without a cross-talk cancellation tone on the target qubit.Both use GaussianSquare CR pulses with total duration 848 dt = 184.4 ns and a pulse duration chosen for a π/2 rotation in the weak-driving regime.
  • B. Constructing and Calibrating a Cross-Resonance Gate: The CR2 echo uses opposite-phase CR pulses and interleaved single-qubit pulses to refocus unwanted interaction-Hamiltonian terms.The CR pulses are applied on the ControlChannel, while the additional single-qubit pulses are applied on the DriveChannel.

C. Quantum Process Tomography of the CR Gate

Quantum process tomography reconstructs the noisy CR-gate process across pulse amplitudes using custom pulse-scheduled tomography circuits. The fitted processes provide Hamiltonian coefficients and identify amplitudes that implement the desired π/2 ZX rotation.

  • Standard quantum process tomography characterizes CR1 and CR2 sequences over a range of CR pulse amplitudes.The tomography module of Qiskit Ignis is used for the measurements.
  • Each qubit is prepared in four input states and measured in the X, Y, and Z bases for the two-qubit tomography circuits.The amplitude-dependent CR pulse is embedded as a user-defined custom gate mapped by the Qiskit Pulse scheduler.
  • The fitted Choi matrices yield effective-Hamiltonian coefficients as functions of pulse amplitude, which are fit to a third-order model.The model identifies the pulse amplitude implementing a θZX = π/2 rotation.
  • The estimated amplitudes for θZX = π/2 are 0.229±0019 for CR1 and 0.098 ± 0005 for CR2.

D. Optimizing CNOT Fidelity with Local Operations

The calibrated CR process maps were converted into CNOT gates by optimizing single-qubit pre- and post-rotations, achieving fidelities comparable to the standard backend CNOT. Qiskit Pulse also exposes readout data across the measurement chain for custom discrimination and correlation studies.

  • CNOT optimization: Fmax = 0.992 and Fmax = 0.994 for CR1 and CR2 process maps after optimizing single-qubit pre- and post-rotation angles.The optimization searches over rotation angles on both control and target qubits.
  • CNOT optimization: F = 0.981 and F = 0.979 were measured for CNOT gates built from CR1 and CR2, respectively, compared with F = 0.984 for the standard backend CNOT.The calibrated gates were constructed with the Qiskit transpiler, pulse scheduler, and device-calibrated single-qubit gates, then evaluated using randomized benchmarking.
  • CNOT optimization: The demonstrated CNOT gates used an echo sequence without a cancellation tone, with all parameters obtained through open-loop calibration.The standard calibration process includes an echo sequence, cancellation tone, and closed-loop amplitude calibration.
  • Readout access: Qiskit Pulse lets users request level-zero, level-one, or level-two readout data and implement custom kernels or discriminators.Level-zero data are digitized time series, level-one data are complex IQ values after kernel processing, and level-two data are classified states.
  • Readout access: The paper illustrates custom discrimination by investigating spurious readout correlations between neighboring qubits 16 and 17 on ibmq singapore.The experiment used four calibration schedules and fitted discriminators to kerneled data.

1. Performing Quantum Process Tomography

The quantum process tomography workflow creates pulse schedules for a calibrated CR1 instruction and executes them through Qiskit’s circuit, transpilation, and scheduling interfaces. The example supports substituting a mock backend for the real IBM Quantum backend.

  • QPT workflow: The example creates quantum process tomography circuits and converts them into pulse schedules using Qiskit Pulse.Process-tomography circuits are generated, transpiled for the backend, and scheduled with the instruction map.
  • Implementation: The CR1 schedule uses pulse parameters determined during calibration before being registered as a reusable instruction.The code labels the instruction uniquely and places the calibrated schedule in the backend instruction map.
  • CR1 pulse construction: A flat-topped Gaussian CR1 pulse is added to the basis gates and instruction-to-schedule map for the selected qubits.The map associates the calibrated CR1 schedule with the circuit instruction named cr1.

2. Performing Randomized Benchmarking

Randomized benchmarking schedules are built by embedding calibrated CR1-based CNOTs and optimized local rotations into quantum circuits, then transpiling and scheduling them for pulse execution. The workflow supports both CNOT control-target orientations.

  • RB workflow: Standard randomized benchmarking schedules are created in Qiskit Pulse using the CR1-CNOT gate described in the experiment.The schedules are generated through the qiskit pulse module.
  • RB workflow: Randomized benchmarking circuits use five seeds and are transpiled and scheduled for the backend through the instruction map.Each seed’s circuit is transpiled before pulse scheduling, and the resulting schedules are collected.
  • CNOT construction: CNOT schedules are built from CR1 with optimized local rotations applied before and after the CR pulse sequence.The local rotation parameters come from the optimization routine, and device-calibrated single-qubit gates surround the CR1 sequence.
  • RB workflow: Two-qubit randomized benchmarking allows either qubit to serve as the control, requiring CNOT schedules for both control-target orientations.The CNOT gate is not identical when control and target are exchanged.

Appendix B: Cross Resonance Phase Calibration

The cross-resonance phase calibration compensates for a hardware-induced phase offset that can create an unwanted ZY interaction. The procedure selects an amplitude for an equal-superposition response and a phase maximizing the target-qubit Y signal.

  • Phase calibration: A transfer-function phase offset φ0 can rotate the CR interaction axis and introduce an unwanted ZY term.The calibrated phase is used to eliminate this contribution.
  • Phase calibration: The echoed CR Hamiltonian contains the desired drive strength Ω(A, φ) and residual interactions ε that are not fully refocused by the echo.The echo reduces the number of significant Hamiltonian terms relative to CR1.
  • Calibration procedure: Aopt = 0.108 produces an equal superposition of target-qubit states from the initialized |00⟩ state.The amplitude sweep measures the target qubit in the Pauli-Z basis.
  • Calibration procedure: φopt = −0.166 rad maximizes |Tr(σyρ)| when the target-qubit readout is measured in the Y basis for both control states.The phase sweep uses initial control states |10⟩ and |00⟩.

Appendix C: Effective Hamiltonian Estimation and Amplitude Calibration

The appendix estimates effective cross-resonance Hamiltonian coefficients from process tomography and calibrates pulse amplitudes using fitted interaction strengths. It also identifies significant Pauli terms and shows how echoing suppresses unwanted interactions.

  • Hamiltonian estimation: For Markovian noise, the Lindblad framework separates unitary and dissipative evolution, enabling Hamiltonian coefficients to be extracted from the generator.The Hamiltonian and dissipative superoperator components are orthogonal under the stated noise model.
  • Hamiltonian estimation: Quantum process tomography is converted into a superoperator, whose matrix logarithm yields a generator for estimating effective Hamiltonian coefficients.The generator is computed as SG = t^-1 log(SE).
  • Hamiltonian characterization: Only ZX, ZY, ZZ, ZI, IX, IY, and IZ are significant in CR1 and CR2; other Pauli terms are negligible.The calibrated phase suppresses ZY, while ZX increases monotonically with pulse amplitude.
  • Hamiltonian characterization: Echoing removes CR1’s large IX, IY, and ZI contributions, except for ZZ, while local gates can correct remaining coherent errors.The comparison is made between the un-echoed CR1 and echoed CR2 sequences.
  • Amplitude calibration: The maximum-entangling amplitude is selected by targeting θZX = π/2, with drive strength related to time-averaged amplitude by Ω = λA.The measured ZX interaction strengths are fitted using a third-order expansion of the CR Hamiltonian.
  • Amplitude calibration: J = 1.87 ± 0.046 MHz and 1.79 ± 0.033 MHz are obtained for CR1 and CR2, respectively.The corresponding λ values are −271.2 ± 12.2 MHz and −288.9 ± 10.2 MHz.

Appendix D: Optimizing CNOT Fidelity with Local Operations

The appendix optimizes local single-qubit pre- and post-rotations to transform measured cross-resonance processes into maximally entangling gates. This optimization removes locally correctable coherent errors but excludes errors from the single-qubit gates.

  • Local-operation optimization: Average gate fidelity is optimized over 12 real parameters governing four single-qubit U3 rotations before and after the cross-resonance process.The rotations act on both the control and target qubits.
  • Target gates: The target unitary is ZX(π/2) for a cross-resonance perfect entangler and CX for a CNOT gate.The optimization seeks local operations that remove correctable coherent errors.
  • Optimized fidelities: Fmax = 0.994 and Fmax = 0.998 are obtained for the measured CR1 and CR2 process maps, respectively.These optimized fidelities quantify the best transformed entangling-gate performance under the local-rotation optimization.
  • Optimization scope: The optimized fidelities underestimate transformed-gate error because errors in the single-qubit gates are neglected.The reported optimization therefore isolates the effect of locally correctable coherent errors.
Loading 2004.06755v1…