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Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum Computers

Prakash Murali, David C. McKay, Margaret Martonosi, Ali Javadi-Abhari

arXiv:2001.02826v1quant-phcs.ET

TL;DR

Crosstalk corrupts quantum states during parallel instruction execution, while its characterization can be expensive and device behavior can vary. The paper combines optimized crosstalk characterization with SMT-based instruction scheduling, achieving substantial error-rate improvements and near-optimal mitigation in practice.

  • Problem

    Crosstalk can corrupt quantum states during parallel execution, and fully characterizing device behavior is computationally intractable or expensive.

  • Method

    The paper uses randomized benchmarking to characterize crosstalk, optimizes characterization overhead, and applies SMT optimization to schedule affected gates.

  • Results

    The scheduler improves SWAP-circuit error rate by up to 5.6x, with a 2x geomean improvement over IBM’s default parallel instruction scheduler, and provides near-optimal mitigation in practice.

  • Takeaways & Limitations

    Software crosstalk mitigation can increase the reliability of noisy quantum computers without requiring hardware-only mitigation.

  • Takeaways & Limitations

    The approach primarily targets nearest-neighbor crosstalk and conservatively models simultaneous triplets using the worst overlapping gate.

Abstract

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Crosstalk is a major source of noise in Noisy Intermediate-Scale Quantum (NISQ) systems and is a fundamental challenge for hardware design. When multiple instructions are executed in parallel, crosstalk between the instructions can corrupt the quantum state and lead to incorrect program execution. Our goal is to mitigate the application impact of crosstalk noise through software techniques. This requires (i) accurate characterization of hardware crosstalk, and (ii) intelligent instruction scheduling to serialize the affected operations. Since crosstalk characterization is computationally expensive, we develop optimizations which reduce the characterization overhead. On three 20-qubit IBMQ systems, we demonstrate two orders of magnitude reduction in characterization time (compute time on the QC device) compared to all-pairs crosstalk measurements. Informed by these characterization, we develop a scheduler that judiciously serializes high crosstalk instructions balancing the need to mitigate crosstalk and exponential decoherence errors from serialization. On real-system runs on three IBMQ systems, our scheduler improves the error rate of application circuits by up to 5.6x, compared to the IBM instruction scheduler and offers near-optimal crosstalk mitigation in practice. In a broader picture, the difficulty of mitigating crosstalk has recently driven QC vendors to move towards sparser qubit connectivity or disabling nearby operations entirely in hardware, which can be detrimental to performance. Our work makes the case for software mitigation of crosstalk errors.

1 Introduction

Crosstalk corrupts parallel quantum operations, creating a scheduling trade-off between crosstalk and decoherence. The paper addresses this trade-off with faster characterization and software scheduling, reporting substantial reliability improvements on IBM systems.

  • Motivation: Crosstalk corrupts quantum states when multiple gates execute simultaneously and can worsen two-qubit gate errors by an order of magnitude.On the studied devices, crosstalk degraded a two-qubit operation’s error rate by up to 11x.
  • Motivation: An ideal schedule balances crosstalk avoidance against exponentially increasing decoherence from longer computation time.Naively serializing high-crosstalk operations can create substantial decoherence error, especially on low-coherence qubits.
  • Approach: Software mitigation requires accurate crosstalk characterization and an intelligent scheduler that uses the measurements to navigate the crosstalk–coherence trade-off.The paper develops both building blocks as its central approach.
  • Characterization: More than 8 hours of characterization compute time was reduced to under 15 minutes on three 20-qubit IBM devices.The optimizations target the expense of measuring crosstalk for every pair of simultaneous operations.
  • Crosstalk characterization: Crosstalk primarily affects nearest-neighbor gates on the three evaluated devices, while its effect on a particular gate varies up to 3x over many days.These observations inform the scope and timing of characterization.
  • Evaluation: SWAP-circuit error rates improved by up to 5.6x, with a 2x geomean improvement over IBM’s default parallel instruction scheduler.The scheduler also improved QAOA cross-entropy loss by up to 3.6x and achieved near-optimal mitigation in practice.

2 QC Background

Quantum computers encode information in qubits and manipulate it with gates, whose errors compound during execution. Because simultaneous-operation errors are not routinely characterized, software can use such measurements to mitigate crosstalk.

  • Principles of Quantum Computing: Qubits can occupy superpositions of basis states, allowing n qubits to represent 2^n basis states simultaneously.A maximal superposition assigns equal probability to the |0⟩ and |1⟩ basis states.
  • Quantum gates: Gates manipulate qubit information through time-dependent physical interactions, including microwave voltage pulses in IBMQ systems.Two-qubit CNOT gates are implemented using cross-resonance effects.
  • Program execution: Quantum applications execute gate sequences on initialized qubits and produce classical bitstrings when readout operations collapse qubit states.Readout maps each measured qubit to |0⟩ or |1⟩.
  • Noise and calibration: Quantum systems exhibit spatial and temporal noise variations from manufacturing, control, gate-implementation, and external-interference imperfections.Systems are calibrated frequently, with gate errors measured using randomized benchmarking.
  • Noise and calibration: Two-qubit CNOT error rates in the studied systems ranged from 0.5–6.5%, averaging 1.8%, while errors compound across gate sequences and readout.Single-qubit operation errors were below 0.1%, and average single-qubit readout error was 4.8%.
  • Crosstalk characterization: Simultaneous-operation error characterization is time-consuming and can provide data that compilers exploit to mitigate crosstalk.Standalone gate error rates are measured daily, whereas simultaneous errors generally are not.

3 Related Work and Novelty

Prior compilation work generally optimizes circuit size, depth, mapping, or duration without modeling crosstalk. This paper instead evaluates schedules on real systems using both spatial and temporal operation placement, balancing crosstalk mitigation against decoherence.

  • Most prior optimizations reduce circuit size, depth, or duration without considering crosstalk effects.
  • Existing hardware-characterization-driven compilers use independent gate-error data but not crosstalk characterization.
  • Hardware schedulers either maximize parallelism or disable nearby simultaneous gates, with excessive serialization increasing decoherence error.
  • This work proposes software scheduling that serializes instructions to avoid crosstalk while balancing decoherence errors.
  • The study evaluates schedule quality on real quantum systems using both when operations run and which operations run in proximity.

4 Crosstalk Mitigation in Software: Design Questions

Crosstalk mitigation requires measuring conditional gate errors and scheduling operations around the resulting hardware behavior. The central design challenge is trading serialization against decoherence from longer execution time.

  • 4.1 Background on Crosstalk Sources in Superconducting Systems: Crosstalk in superconducting systems arises from unwanted interactions and control-signal leakage, especially through always-on coupling among nearby qubits.
  • 4.2 Crosstalk Characterization: Conditional error rates reveal crosstalk by comparing simultaneous gate errors with independently measured gate errors.
  • 4.2 Crosstalk Characterization: Randomized Benchmarking measures gate error rates through random circuits with repeated gate invocations and fitted experimental results.
  • 4.2 Crosstalk Characterization: 221 pairs of SRB experiments are required on IBMQ Poughkeepsie because conditional errors are unavailable from daily calibration data.
  • 4.3 Crosstalk-Adaptive Scheduling: Serializing interfering operations can reduce crosstalk but increases decoherence, motivating compiler parallelism whenever possible.

5 Reducing the Crosstalk Characterization Overhead

The characterization strategy reduces measurement overhead by exploiting crosstalk locality, parallelizing sufficiently separated experiments, and repeatedly measuring stable high-crosstalk pairs. Across the evaluated systems, the combined optimizations reduce characterization to under fifteen minutes.

  • Crosstalk affects gate error rates up to 11x, while high-crosstalk pairs on Poughkeepsie occur only among nearby gates.Only 5 of 221 gate pairs are high-crosstalk pairs there, and each interfering pair is separated by 1 hop.
  • Conditional error rates vary up to 2x on Poughkeepsie and up to 3x across the other systems, while high-crosstalk pair identities tend to remain stable across days.
  • The initial workflow characterizes all relevant gate pairs, requiring over 8 hours of real-system compute time for IBMQ Poughkeepsie.This entails 221 pairs of SRB experiments performed on hardware rather than in simulation.
  • Optimization 1: Characterize only 1-hop pairs: The first optimization measures only 1-hop gate pairs because device crosstalk is significant primarily at that distance.The paper notes that packaging imperfections can produce longer-range effects in some older systems.
  • Optimization 2: Parallelize SRB experiments of multiple gate pairs: The second optimization parallelizes SRB experiments for gate pairs separated by at least two hops using a randomized first-fit bin-packing heuristic.
  • Optimization 3: Characterize high crosstalk pairs only: The third optimization measures high-crosstalk pairs daily and the remaining 1-hop pairs periodically because high-crosstalk pairs remain relatively stable.
  • The combined optimizations reduce characterization time for the three systems to under fifteen minutes, with the resulting data reusable by compilation jobs during that period.

6 Crosstalk Mitigation Through Instruction Scheduling: Overview

XtalkSched schedules a hardware-compliant program using crosstalk and calibration data, with an SMT optimization encoding dependencies, gate errors, and decoherence. Its objective trades serialization against parallel execution to find an error-minimizing schedule.

  • The scheduler receives a hardware-compliant program IR and calibration data to determine each gate’s start time.Calibration inputs include independent error rates, coherence time, and gate duration.
  • The scheduling problem is formulated as a constrained SMT optimization with start-time and gate-error variables plus dependency constraints.
  • Overlapping operations receive conditional error rates, while nonoverlapping gates use crosstalk-free independent error rates.
  • Decoherence is modeled as an exponential penalty based on each qubit’s elapsed lifetime and coherence time.
  • The objective minimizes the product of crosstalk-influenced gate error rates and decoherence-based qubit error rates.
  • Serializing high-crosstalk gates lowers gate-error terms but raises decoherence terms, whereas parallel execution produces the opposite tradeoff.
  • XtalkSched enforces the optimized ordering by inserting barriers and is compared with SerialSched and ParSched.

7 Instruction Scheduling: Optimization Details

XtalkSched formulates instruction scheduling as an optimization over dependencies, crosstalk-dependent gate errors, qubit decoherence, and hardware constraints. Its objective explicitly balances serialization that reduces crosstalk against longer execution that increases decoherence.

  • 7.1 Variables: Each gate variable records its start time, duration, and error rate, while qubit variables record coherence error rates and gate dependencies constrain execution order.The dependency relation specifies when one gate depends on another.
  • 7.2 Constraints: Gate durations come from machine documentation or calibration data and determine the schedule’s duration variables.
  • 7.2 Constraints: Candidate-overlap sets contain operations that are neither ancestors nor descendants of a gate, and overlap indicators record whether those operations execute concurrently.The scheduler constructs these sets from the program dependency graph.
  • 7.2 Constraints: For each overlap scenario, the gate error is set to the maximum conditional error among overlapping gates, conservatively modeling the worst crosstalk source.The model assumes no significant additional worsening from simultaneous triplets of gates.
  • 7.2 Constraints: The formulation enumerates 2^|CanOlp(g_i)| overlap cases, including the empty subset when no candidate operation overlaps.In practice, the candidate-overlap set is small because it includes only overlapping gates with high conditional error rates.
  • 7.2 Constraints: Decoherence error is computed from each qubit’s scheduled lifetime, using the minimum of its T1 and T2 coherence times as the available compute time.The lifetime spans the first gate’s start to the last gate’s finish, and error increases exponentially with computation time.
  • 7.2 Constraints: IBMQ-specific constraints enforce non-overlap or containment of gates, simultaneous readout timing, and right-justified schedules because circuit-level barriers cannot express partial overlaps.These constraints reflect current IBMQ control and readout behavior.
  • 7.3 Objective Function: The objective minimizes the product of gate and decoherence errors, linearized with logarithms and optionally weighted by crosstalk factor ω.Serializing gates lowers crosstalk error but increases decoherence error, whereas parallelization has the opposite tradeoff.

8 Experimental Setup

The evaluation characterizes crosstalk and compares XtalkSched with serialized and parallel baselines on three IBM systems. It uses SWAP, QAOA, and Hidden Shift circuits with application-specific error metrics and calibrated hardware data.

  • Implementation: The characterization methods use IBM Qiskit Ignis, while XtalkSched is implemented as Qiskit Terra compilation passes using the Z3 SMT solver.
  • Baselines: The scheduler is evaluated against SerialSched, which serializes every operation, and ParSched, IBM Qiskit’s current scheduler.
  • SWAP circuits: SWAP experiments use meet-in-the-middle paths between device qubit pairs and focus on 46 circuits containing at least one high-crosstalk CNOT pair.
  • QAOA circuits: QAOA experiments use four-qubit, 43-gate circuits with nine two-qubit gates across four crosstalk-prone regions of IBMQ Poughkeepsie.
  • Crosstalk characterization: Crosstalk characterization compares all-pairs simultaneous-gate measurements with three overhead-reduction optimizations using SRB experiment counts and machine compute time.
  • Metrics: QAOA accuracy is measured by cross-entropy over 8192 trials, while Hidden Shift error is the fraction of trials missing the expected bit string.
  • Hardware: Experiments use three 20-qubit IBM systems and daily calibration data containing gate durations, independent gate errors, and qubit T1 and T2 times.
  • Figure 5: Figure 5 compares measured SWAP error rates across schedulers and systems, plus program durations on IBMQ Poughkeepsie; lower values are better for both metrics.

9 Optimizing Application Error Rate

XtalkSched improves application reliability by selectively serializing crosstalk-prone operations while retaining parallelism elsewhere. Across experiments, it trades modest duration increases for lower error and adapts its behavior to application sensitivity and hardware coherence.

  • SWAP comparisons: Up to 5.6x lower SWAP-circuit error than ParSched is achieved across the three IBM systems, with a 2x geometric-mean improvement.On IBMQ Poughkeepsie, the maximum reductions are 4.9x versus ParSched and 9.2x versus SerialSched.
  • SWAP comparisons: XtalkSched schedules SWAPs on distant, non-crosstalking qubits in parallel while serializing nearby operations that interfere.This combines ParSched’s shorter execution with SerialSched’s crosstalk avoidance.
  • Ordering: XtalkSched orders serialized operations to minimize the lifetime of qubits with especially short coherence times.On IBMQ Poughkeepsie, qubit 10 has coherence below 6us, nearly 10X lower than the system average.
  • Optimality: For crosstalk-affected qubits on IBMQ Poughkeepsie, XtalkSched provides near-optimal mitigation and improved error rates.
  • Weight sensitivity: QAOA cross-entropy varies with ω: ω = 1 behaves like full serialization, whereas ω = 0 behaves like full parallelization.
  • Weight sensitivity: Replacing Hidden Shift CNOTs with redundant triples makes weights from 0.2 to 0.5 improve over ω = 0, with best-case improvements up to 3x.
  • Scalability: For 18-qubit, 500-gate quantum-supremacy instances, compilation takes less than 2 minutes, and scaling depends primarily on gate count.

10 Fast Crosstalk Characterization

The paper reduces the cost of characterizing crosstalk and shows how scheduling can balance crosstalk against decoherence. Its scheduler approaches crosstalk-free error rates in practice.

  • Characterization overhead: 246 experiments and over 8 hours per system make all-pairs crosstalk characterization prohibitively expensive.Each experiment requires thousands of random trials, potentially consuming a third of a system’s lifetime.
  • Scheduling tradeoff: SerialSched incurs high decoherence from fully serializing four SWAPs, whereas ParSched incurs high crosstalk from parallel CNOT execution.XtalkSched addresses both errors by selectively serializing operations and ordering gates around qubit coherence times.
  • Scheduling tradeoff: XtalkSched error rates are very close to ideal crosstalk-free SWAP error rates on IBMQ Poughkeepsie.The ideal rates use the lowest-error schedules measured on crosstalk-free paths.

11 Conclusions

The paper demonstrates software mitigation of crosstalk through efficient characterization and instruction scheduling. Across IBMQ systems and application benchmarks, the approach substantially improves reliability while remaining near-optimal in practice.

  • Conclusions: Geomean 1.8x lower QAOA cross-entropy loss than ParSched and geomean 2x lower loss than SeriesSched are reported.The improvements reach up to 3.6x and 4.3x, respectively.
  • Conclusions: Software crosstalk mitigation can greatly increase the reliability of noisy quantum computers.The conclusion frames software mitigation as a practical alternative to relying only on hardware changes.
  • Conclusions: The scheduler is available open source in Qiskit Terra.Its implementation is provided in the crosstalk_adaptive_schedule.py pass.
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