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A Case for Variability-Aware Policies for NISQ-Era Quantum Computers

Swamit S. Tannu, Moinuddin K. Qureshi

arXiv:1805.10224v1quant-phcs.ET

TL;DR

NISQ computers lack sufficient resources for quantum error correction, while restricted connectivity and component-level reliability variation complicate qubit movement and allocation. The paper evaluates reliability and proposes variation-aware policies that favor stronger qubits and links, improving system reliability and sometimes outperforming concurrent execution.

  • Problem

    NISQ computers cannot generally use quantum error correction, and restricted connectivity complicates qubit movement and allocation.

  • Method

    The paper develops MIBF and PST reliability metrics, evaluates IBM-Q20 using applications and kernels, and proposes VQM and VQA policies based on qubit- and link-level reliability.

  • Results

    Device variation significantly affects system-level reliability, while variation-aware policies steer operations toward stronger qubits and links.

  • Takeaways & Limitations

    In some scenarios, executing one strong program copy achieves better successful trials per unit time than executing two concurrent copies.

  • Takeaways & Limitations

    The evaluation uses an iterative NISQ model and small kernels, so PST may not be meaningful for all applications and assumptions may change as the technology matures.

Abstract

from arXiv · show

Recently, IBM, Google, and Intel showcased quantum computers ranging from 49 to 72 qubits. While these systems represent a significant milestone in the advancement of quantum computing, existing and near-term quantum computers are not yet large enough to fully support quantum error-correction. Such systems with few tens to few hundreds of qubits are termed as Noisy Intermediate Scale Quantum computers (NISQ), and these systems can provide benefits for a class of quantum algorithms. In this paper, we study the problems of Qubit-Allocation (mapping of program qubits to machine qubits) and Qubit-Movement(routing qubits from one location to another to perform entanglement). We observe that there exists variation in the error rates of different qubits and links, which can have an impact on the decisions for qubit movement and qubit allocation. We analyze characterization data for the IBM-Q20 quantum computer gathered over 52 days to understand and quantify the variation in the error-rates and find that there is indeed significant variability in the error rates of the qubits and the links connecting them. We define reliability metrics for NISQ computers and show that the device variability has the substantial impact on the overall system reliability. To exploit the variability in error rate, we propose Variation-Aware Qubit Movement (VQM) and Variation-Aware Qubit Allocation (VQA), policies that optimize the movement and allocation of qubits to avoid the weaker qubits and links and guide more operations towards the stronger qubits and links. We show that our Variation-Aware policies improve the reliability of the NISQ system up to 2.5x.

I. INTRODUCTION

NISQ computers lack the resources for quantum error correction but remain useful for some applications, making reliable qubit movement and allocation important. The paper measures device variability and proposes policies that exploit stronger qubits and links to improve system reliability.

  • Motivation: NISQ computers with 10 to 1000 qubits generally cannot use quantum error correction because encoding one fault-tolerant qubit typically requires 10-50 physical qubits.They can nevertheless benefit a class of quantum applications.
  • Problem: Restricted connectivity constrains which qubits can be entangled and makes qubit movement and allocation necessary for quantum programs.Qubit movement routes data between locations, while allocation maps program qubits to physical qubits.
  • Measurement: IBM-Q20 characterization data collected over 52 days shows significant variation in coherence times and single- and two-qubit operation error rates.The analysis covers all 20 qubits and links between them.
  • Reliability Analysis: The paper develops Mean Instructions Before Failure (MIBF) and Probability of Successful Trial (PST) to evaluate NISQ system reliability.MIBF targets long-running programs, whereas PST measures successful completion without error.
  • Variation-Aware Policies: VQM routes qubits using link reliability, while VQA maps program qubits to physical qubits to improve overall system reliability.VQM can trade additional SWAP instructions for higher success probability, and VQA favors stronger links.
  • Results: VQM improves MIBF up to 1.5x, and variation-aware partitioning can make one strong program copy outperform two concurrent copies in certain scenarios.The partitioning comparison uses successful trials per unit time as the overall-performance measure.

II. BACKGROUND AND MOTIVATION

Quantum computation uses qubit states, entanglement, and operations, but restricted connectivity and imperfect retention and gate operations introduce architectural reliability challenges. SWAP operations provide a way to move qubit data across the restricted network.

  • A. Background on Quantum Computing: A qubit can occupy an arbitrary point on the Bloch sphere as a superposition of two basis states, and quantum operations move its state across the sphere.This state representation differs from conventional binary data.
  • A. Background on Quantum Computing: Entanglement produces correlated collective states through two-qubit operations such as Controlled-NOT instructions.Manipulating one qubit can affect the states of other entangled qubits.
  • B. Restricted Connectivity: Superconducting quantum computers use restricted networks connecting neighboring qubits, limiting which pairs can be directly entangled.SWAP operations move qubit data to enable entanglement between arbitrary qubits.
  • C. Errors: Retention errors arise because qubits preserve data for limited coherence times, while operational errors occur when quantum gates alter states incorrectly.Coherence errors include T1 and T2 phenomena, and gate errors are defined by the probability of an erroneous operation.
  • C. Errors: Superconducting quantum-computer coherence times improved from 1 nano-second to 100 micro-seconds over the last decade.The passage also reports an improving trend in existing superconducting qubits.

C. Quantum Error Correction and Overheads

NISQ computers lack sufficient qubits for practical quantum error correction, so this paper examines how restricted connectivity and nonuniform operation reliability affect qubit movement and allocation policies.

  • 10x-50x physical qubits are required to encode one fault-tolerant qubit, exceeding the capacity of current and near-term NISQ machines.
  • Restricted connectivity forces communication between nonadjacent qubits to use intermediate qubits and SWAP operations.
  • Qubit-Movement Policy: Qubit-Movement selects routes for moving data, traditionally minimizing the number of SWAP instructions.
  • Qubit-Allocation Policy: Qubit-Allocation maps program qubits to physical qubits, preferring nearby placements for frequently communicating qubits.
  • Existing movement and allocation policies assume uniform SWAP reliability, despite significant variation among qubits and links.

III. ANALYZING VARIATION IN IBM-Q20

The IBM-Q20 characterization study quantifies variation in coherence times and single-qubit operation error rates across the machine using repeated observations collected over more than 50 days.

  • More than 50 characterization reports were gathered over 52 days for IBM-Q20, covering coherence times and operation error rates.
  • Distribution of Coherence Times: T1 coherence times show a wider spread than T2 coherence times across the 20 qubits.The data covers more than 50 observations.
  • Distribution of Coherence Times: T1 coherence time has mean 80.32µS and standard deviation 35.23µS.
  • Distribution of Coherence Times: T2 coherence time has mean 42.13µS and standard deviation 13.34µS.
  • Distribution of Error-Rate of Single-Qubit Operations: Single-qubit operation error rates show a large fraction below 1%.The paper attributes variation in operation robustness to device nonlinearity and changes in biasing or experimental conditions.

C. Distribution of Error-Rate of Two-Qubit Operations

Two-qubit operations are central to entanglement and data movement, yet their link error rates vary substantially over space and time, motivating reliability-aware evaluation and policies.

  • Distribution of Error-Rate of Two-Qubit Operations: 4.3% mean error rate and 3.02% standard deviation characterize two-qubit operations across 76 IBM-Q20 coupling links.
  • Two-qubit operations are essential for entangling states and moving data, making their errors especially relevant to NISQ programs.
  • A fraction of coupling links is significantly weaker than most links, demonstrating spatial variation in two-qubit operation reliability.
  • Link error rates can change across calibration points because of tuning parameters, drift, local temperature gradients, and other experimental factors.
  • The IBM-Q20 layout represents qubits as nodes and coupling links as directed edges weighted by average failure probability.The best links have error rate 0.02 and the worst has 0.15, a 7.5x strength difference.
  • The paper uses system-level reliability metrics and evaluates policies against observed device variability.

A. Evaluation Infrastructure

The evaluation infrastructure uses Monte-Carlo simulation to measure NISQ reliability with workload-specific metrics for successful completion and failure-free execution.

  • 1 million trials are performed for each evaluation using a simulator that models programs, layouts, error rates, and management policies.The simulator records whether each program completes without error and how many instructions execute before failure.
  • PST measures the probability that a program completes without any errors, calculated as successful trials divided by total trials.
  • PST depends on error distribution and program length, making it unsuitable for long programs with negligible completion probability.
  • MIBF measures the average number of instructions executed before the first error for long-running programs.It is computed by repeatedly running trials until failure and averaging the recorded instructions before failure.
  • Benchmarks are classified as terminating or non-terminating using a 0.1% PST threshold, with PST or MIBF selected accordingly.

V. VARIATION-AWARE QUBIT MOVEMENT

Variation-Aware Qubit Movement selects routes using link reliability rather than shortest-path length alone, while optionally limiting additional SWAP hops.

  • V. VARIATION-AWARE QUBIT MOVEMENT: Shortest-route policies can choose unreliable links even when alternative routes have identical SWAP counts or higher overall success probability.
  • V. VARIATION-AWARE QUBIT MOVEMENT: VQM selects qubit-movement paths with the highest reliability by accounting for variation in per-link error rates.It actively avoids paths with poor reliability.
  • V. VARIATION-AWARE QUBIT MOVEMENT: VQM computes route reliability as the product of link success probabilities and selects routes using a compile-time cost graph.This assumes characterization data remains valid during workload execution.
  • V. VARIATION-AWARE QUBIT MOVEMENT: VQM may choose a longer path when it has higher reliability, increasing SWAP overhead in exchange for avoiding weaker links.
  • V. VARIATION-AWARE QUBIT MOVEMENT: The Maximum Additional Hop parameter limits extra SWAPs; evaluations use MAH = 4 and include failures from added hops.

D. Impact of VQM on Probability of Successful Trials

VQM improves successful-trial probability and failure-free execution relative to a shortest-route, variation-unaware baseline, with gains varying by benchmark.

  • D. Impact of VQM on Probability of Successful Trials: 2.5x, 1.46x, and 1.66x Relative-PST improvements occur for ising, qft, and cnt35, respectively.The baseline uses shortest routes while ignoring link strengths.
  • D. Impact of VQM on Probability of Successful Trials: VQM avoids unreliable links by taking more robust paths, helping benchmarks whose baseline executions fail because of a small fraction of weak links.
  • E. Impact of VQM on Mean Instructions Before Failure: 10% to 80% MIBF improvements are reported across five benchmarks compiled with VQM.
  • E. Impact of VQM on Mean Instructions Before Failure: The largest MIBF improvement occurs for rnd2, which performs a small number of long-range SWAPs followed by many single-qubit operations.

F. Impact of Inter-Day Variation in Error Rates of IBM-Q20

The paper evaluates variation-aware allocation alongside inter-day reliability variation, showing that allocation should account for both link strength and program access patterns.

  • F. Inter-Day Variation and Allocation: Inter-day error-rate variation is evaluated by recompiling the ising design with characterization data from each day and comparing VQM with the baseline.
  • F. Inter-Day Variation and Allocation: Allocation decisions affect later data-movement patterns because placing qubits far apart requires more SWAP operations.
  • F. Inter-Day Variation and Allocation: Variation-unaware allocation may select neighboring qubits connected by the weakest link, whereas variation-aware allocation selects stronger links.
  • F. Inter-Day Variation and Allocation: VQA maps frequently operated qubits to a strongest qubit block with high connectivity and reliable coupling links.Connectivity-strength is defined as the sum of coupling-link success probabilities.
  • F. Inter-Day Variation and Allocation: VQA uses locality-aware allocation to balance reliability against SWAP count based on qubit access patterns in the first-N instructions.

D. Impact of VQA on Probability of Successful Trials

VQA improves successful-trial reliability for some workloads by complementing VQM, especially when fewer program qubits can be mapped across more physical qubits. Its benefits are workload-dependent because initial mappings can later expose frequently used or dormant qubits to weaker links.

  • VQA benefit by workload size: VQA provides greater PST improvement when fewer program qubits are mapped to a larger physical-qubit set.For example, qft-10 improves more than qft-16, with a similar pattern for ising.
  • VQA benefit by workload size: VQA is built on VQM and improves PST for some workloads, including qft and ising.The comparison reports relative PST normalized to the baseline for VQM alone versus VQM combined with VQA.
  • Workload dependence: VQA can significantly improve normalized MIBF for inc, dist, and sqrt, but degrades it for gse and rnd2.The degradation is associated with mapping based on early instructions, random CNOT chains, and dormant qubits that later become active.
  • Partitioning trade-off: Running two copies can restrict mappings and force use of weaker links, whereas one strong copy can select stronger qubits and links.In the six-qubit mesh example, two-copy execution cannot use the strongest link CD because of connectivity constraints.

B. Benchmark-Based Evaluation

The benchmark-based evaluation combines partitioning infrastructure with PST, MIBF, and STPT analyses to assess variation-aware policies. Results show that the better choice between one strong copy and two copies depends on the workload, while the study remains limited by simplifying assumptions and small benchmark representativeness.

  • Evaluation methodology: STPT captures both PST and the increased trial rate from running two copies.The evaluation compares one strong copy with two copies using normalized STPT, with benchmarks modified to ten qubits.
  • Evaluation methodology: The two-copy simulation explores all possible partitions while keeping movement and mapping algorithms identical across copy configurations.Only the number of available qubits differs between the compared modes.
  • Benchmark results: Two-copy execution is better for ising, while one strong copy is better for qft.The paper uses this workload dependence to motivate choosing the solution with higher estimated STPT.
  • Study limitations: The evaluation uses an iterative NISQ model, small kernels, random benchmarks, and simplifying error assumptions.The stated assumptions include uncorrelated errors, static error rates, and ignored retention errors; these choices may limit representativeness as applications and devices mature.
  • Reliability metrics: PST and MIBF quantify reliability impacts from device variation, policy decisions, and benchmark-dependent behavior for fixed system configurations.This distinguishes them from the application-agnostic Quantum Volume metric.

X. SUMMARY

The paper studies qubit allocation and movement on restricted-connectivity quantum computers, where component reliability varies. It introduces variation-aware policies and reliability evaluation methods to favor stronger links and avoid weaker ones.

  • Scope and problem: The paper studies Qubit-Allocation and Qubit-Movement policies for available quantum computers with restricted connectivity.Allocation maps program qubits to machine qubits, while movement routes qubits to enable entanglement.
  • Evaluation: The evaluation methodology defines PST and MIBF to assess device variation and management-policy effects on system-level reliability.These metrics provide reliability measures for the paper’s policy comparisons.
  • Variation-aware policies: VQM selects movement routes with the lowest probability of failure by accounting for link variation.The policy is designed to avoid unreliable links during qubit movement.
  • Variation-aware policies: VQA maps program qubits to use the strongest links and avoid weaker links.The paper also applies its models to resource-sharing and partition decisions such as one strong copy versus two concurrent copies.
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