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A Compilation Framework for Quantum Circuits with Mid-Circuit Measurement Error Awareness

Ming Zhong, Zhemin Zhang, Xiangyu Ren, Chenghong Zhu, Siyuan Niu, Zhiding Liang

TL;DR

MCM enables dynamic quantum circuits and qubit reuse but introduces pronounced, qubit-dependent errors, challenging traditional compilers that ignore this heterogeneity. MERA addresses this gap by performing lightweight profiling to obtain per-qubit MCM error distributions (stable for ~24 hours) and integrating this information into a three-stage workflow: MCM-aware layout, routing, and ALAP scheduling with context-aware dynamic decoupling (CADD). The framework normalizes and leverages MCM error data to bias qubit mapping, SWAP decisions, and pulse scheduling, achieving average fidelity improvements of $24.94\%$–$52.00\%$ over Qiskit-Compiler and up to $122.58\%$ over QR-Map across 27 benchmarks, including real-device gains on IBM Eagle and Heron. These results demonstrate MERA's effectiveness for MCM-dominated dynamic circuits and its potential as an add-on to existing compilation frameworks, with practical impact for resource-efficient quantum computing and error correction workflows.

Abstract

Mid-circuit measurement (MCM) provides the capability for qubit reuse and dynamic control in quantum processors, enabling more resource-efficient algorithms and supporting error-correction procedures. However, MCM introduces several sources of error, including measurement-induced crosstalk, idling-qubit decoherence, and reset infidelity, and these errors exhibit pronounced qubit-dependent variability within a single device. Since existing compilers such as the Qiskit-compiler and QR-Map (the state-of-art qubit reuse compiler) do not account for this variability, circuits with frequent MCM operations often experience substantial fidelity loss. In thie paper, we propose MERA, a compilation framework that performs MCM-error-aware layout, routing, and scheduling. MERA leverages lightweight profiling to obtain a stable per-qubit MCM error distribution, which it uses to guide error-aware qubit mapping and SWAP insertions. To further mitigate MCM-related decoherence and crosstalk, MERA augments as-late-as-possible scheduling with context-aware dynamic decoupling. Evaluated on 27 benchmark circuits, MERA achieves 24.94% -- 52.00% fidelity improvement over the Qiskit compiler (optimization level 3) without introducing additional overhead. On QR-Map-generated circuits, it improves fidelity by 29.26% on average and up to 122.58% in the best case, demonstrating its effectiveness for dynamic circuits dominated by MCM operations.

A Compilation Framework for Quantum Circuits with Mid-Circuit Measurement Error Awareness

TL;DR

MCM enables dynamic quantum circuits and qubit reuse but introduces pronounced, qubit-dependent errors, challenging traditional compilers that ignore this heterogeneity. MERA addresses this gap by performing lightweight profiling to obtain per-qubit MCM error distributions (stable for ~24 hours) and integrating this information into a three-stage workflow: MCM-aware layout, routing, and ALAP scheduling with context-aware dynamic decoupling (CADD). The framework normalizes and leverages MCM error data to bias qubit mapping, SWAP decisions, and pulse scheduling, achieving average fidelity improvements of – over Qiskit-Compiler and up to over QR-Map across 27 benchmarks, including real-device gains on IBM Eagle and Heron. These results demonstrate MERA's effectiveness for MCM-dominated dynamic circuits and its potential as an add-on to existing compilation frameworks, with practical impact for resource-efficient quantum computing and error correction workflows.

Abstract

Mid-circuit measurement (MCM) provides the capability for qubit reuse and dynamic control in quantum processors, enabling more resource-efficient algorithms and supporting error-correction procedures. However, MCM introduces several sources of error, including measurement-induced crosstalk, idling-qubit decoherence, and reset infidelity, and these errors exhibit pronounced qubit-dependent variability within a single device. Since existing compilers such as the Qiskit-compiler and QR-Map (the state-of-art qubit reuse compiler) do not account for this variability, circuits with frequent MCM operations often experience substantial fidelity loss. In thie paper, we propose MERA, a compilation framework that performs MCM-error-aware layout, routing, and scheduling. MERA leverages lightweight profiling to obtain a stable per-qubit MCM error distribution, which it uses to guide error-aware qubit mapping and SWAP insertions. To further mitigate MCM-related decoherence and crosstalk, MERA augments as-late-as-possible scheduling with context-aware dynamic decoupling. Evaluated on 27 benchmark circuits, MERA achieves 24.94% -- 52.00% fidelity improvement over the Qiskit compiler (optimization level 3) without introducing additional overhead. On QR-Map-generated circuits, it improves fidelity by 29.26% on average and up to 122.58% in the best case, demonstrating its effectiveness for dynamic circuits dominated by MCM operations.

Paper Structure

This paper contains 26 sections, 6 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Middle-circuit-measurement
  4. Error sources of MCM
  5. Motivation
  6. MCM Error Profiling
  7. Profiling Approach
  8. Profiling Results
  9. Temporal Stability of MCM Errors
  10. MERA: An MCM-Error-Aware Compiler
  11. Overview of MERA
  12. Layout Stage
  13. Logical Graph Analysis
  14. MCM Error Normalization and Seed Selection
  15. Layout Candidate Generation and Expansion
  16. ...and 11 more sections

Figures (7)

  • Figure 1: Representative circuits containing MCM operations.
  • Figure 2: MCM error distributions for quantum processors.
  • Figure 3: Stability of MCM errors in quantum processors.
  • Figure 4: The workflow of MERA. More MCMs (on $q_2$), and single- and two-qubit gates (on $q_1$ -- $q_4$) are omitted for brevity.
  • Figure 5: Layouts with and without MCM error normalization. The 1.0% -- 20.0% range in the error map is nonlinearly scaled to highlight subtle differences in color contrast.
  • ...and 2 more figures