Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Quantum Error Mitigation: Global and Local ZNE encodings

Maria Gragera Garces

TL;DR

Distributed quantum computing introduces network-induced noise that complicates error mitigation. We compare Global ZNE (applied before circuit partitioning) with Local ZNE (applied to each sub-circuit after partitioning) in teleportation-enabled distributed circuits. Global ZNE achieves up to 48% error reduction across six partitions, at the cost of 6x–10x circuit-depth overhead, while Local ZNE yields more modest and less consistent gains (1%–19%) with about 3x overhead. Surprisingly, increasing the number of QPUs or network noise can improve mitigation in some configurations, motivating a nuanced view of how circuit structure, partitioning, and network noise interact in distributed error mitigation.

Abstract

Errors are the primary bottleneck preventing practical quantum computing. This challenge is exacerbated in the distributed quantum computing regime, where quantum networks introduce additional communication-induced noise. While error mitigation techniques such as Zero Noise Extrapolation (ZNE) have proven effective for standalone quantum processors, their behavior in distributed architectures is not yet well understood. We investigate ZNE in this setting by comparing Global optimization (ZNE is applied prior to circuit partitioning), against Local optimization (ZNE is applied independently to each sub-circuit). Partitioning is performed on a monolithic circuit, which is then transformed into a distributed implementation by inserting noisy teleportation-based communication primitives between sub-circuits. We evaluate both approaches across varying numbers of quantum processing units (QPUs) and under heterogeneous local and network noise conditions. Our results demonstrate that Global ZNE exhibits superior scalability, achieving error reductions of up to $48\%$ across six QPUs. Moreover, we observe counterintuitive noise behavior, where increasing the number of QPUs improves mitigation effectiveness despite higher communication overhead. These findings highlight fundamental trade-offs in distributed quantum error mitigation and raise new questions regarding the interplay between circuit structure, partitioning strategies, and network noise.

Distributed Quantum Error Mitigation: Global and Local ZNE encodings

TL;DR

Distributed quantum computing introduces network-induced noise that complicates error mitigation. We compare Global ZNE (applied before circuit partitioning) with Local ZNE (applied to each sub-circuit after partitioning) in teleportation-enabled distributed circuits. Global ZNE achieves up to 48% error reduction across six partitions, at the cost of 6x–10x circuit-depth overhead, while Local ZNE yields more modest and less consistent gains (1%–19%) with about 3x overhead. Surprisingly, increasing the number of QPUs or network noise can improve mitigation in some configurations, motivating a nuanced view of how circuit structure, partitioning, and network noise interact in distributed error mitigation.

Abstract

Errors are the primary bottleneck preventing practical quantum computing. This challenge is exacerbated in the distributed quantum computing regime, where quantum networks introduce additional communication-induced noise. While error mitigation techniques such as Zero Noise Extrapolation (ZNE) have proven effective for standalone quantum processors, their behavior in distributed architectures is not yet well understood. We investigate ZNE in this setting by comparing Global optimization (ZNE is applied prior to circuit partitioning), against Local optimization (ZNE is applied independently to each sub-circuit). Partitioning is performed on a monolithic circuit, which is then transformed into a distributed implementation by inserting noisy teleportation-based communication primitives between sub-circuits. We evaluate both approaches across varying numbers of quantum processing units (QPUs) and under heterogeneous local and network noise conditions. Our results demonstrate that Global ZNE exhibits superior scalability, achieving error reductions of up to across six QPUs. Moreover, we observe counterintuitive noise behavior, where increasing the number of QPUs improves mitigation effectiveness despite higher communication overhead. These findings highlight fundamental trade-offs in distributed quantum error mitigation and raise new questions regarding the interplay between circuit structure, partitioning strategies, and network noise.
Paper Structure (22 sections, 5 figures)

This paper contains 22 sections, 5 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Distributed Quantum Circuits
  4. Zero Noise Extrapolation
  5. Methodology
  6. Experimental Setup
  7. Circuit Partitioning
  8. Communication Primitives
  9. ZNE Application Strategies
  10. Results
  11. Scalability
  12. Network Noise Resilience
  13. Local Noise Sensitivity
  14. Discussion
  15. Global vs Local Optimisation
  16. ...and 7 more sections

Figures (5)

  • Figure 1: Teleportation (TP) implementation of a Local CNOT gate between two QPUs. Adapted from wu2022autocomm.
  • Figure 2: Performance of ZNE strategies across partition counts, tested Local and communication error levels.
  • Figure 3: Circuit Depth Penalty across partition counts.
  • Figure 4: Error reduction heatmaps showing the interaction between partition count and communication noise multiplier. Values represent mean error reduction (fractional improvement in expectation value error) after outlier removal using robust trimmed mean. Data is accounted from all tested local noise levels.
  • Figure 5: Strategy comparison showing performance versus Local noise levels and overall performance distribution