Quantum Networks’ Errors Tackled with New Noise-Reduction Technique
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Errors represent a substantial obstacle to realising practical quantum computation.
Maria Gragera Garces from the University of Edinburgh, alongside collaborators, investigates Zero Noise Extrapolation (ZNE) as a means of tackling these errors specifically within distributed quantum systems. Their research compares applying ZNE globally, before circuit partitioning, with a local approach where ZNE is applied to individual sub-circuits. By modelling distributed computation via noisy teleportation between quantum processing units, the team evaluated both strategies across different system sizes and noise profiles. The findings demonstrate that global ZNE offers better scalability, achieving error reductions of up to across six quantum processing units, and surprisingly reveal that increasing their number can actually improve mitigation despite increased communication demands. This work therefore illuminates crucial trade-offs in distributed quantum error mitigation and provides valuable insight into optimising circuit design and partitioning strategies for future quantum networks. The research addresses a gap in understanding how error mitigation techniques, effective on standalone quantum processors, behave when applied to distributed systems. Experiments were conducted using three algorithms from the MQT Bench suite: Greenberger-Horne-Zeilinger (GHZ) state preparation, Deutsch-Jozsa (DJ), and W state preparation, providing a diverse assessment across varying circuit structures and computational patterns. Local gates were subjected to a base noise level, denoted as pLocal, representing the probability of a qubit error during gate operation under a depolarizing channel model. Non-local operations, simulating communication between quantum processing units, experienced amplified noise, pcomm = α · pLocal, where α ranged from 1.0 to 1.2 to represent elevated communication error rates. The study systematically varied pLocal from 0.001 to 0.02 and tested partition counts ranging from 2 to 6, defining partitions as the number of sub-circuits or quantum processing units. Each experimental configuration was executed with 200 measurement shots to gather sufficient statistical data. Quantum teleportation implemented all non-local operations, enabling the simulation of communication-induced noise. Circuit partitioning employed a greedy community detection-based strategy, constructing an interaction graph representing qubit connectivity and iteratively merging or splitting communities to achieve the target partition count. Mitigation strategies were evaluated using three primary metrics: ZNE error, calculated as the absolute difference between measured and ideal expectation values; error reduction, representing the fractional improvement in expectation value error; and depth overhead, quantifying the ratio of amplified circuit depth to the original circuit depth.
This research investigated ZNE within distributed quantum computing architectures, comparing Global optimisation, where ZNE is applied before circuit partitioning, against Local optimisation, applying ZNE independently to each sub-circuit. Circuits were partitioned and transformed into a distributed implementation utilising noisy teleportation-based communication primitives between sub-circuits. Evaluations were performed with varying numbers of QPUs and heterogeneous local and network noise conditions to assess performance. The study demonstrates that Global ZNE exhibits superior scalability in mitigating errors within distributed systems. Increasing the number of QPUs unexpectedly improved mitigation effectiveness, despite the associated increase in communication overhead. This counterintuitive behaviour suggests a complex interplay between circuit structure, partitioning strategies, and network noise. Over 3,500 simulations were conducted using real circuits from the MQT Bench suite, executed on Qiskit Aer with custom noise models capturing both intra-device and inter-device errors. Distributed circuits were abstracted as graphs, with nodes representing qubits and edges representing two-qubit gates, then partitioned into sub-circuits for execution on separate QPUs. Gates spanning partition boundaries were replaced with teleportation, introducing computational overhead and communication-induced noise expected to exceed intra-device noise. ZNE was implemented using Mitiq via unitary folding with linear extrapolation, exploring the optimal timing for application, before or after partitioning. Local gates experienced a base noise level, denoted as pLocal, representing the probability of a gate applying an error, while non-local operations experienced amplified noise, defined as pcomm = α · pLocal, where α ranged from 1.0 to 1.2. The study compared two approaches to applying ZNE: Global optimization, applied before circuit partitioning, and Local optimization, applied independently to each sub-circuit. Circuits were partitioned and implemented using noisy teleportation to simulate communication between quantum processing units. Results indicate that Global ZNE demonstrates better scalability, achieving error reductions of up to across six quantum processing units. Furthermore, the research revealed counterintuitive behaviour where increasing the number of quantum processing units improved error mitigation despite increased communication overhead. Analysis suggests Global ZNE’s success stems from its ability to model error correlations across the entire circuit, while Local ZNE is limited by its focus on individual sub-circuits. Although Local ZNE exhibited more stable performance, it generally achieved lower error reduction than the Global approach. The authors acknowledge a trade-off between error reduction magnitude and stability, with Global ZNE showing higher variance in its performance. Future research could explore partitioning strategies that better capture inter-QPU error propagation, potentially enhancing the effectiveness of Local ZNE or developing hybrid approaches that combine the strengths of both methods. These findings highlight the complex interplay between circuit structure, partitioning, network noise, and error mitigation in distributed quantum systems. 👉 More information 🗞 Distributed Quantum Error Mitigation: Global and Local ZNE encodings 🧠 ArXiv: https://arxiv.org/abs/2602.04981 Tags: