Distributed Quantum Error Mitigation: Global and Local ZNE encodings

The gist: Global ZNE exhibits superior scalability, achieving error reductions of up to 48% across six QPUs

How it works

The study investigates Zero Noise Extrapolation (ZNE) in a distributed quantum computing (DQC) setting by comparing Global optimization against Local optimization. The core comparison is between applying ZNE prior to circuit partitioning, termed Global optimisation, and applying it independently to each sub-circuit, termed Local optimisation. Partitioning is performed on a monolithic circuit and then transformed into a distributed implementation by inserting noisy teleportation-based communication primitives between subcircuits.

Experimental Setup

The experimental evaluation comprised over 3,500 simulations using real circuits from the MQT Bench suite executed on Qiskit Aer with custom noise models capturing both intra-device and inter-device errors. Local gates experienced a base noise level pLocal, while non-local operations (communication primitives) experienced amplified noise pcomm = α · pLocal, where α ∈ [1.0, 1.1, 1.2] is the communication noise multiplier. The researchers varied Local noise levels from 0.001 to 0.02 and tested partition counts ranging from 2 to 6.

Circuit Partitioning and Communication

To partition quantum circuits across multiple quantum processing units, a greedy community detection-based strategy was adopted that exploits the structure of qubit interactions. This procedure involves three stages: 1) Community identification using greedy modularity optimization applied to the interaction graph 2) Community adjustment to match a target partition count k and 3) Partition assignment based on the adjusted community structure. Gates spanning partition boundaries are replaced with non-local communication primitives such as teleportation (TP), which transfers quantum states using pre-shared entanglement over a quantum channel.

Key Metrics and Trade-offs

The study evaluates mitigation strategies using three primary metrics: ZNE error, Error reduction, and Depth overhead. The Error Reduction is defined as Error Reduction = Ebaseline − EZNE / Ebaseline (4). Depth Overhead is the ratio of the amplified circuit depth to the original circuit depth (5). The Global ZNE strategy consistently achieves positive error reduction compared to the non-error-mitigated distributed baseline, reaching an error reduction of roughly 48% at six partitions.

Unexpected Noise Behavior and Conclusions

The results reveal counterintuitive noise behavior where increasing the number of QPUs improves mitigation effectiveness despite higher communication overhead. Global ZNE achieves its highest error reduction at the lowest tested noise level, but exhibits highly variable performance as Local noise increases. The stark contrast between Global and Local ZNE performance suggests that Global ZNE succeeds because noise amplification operates on the complete circuit topology, allowing the extrapolation model to capture error correlations that span partition boundaries. Despite the computational cost, at the highest tested partition count of 6, per-device circuit depth of Global ZNE falls to that of the original monolithic circuit without error mitigation. The paper concludes that Global ZNE is superior in scalability and that Local ZNE lacks the circuit-wide perspective needed to model inter-QPU error propagation.

Limitations and Future Directions

Limitations include reliance on the Qiskit Aer simulator with simplified noise models, which does not capture real hardware errors like crosstalk or gate-dependent error rates. Furthermore, the model assumes perfect, instantaneous entanglement generation and ideal all-to-all connectivity in realistic networks. Future work should explore targeted error correction of network-induced noise applied in conjunction with Local ZNE encodings. The study also suggests that higher quantum network channel noise can yield comparable or even superior error reduction relative to lower noise levels.

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Distributed Quantum Error Mitigation: Global and Local ZNE encodings Maria Gragera Garces Quantum Software Lab, University of Edinburgh Scotland, UK 0009-0000-9018-7435 Accepted at IEEE INFOCOM 26 (QUNAP) 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 subcircuits. 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. Index Terms—Error mitigation, Distributed Quantum Computing I. INTRODUCTION Quantum computing promises efficient solutions to problems that are intractable for classical systems, yet practical algorithms require thousands to millions of qubits [1], far exceeding the qubit counts, connectivity, and noise limits of individual devices. This gap has driven the emergence of distributed quantum computing (DQC), where circuits are partitioned across devices interconnected by quantum networks, mirroring classical computing’s evolution toward distributed architectures and already being necessitated at small scales in systems like IBM’s Heron chips and Xanadu’s Aurora device [2]. This distribution of quantum compute over a quantum network will come with many challenges including new resouces to manage (entanglement) and new sources of noise [2]. In this work, we explore how error mitigation, particularly Zero Noise Extrapolation (ZNE), a cheaper near-term alternative to quantum error correction, performs in a DQC setting. We investigate whether Global optimisation (applying ZNE before circuit partitioning) or Local optimisation (applying ZNE independently to each sub-circuit) represents a more effective approach. While error mitigation techniques have been extensively studied for standalone quantum processors, very little prior work exists at the intersection of error mitigation and DQC [3]. Existing work relies on basic strategies such as routing computations to higher-quality qubits [3], rather than adapting sophisticated mitigation techniques to the distributed setting. This work represents the first empirical exploration of how state-of-the-art error mitigation strategies interact with circuit partitioning and quantum network communication. Our experimental evaluation comprises over 3,500 simulations using real circuits from the MQT Bench suite [4], executed on Qiskit Aer, with custom noise models that capture both intra-device and inter-device errors.

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A. Distributed Quantum Circuits Current quantum computers face significant limitations in qubit count and connectivity, preventing the execution of many practical algorithms on a single device. DQC addresses this challenge by partitioning circuits across multiple quantum processors connected via a quantum network [2]. To distribute a quantum circuit, we first abstract it as a graph 1 where nodes represent qubits and edges represent twoqubit gates. Graph partitioners then partition this structure into sub-circuits, each executable on a separate quantum processor. Gates spanning partition boundaries must be replaced with non-local communication primitives such as teleportation (TP), which transfers quantum states using pre-shared entanglement over a quantum channel. While these non-local gates enable inter-QPU quantum operations, they introduce additional computational overhead and communication-induced noise, expected to exceed intra-device noise [2].

B. Zero Noise Extrapolation Zero Noise Extrapolation (ZNE) is a quantum error mitigation technique that estimates the noise-free expectation value of an observable without requiring additional qubits or quantum error correction [6], [7]. ZNE operates in two phases: 1) Noise scaling: the circuit is executed at multiple artificially increased noise levels by gate folding (repeating gates to artificially increase depth) or pulse stretching (slowing gate pulses to amplify decoherence) 2) Extrapolation: the measured expectation values are fitted to a functional form (linear, polynomial, or exponential) and extrapolated to the zero-noise limit.

1. textbf Supervised Distributed Training for Quantum Networks: Global ZNE Encoding on Circuit Partitioning Enables Robust Learning. The system can perform machine learning tasks across distributed QPUs by applying Global ZNE before circuit partitioning, which is shown to achieve superior scalability, achieving error reductions of up to 48% across six QPUs. This allows the AI to maintain high fidelity during complex, large-scale distributed computations despite communication noise.

2. textbf Adaptive Noise Modeling for Distributed Inference: Exploiting Non-Monotonic Noise Behavior for Enhanced Accuracy. The system can perform inference tasks by utilizing Global ZNE which demonstrates that higher quantum network channel noise yields comparable or even superior error reduction relative to lower noise levels. This capability allows the AI to maintain better predictive accuracy when deployed on noisy, real-world distributed quantum hardware compared to models relying on simpler error assumptions.

3. textbf Scalable Error Mitigation Strategy: Implementing Local ZNE for Resource-Constrained Sub-tasks. The system can execute specialized, smaller tasks independently by employing Local optimisation, which maintains a more modest overhead of approximately 3× and shows remarkable stability across varying partition counts. This enables the AI to efficiently manage workloads where individual sub-circuits have distinct noise profiles without incurring the severe depth penalty associated with global mitigation.