Probing the Error-Mitigation Threshold with Matrix Product States

Abstract:Quantum error mitigation relies on accurate noise characterization, but mismatches between the actual and characterized noise can be amplified and drive a sharp threshold between successful and failed mitigation. In random circuits, this threshold maps onto a random-field Ising transition, but previous exact numerics were limited to small one-dimensional and all-to-all systems, leaving explicit two-dimensional architectures unresolved. We develop a fixed-bond-dimension matrix-product-state method for the replicated transfer dynamics that extends threshold calculations beyond exact propagation while retaining the finite-size signatures of the transition. At system sizes beyond previous exact studies, we recover the predicted absence of a threshold for quenched disorder in 1D, obtain a sharper annealed all-to-all critical point, and resolve architecture-dependent finite-depth thresholds in 2D square and heavy-hex circuits. These results establish replicated tensor-network dynamics as a practical tool for probing error-mitigation thresholds in large and higher-dimensional noisy circuits.

arXiv:2609.10929 [quant-ph]

(or arXiv:2609.10929v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.10929 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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