Probing the Error-Mitigation Threshold with Matrix Product States

• URL: http://arxiv.org/abs/2609.10929v1
• Date: Thu, 10 Sep 2026 00:29:38 GMT
• Title: Probing the Error-Mitigation Threshold with Matrix Product States
• Abstract summary: Quantum error mitigation relies on accurate noise characterization.<n> mismatches between the actual and characterized noise can be amplified and drive a sharp threshold between successful and failed mitigation.<n>We develop a fixed-bond-dimension matrix-product-state method for the replicated transfer dynamics.
• Score: 2.2940141855172036
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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