Verifying random matrix product states with autoregressive local measurements

• URL: http://arxiv.org/abs/2604.16578v1
• Date: Fri, 17 Apr 2026 13:12:27 GMT
• Title: Verifying random matrix product states with autoregressive local measurements
• Abstract summary: Matrix product states (MPS) are a central language for one-dimensional quantum matter.<n>We introduce an emphautoregressive importance sampler that draws Pauli strings sequentially from efficiently computable conditional distributions.<n>We also develop a grouped extension that constructs qubit-wise commuting measurement settings via a emphsorting string.
• Score: 7.085044605508094
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Matrix product states (MPS) are a central language for one-dimensional quantum matter and a practical target for near-term quantum simulators and variational algorithms. Yet, while substantial effort has focused on preparing MPS with shallow circuits, scalable methods to \emph{verify} that a many-body device has actually produced the intended state remain underdeveloped. Direct fidelity estimation (DFE) relies only on local Pauli measurements, but in many-body settings it suffers an exponential classical overhead from the preprocessing needed to sample Pauli strings. We eliminate this obstacle by introducing an \emph{autoregressive} importance sampler that draws Pauli strings sequentially from efficiently computable conditional distributions, reducing the per-shot classical overhead to linear scaling in the number of qubits. We further develop a grouped extension that constructs qubit-wise commuting measurement settings via a \emph{sorting string} and simultaneously estimates the entire commuting group from a single setting, significantly reducing estimator variance while preserving efficient postprocessing. Our approach extends naturally to matrix product operators (MPO), enabling scalable verification of tensor-network states and observables in long one-dimensional quantum systems. We utilize random MPS as a natural benchmark for generic 1D entangled states.

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