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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.16578 |
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| _version_ | 1866914485375074304 |
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| author | Cha, Hyunho Kim, Subin Lee, Jungwoo |
| author_facet | Cha, Hyunho Kim, Subin Lee, Jungwoo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16578 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Verifying random matrix product states with autoregressive local measurements Cha, Hyunho Kim, Subin Lee, Jungwoo Quantum Physics 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. |
| title | Verifying random matrix product states with autoregressive local measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.16578 |