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Physical Review Letters

Symmetry Speeds Up Quantum Measurements

Hu Chen, Bujiao Wu, Qian-Xi Zhang, Qi-Ming Ding, Haozhao Wu, Mei-Shi Su, Ya-Li Mao, Xiao Yuan, Zheng-Da Li

Published Aug 20, 2026• 0 citations
Publisher

Abstract

Estimating the properties of quantum states is a fundamental task in both theoretical and experimental quantum physics. While numerous Pauli-based measurement strategies have been proposed, none explicitly exploit prior knowledge of structural features such as symmetry. Here, we introduce a compact measurement scheme that exploits symmetry to speed up quantum measurements. By incorporating symmetry into the measurement design, our approach can rigorously reduce sample complexity for symmetric states and suitable observables. We provide a theoretical analysis showing that, for specific observables, the variance of our estimator admits polynomial or even exponential improvements in the required number of state copies. To demonstrate practicality, we implement the scheme on photonic quantum platforms, preparing high-fidelity Greenberger-Horne-Zeilinger (GHZ) and W states. The experimental results confirm substantial gains in estimation accuracy for both linear and nonlinear properties. Our work suggests that symmetry and other structural properties of quantum states can be systematically exploited as algorithmic resources, opening new avenues for scalable characterization and verification of complex quantum systems on near-term and fault-tolerant devices.

DOI
10.1103/q9lf-cp11

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Preparation and verification of specific quantum states is an important capability for quantum devices to realise advantages over classical computations and algorithms. In this work, we have demonstrated an end-to-end framework that combines resource-efficient quantum state preparation with rapid, robust fidelity verification on near-term quantum hardware. By experimentally preparing and validating a structured complex quantum state encoding a digitized acoustic signal on the Quantinuum H2-1 trapped-ion platform, we achieved a high hardware fidelity of Fhw=0.929F_{\mathrm{hw}} = 0.929Fhw​=0.929. Crucially, this milestone was realized without relying on idealized assumptions or deep fault-tolerant overhead, but rather through resource-minimal circuits optimized for NISQ-era and early fault-tolerant devices. Furthermore, we addressed a key limitation in current quantum state certification. While validation methods like shadow overlap work well for random states, their sample complexity can become prohibitively high for the structured states used in practical algorithms. We mitigate this by introducing a pre-measurement basis-change technique that reduces the verification parameter, τττ, by over 10 orders of magnitude for structured targets. This approach tightens the theoretical certification guarantees of the shadow overlap method and integrates tensor-network preparation and shadow validation into a unified workflow. These results shift the paradigm of how structured classical data can be mapped to and verified on quantum hardware under realistic noise and measurement budgets. By compressing a robust verification procedure to just 1,000 measurement shots, this framework offers an immediate, scalable benchmarking standard.
We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state. This consists in performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multicopy observables and present performance guarantees in terms of variance bounds that depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through experimental and numerical examples detecting mixed-state entanglement, and estimating polynomial approximations of the von Neumann entropy and state fidelities. Published by the American Physical Society 2024