Enhanced estimation of quantum properties with common randomized measurements

Abstract

We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves 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 multi-copy observables and present performance guarantees in terms of variance bounds which depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through numerical experiments estimating polynomial approximations of the von Neumann entropy and quantum state fidelities.

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• Entanglement swapping in critical quantum spin chains
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
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• Nearly query-optimal classical shadow estimation of unitary channels
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• Quantum circuit complexity and unsupervised machine learning of topological order
• Analytically Continuing the Randomized Measurement Toolbox
• Learning mixed quantum states in large-scale experiments
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter