Thrifty shadow estimation: re-using quantum circuits and bounding tails

Abstract

Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this paper we study the statistical efficiency of this approach in light of near-term quantum computing. We propose a more practical variant of the protocol, thrifty shadow estimation, in which quantum circuits are reused many times instead of having to be freshly generated for each measurement. We show that reuse is maximally effective when sampling Haar random unitaries, and maximally ineffective when sampling from the Clifford group, i.e., one should not reuse circuits when performing shadow estimation with the Clifford group. We provide an efficiently simulable family of quantum circuits that interpolates between these extremes, which we believe should be used instead of the Clifford group. Finally, we consider tail bounds for shadow estimation and discuss when median-of-means estimation can be replaced with standard mean estimation.

19 pages, one figure

References in corpus (3)

• Robust randomized benchmarking of quantum processes
• The randomized measurement toolbox
• Performance analysis of multi-shot shadow estimation

Cited by in corpus (17)

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• Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Learning Properties of Quantum States Without the I.I.D. Assumption
• On the connection between least squares, regularization, and classical shadows
• Low variance estimations of many observables with tensor networks and informationally-complete measurements
• Nearly query-optimal classical shadow estimation of unitary channels
• Holographic Classical Shadow Tomography
• Fundamental solutions of heat equation on unitary groups establish an improved relation between $\epsilon$-nets and approximate unitary $t$-designs
• Generalized group designs: constructing novel unitary 2-, 3- and 4-designs
• Classical Shadows with Improved Median-of-Means Estimation
• Optimizing Circuit Reusing and its Application in Randomized Benchmarking
• Optimal randomized measurements for a family of non-linear quantum properties