Experimental quantum state measurement with classical shadows

TL;DR

This paper experimentally demonstrates the use of classical shadows for efficient quantum state measurement, enabling estimation of multiple properties with fewer measurements on noisy intermediate-scale quantum hardware.

Contribution

It provides the first experimental validation of classical shadows in a realistic setting with noise and finite measurements, including nonlinear functions and entanglement analysis.

Findings

Classical shadows outperform traditional measurement strategies in noisy conditions.

Efficient estimation of multiple observables and nonlinear functions demonstrated.

Entanglement analysis using classical shadows verified on a four-qubit GHZ state.

Abstract

A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], a thrifty scheme showed how to project the quantum state into classical shadows and simultaneously predict $M$ different functions of a state with only $\mathcal{O}(\log_2 M)$ measurements, independent of the system size and saturating the information-theoretical limit. Here, we experimentally explore the feasibility of the scheme in the realistic scenario with a finite number of measurements and noisy operations. We prepare a four-qubit GHZ state and show how to estimate expectation values of multiple observables and Hamiltonians. We compare the measurement strategies with uniform, biased, and derandomized classical shadows to conventional ones that sequentially measure each state function exploiting either importance sampling or observable grouping. We next demonstrate the estimation of nonlinear functions using classical shadows and analyze the entanglement of the prepared quantum state. Our experiment verifies the efficacy of exploiting (derandomized) classical shadows and sheds light on efficient quantum computing with noisy intermediate-scale quantum hardware.