Experimental quantum state measurement with classical shadows

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.

20 pages, 13 figures, 2 tables

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• Shadow process tomography of quantum channels
• Overlapped grouping measurement: A unified framework for measuring quantum states
• Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
• Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
• Classical shadows with Pauli-invariant unitary ensembles
• Analysing quantum systems with randomised measurements
• Closed-form analytic expressions for shadow estimation with brickwork circuits
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Low-depth Hamiltonian Simulation by Adaptive Product Formula
• Towards a variational Jordan-Lee-Preskill quantum algorithm
• Machine learning on quantum experimental data toward solving quantum many-body problems
• Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity
• Enhanced estimation of quantum properties with common randomized measurements
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Quantification of Entanglement and Coherence with Purity Detection
• Efficient Characterizations of Multiphoton States with an Ultra-thin Optical Device
• Collective randomized measurements in quantum information processing
• Measurement optimization of variational quantum simulation by classical shadow and derandomization
• Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
• Neural-Shadow Quantum State Tomography
• Optimising quantum tomography via shadow inversion
• Stability of classical shadows under gate-dependent noise
• Quantum algorithms for generator coordinate methods
• Quantum reservoir computing for photonic entanglement witnessing
• Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
• Measuring energy by measuring any other observable
• Experimental Examination of Entanglement Estimates
• The topology of data hides in quantum thermal states
• Experimental investigation of quantum uncertainty relations with classical shadows
• Experimental distillation of tripartite quantum steering with an optimal local filtering operation
• Classical shadows meet quantum optimal mass transport
• Estimating many properties of a quantum state via quantum reservoir processing
• On the connection between least squares, regularization, and classical shadows
• Holographic Classical Shadow Tomography
• Tomography of parametrized quantum states
• Quantum speed limit for the OTOC from an open systems perspective
• The tightness of multipartite coherence from spectrum estimation
• The Efficiency Frontier: Classical Shadows versus Direct Quantum Measurement
• Entropy density benchmarking of near-term quantum circuits
• Classical Shadows with Improved Median-of-Means Estimation