Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables

Abstract

Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this work we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose marginals yield noisy (unsharp) versions of the target set of non-commuting Pauli observables. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We compare this strategy to the classical shadow formalism and show that our method yields the same performance as the locally biased classical shadow protocol. We also highlight some general connections between the two approaches by showing that classical shadows can be used to construct joint measurements and vice versa. Finally, we adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy. This can provide significant efficiency improvements compared to known generalisations of classical shadows to noisy scenarios.

14 pages, updated in line with published version

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Cited by in corpus (9)

• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
• Distributed quantum incompatibility
• Robust ultra-shallow shadows
• A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
• Estimating many properties of a quantum state via quantum reservoir processing
• Holographic Classical Shadow Tomography
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• Characterizing errors in parameter estimation by local measurements