On Classical and Hybrid Shadows of Quantum States

Abstract

Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In this note we offer some comments on this approach. We note that the resources needed to form classical shadows with bounded relative error depend strongly on the target state. We then comment on the advantages and limitations of using classical shadows to simulate many-body dynamics. In addition, we introduce the notion of a hybrid shadow, constructed from measurements on a part of the system instead of the entirety, which provides a framework to gain more insight into the nature of shadow states as one reduces the size of the subsystem measured, and a potential alternative to compressing quantum states.

8+3 pages, 4+1 figures

References in corpus (2)

• The randomized measurement toolbox
• An approximate description of quantum states

Cited by in corpus (7)

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• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
• Randomness-enhanced expressivity of quantum neural networks
• Efficient Local Classical Shadow Tomography with Number Conservation
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• Tomography of parametrized quantum states
• Classical Shadows with Improved Median-of-Means Estimation