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On Classical and Hybrid Shadows of Quantum States

by Saumya Shivam, C. W. von Keyserlingk, S. L. Sondhi

Submission summary

As Contributors: Saumya Shivam
Arxiv Link: https://arxiv.org/abs/2206.06616v1 (pdf)
Date submitted: 2022-06-15 02:34
Submitted by: Shivam, Saumya
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approaches: Theoretical, Computational

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.

Current status:
Editor-in-charge assigned


Submission & Refereeing History

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Submission 2206.06616v1 on 15 June 2022

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