SciPost Physics

SciPost Phys. 14, 094 (2023) · published 4 May 2023

• doi: 10.21468/SciPostPhys.14.5.094
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Ippoliti et al., Learnability Transitions in Monitored Quantum Dynamics via Eavesdropper’s Classical Shadows
  PRX Quantum 5, 020304 (2024) [Crossref]
• Ippoliti et al., Operator Relaxation and the Optimal Depth of Classical Shadows
  Phys. Rev. Lett. 130, 230403 (2023) [Crossref]
• Wu et al., Randomness-Enhanced Expressivity of Quantum Neural Networks
  Phys. Rev. Lett. 132, 010602 (2024) [Crossref]