On Classical and Hybrid Shadows of Quantum States

TL;DR

This paper discusses classical shadows for quantum states, highlighting their resource dependence, limitations in simulating many-body dynamics, and introduces hybrid shadows as a new approach for partial system measurements.

Contribution

It provides insights into resource requirements for classical shadows, analyzes their limitations, and proposes hybrid shadows as a novel method for partial quantum state measurement.

Findings

Resource needs depend on target state complexity.

Classical shadows have limitations in simulating dynamics.

Hybrid shadows offer a new perspective for partial measurements.

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.