Shadow tomography from emergent state designs in analog quantum simulators

TL;DR

This paper presents a global-control-based shadow tomography method for analog quantum simulators, leveraging emergent state designs in chaotic systems to efficiently infer many properties of quantum states, including nonlinear functions.

Contribution

It introduces a novel protocol that uses global unitaries and measurements to perform shadow tomography, suitable for analog quantum simulators, and connects emergent state designs to property inference.

Findings

Protocol enables inference of nonlinear functions like Renyi entropies.

Achieves the same efficiency as classical shadow tomography with only global operations.

Applicable to ultracold atoms and Rydberg atom arrays.

Abstract

We introduce a method that allows one to infer many properties of a quantum state -- including nonlinear functions such as R\'enyi entropies -- using only global control over the constituent degrees of freedom. In this protocol, the state of interest is first entangled with a set of ancillas under a fixed global unitary, before projective measurements are made. We show that when the unitary is sufficiently entangling, a universal relationship between the statistics of the measurement outcomes and properties of the state emerges, which can be connected to the recently discovered phenomenon of emergent quantum state designs in chaotic systems. Thanks to this relationship, arbitrary observables can be reconstructed using the same number of experimental repetitions that would be required in classical shadow tomography [Huang et al., Nat. Phys. 16, 1050 (2020)]. Unlike previous approaches to shadow tomography, our protocol can be implemented using only global operations, as opposed to qubit-selective logic gates, which makes it particularly well-suited to analog quantum simulators, including ultracold atoms in optical lattices and arrays of Rydberg atoms.