Measuring Arbitrary Physical Properties in Analog Quantum Simulation: Ancilla-Assisted Classical Shadow Tomography

Extracting physical properties that are not directly accessible from the standard measurement basis is one of the central challenges in existing analog quantum simulation platforms. Here, we propose and analyze a novel approach to efficiently extract many physical properties without having to apply sophisticated controls. Our protocol simply involves introducing ancillary degrees of freedom in a predetermined state and evolving the joint system under its natural dynamics. Since quantum many-body dynamics is generally ergodic in nature, a subsequent measurement of the joint system in the fixed, standard basis amounts to an effective random-basis measurement on the original system, from which nontrivial properties can be extracted via classical data processing. Under certain conditions, our method approaches an information-theoretically optimal method called classical shadow tomography. We numerically demonstrate our protocol in systems of spins and itinerant particles, and extract quantities such as the entanglement entropy and many-body Chern number which are otherwise difficult to measure. Our protocol constitutes an example in which the ergodicity of quantum dynamics — a ubiquitous feature of nature — is leveraged as a resource, enabling a quantum application.