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

We propose and analyze a scalable protocol to efficiently extract many physical properties of states prepared in analog quantum simulators. Our protocol leverages the ergodic nature of generic quantum dynamics. The protocol does not require sophisticated controls and can be generically implemented in today's analog quantum simulation platforms. Our protocol involves introducing ancillary degrees of freedom in a predetermined state to a system of interest, quenching the joint system under Hamiltonian dynamics native to the particular experimental platform, and then measuring globally in a single, fixed basis. We show that arbitrary information of the original quantum state is contained within such measurement data, and can be extracted using a classical data-processing procedure. We numerically demonstrate our approach with a number of practical examples, measuring quantities such as the entanglement entropy, many-body Chern number, and superconducting orders, only assuming existing technological capabilities. Our protocol excitingly promises to overcome limited controllability and, thus, enhance the versatility and utility of near-term quantum technologies.