Predicting Arbitrary State Properties from Single Hamiltonian Quench Dynamics*

Extracting arbitrary state properties from analog quantum simulations presents a significant challenge due to the necessity of diverse basis measurements. Recent advancements in randomized measurement schemes have successfully reduced measurement sample complexity, yet they demand precise control over each qubit. In this work, we propose the Hamiltonian shadow protocol, which solely depends on quench dynamics with a single Hamiltonian, without any ancillary systems. We provide a theoretical guarantee that our protocol can unbiasedly predict arbitrary state properties. We also derive the sample complexity of this protocol and show it performs similarly to the classical shadow protocol. Hamiltonian shadow protocol does not require any sophisticated control and is universally applicable to various analog quantum systems, as illustrated through numerical demonstrations with Rydberg atom arrays under realistic parameter settings. The new protocol significantly broadens the application of randomized measurements for analog quantum simulators without precise control and ancillary systems.