Adaptive randomized Pauli measurement

Quantum simulators and computers are powerful platforms for investigating the physics of strongly-correlated quantum systems. To fully utilize their potential, however, one needs to efficiently extract physically relevant features from the simulated many-body states. Here, we propose such an adaptive randomized measurement protocol. Instead of performing fully randomized measurements, our approach adaptively changes its measurement basis at each step, based on Bayesian inference of prior measurement outcomes. We demonstrate the utility of our protocol by applying it to spontaneously symmetry breaking and symmetry-protected topological (SPT) phases, from which we successfully extract the classifying observables such as order parameters and SPT invariants, and to learning stabilizer states. These establish a practical, physics-oriented protocol, which can potentially lead to new scientific discoveries in near-term quantum simulations of strongly-correlated many-body systems.