Title: Efficient learning of extensive observables of quantum states

 

Abstract: Estimating the physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions under which it is possible to infer the expectation value of all quasi-local observables of a state up to a relative error from a number of samples that scales polylogarithmically in system size and polynomially in the locality of the target observables. This constitutes an exponential improvement over known tomography methods in some regimes. We achieve our results by combining one of the most well-established techniques to learn quantum states, the maximum entropy method, with techniques from the emerging field of quantum optimal transport. We conjecture that our condition holds for all states exhibiting exponential decay of correlations and establish it for several subsets thereof. These include widely studied classes of states such as one-dimensional Gibbs and gapped ground states and high-temperature Gibbs states in any dimension.  Moreover, we show improvements of the maximum entropy method beyond the sample complexity of independent interest. These include identifying regimes in which it is possible to perform the postprocessing efficiently and novel bounds on the condition number of covariance matrices of many-body states.

 

This is joint work with Cambyse Rouzé (TU Munich).

 

Meeting ID: 985 1551 2137

Passcode: 436965