Theory Seminar: Efficient learning of thermal phases of matter
Cambyse Rouzé, TUM
Theory Seminar at MPQ lecture hall & Zoom
Wednesday, February 22nd, 11:30am (MEZ)
In this talk, we will consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of extensive, linear and non-linear observables; and (b) learning the expectation values of local observables within a thermal phase of matter. In both cases, we wish to minimise the number of samples we use to learn these properties to a given precision. For the first task, we develop new techniques to learn parameterisations of classes of systems, including quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations and the approximate Markov property. We show it is possible to infer the expectation values of all extensive properties of the state from a number of copies that not only scales polylogarithmically with the system size, but polynomially in the observable's locality -- an exponential improvement over previous methods. For the second task, we develop efficient algorithms for learning observables in a thermal phase of matter of a quantum system. By exploiting the locality of the Hamiltonian, we show that sums of local observables can be learned with high probability using a number of samples that scales logarithmically with the size of the system, and quasi-polynomially with the required precision. In addition, our sample complexity applies to the worse case setting in contrast with standard machine learning techniques. This is based on joint work (arXiv:2301.12946) with Emilio Onorati (TUM), Daniel Stilck Franca (ENS Lyon) and James Watson (Maryland).