Inverse inference of a quantum spin glass

Abstract

In statistical physics, inverse problems arise when we need to design a manybody system with particular desired properties. Rather than calculating observables based on known model parameters, inverse problems involve inferring the parameters of a model based on observations. In my final degree project, we studied the inverse problem for the Viana-Bray spin glass model with a discrete distribution of the couplings, and with simulated annealing, we tried to infer the couplings of the system with the maximum pseudolikelihood method. In this project, we studied the inverse problem for the quantum Viana-Bray spin glass model with the same coupling distribution. The goal was to extend the pseudolikelihood maximization approach to a quantum spin glass with a transverse field since most research efforts have focused on the classical version and hardly anything is known about its quantum counterpart. To achieve this, we generated equilibrium configurations from the quantum partition function using quantum Monte Carlo techniques, and then we employed simulated annealing to maximize the pseudolikelihood function and infer the couplings of the system. We derived a modified version of the pseudolikelihood function from the initial proposal after closely following the approach used in the classical case. We found that when introducing the transverse field in the system, the algorithm was still able to infer the couplings; however, because of how the quantum system is treated, certain modifications had to be made to the pseudolikelihood method. Moreover, as in the classical case, we found that the algorithm performed the best around the phase transition boundaries.