Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures

Kohji Nishimura, Hidetoshi Nishimori, Andrew J. Ochoa, Helmut G. Katzgraber

Published 2016-05-11Version 1

We study the problem to infer the ground state of a spin-glass Hamiltonian using data from a Hamiltonian with interactions disturbed by noise, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the ground state is best inferred when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on post-processing of quantum annealing on a noisy device are discussed.