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

TL;DR

This paper investigates how finite-temperature effects can improve the inference of ground states in noisy spin-glass systems, with implications for quantum annealing performance on imperfect hardware.

Contribution

It demonstrates that an optimal finite temperature exists for ground state inference in noisy spin glasses, supported by numerical and mean-field analyses.

Findings

Optimal finite temperature minimizes Hamming distance to ground state.

Numerical transfer-matrix method confirms the existence of this temperature.

Mean-field calculations provide explicit expression for the optimal temperature.

Abstract

We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized 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 in the sense of smallest Hamming distance 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 postprocessing of quantum annealing on a noisy device are discussed.