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We study the problem to infer the ground state of a spin-glass Hamiltonianusing data from another Hamiltonian with interactions disturbed by noise fromthe original Hamiltonian, motivated by the ground-state inference in quantumannealing on a noisy device. It is shown that the average Hamming distancebetween the inferred spin configuration and the true ground state is minimizedwhen the temperature of the noisy system is kept at a finite value, and not atzero temperature. We present a spin-glass generalization of a well-establishedresult that the ground state of a purely ferromagnetic Hamiltonian is bestinferred at a finite temperature in the sense of smallest Hamming distance whenthe original ferromagnetic interactions are disturbed by noise. We use thenumerical transfer-matrix method to establish the existence of an optimalfinite temperature in one- and two-dimensional systems. Our numerical resultsare supported by mean-field calculations, which give an explicit expression ofthe optimal temperature to infer the spin-glass ground state as a function ofvariances of the distributions of the original interactions and the noise. Themean-field prediction is in qualitative agreement with numerical data.Implications on postprocessing of quantum annealing on a noisy device arediscussed.

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