  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.
