Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and
decoding to suppress and correct errors that degrade the performance of quantum annealers in solving
optimization problems. While QAC has been experimentally demonstrated to successfully error correct a
range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here
we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models
using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising
model as well as the quantum Hopfield model. We demonstrate that for p ¼ 2, where the phase transition is
of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p ≥ 3,
where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty
values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection
from excitations that occur near the quantum critical point. We find similar results for the Hopfield model,
thus demonstrating that our conclusions hold in the presence of disorder
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