Journal Article Mean field analysis of quantum error correction

西森, 秀稔  ,  NISHIMORI, HIDETOSHI  ,  Matsuura, Shunji  ,  Albash, Tameem  ,  Lidar, Daniel

1152016-06 , American Physical Society
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties anddecoding to suppress and correct errors that degrade the performance of quantum annealers in solvingoptimization problems. While QAC has been experimentally demonstrated to successfully error correct arange of optimization problems, a clear understanding of its operating mechanism has been lacking. Herewe bridge this gap using tools from quantum statistical mechanics. We study analytically tractable modelsusing a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Isingmodel as well as the quantum Hopfield model. We demonstrate that for p ¼ 2, where the phase transition isof 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 penaltyvalues and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protectionfrom 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

Number of accesses :  

Other information