Mean Field Analysis of Quantum Annealing Correction.
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=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.
Niels Bohr International Academy and Center for Quantum Devices, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark.|Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan.
Shunji
S
Matsuura
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan.
Hidetoshi
H
Nishimori
Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA.|Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.|Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA.
Tameem
T
Albash
Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.|Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA.|Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA.|Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA.
Daniel A
DA
Lidar