Matsuura Shunji, Nishimori Hidetoshi, Albash Tameem, Lidar Daniel A
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.
Phys Rev Lett. 2016 Jun 3;116(22):220501. doi: 10.1103/PhysRevLett.116.220501. Epub 2016 Jun 1.
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.
量子退火校正（QAC）是一种将编码与能量惩罚以及解码相结合的方法，用于抑制和纠正那些在求解优化问题时会降低量子退火器性能的错误。虽然QAC已通过实验证明能成功地对一系列优化问题进行纠错，但对其运行机制仍缺乏清晰的理解。在此，我们用量子统计力学的工具填补这一空白。我们使用平均场分析研究易于解析处理的模型，特别是p体铁磁无限程横向场伊辛模型以及量子霍普菲尔德模型。我们证明，对于p = 2（此时相变是二阶的），QAC将相变推向越来越大的横向场强度。对于p≥3（此时相变是一阶的），QAC会软化小能量惩罚值下能隙的闭合，并在能量惩罚值足够大时防止其闭合。因此，QAC可保护免受量子临界点附近出现的激发影响。我们在霍普菲尔德模型中也发现了类似结果，从而表明我们的结论在存在无序的情况下也成立。
