论文标题
在具有多个局部最小值的连续空间中进行量子和经典退火
Quantum and classical annealing in a continuous space with multiple local minima
论文作者
论文摘要
量子退火方案应用于具有一维连续自由度的优化问题，这是Shinomoto和Kabashima提出的问题的变体。能量景观具有许多局部最小值，并且预计模拟退火的经典方法在对数中的收敛速度会缓慢地收敛到全球最小值。我们通过广泛的数值分析表明，量子退火产生了功率定律收敛，从而对模拟退火进行了指数改进。功率更大，因此收敛速度比现有现象学理论的预测更快。模拟退火的性能显示通过跨能屏障引入准全球搜索，从而增强了幂律的收敛性，但功率比量子案例较小，因此即使在准全球形搜索过程中，经典的收敛速度也较慢。我们还揭示了绝热的量子动态，尤其是量子隧道，通过精心选择退火时间表将系统转向全球最小值。后一个结果明确将隧道在量子退火中的作用与通过模拟退火通过随机优化的经典对应物进行了对比。
The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima, and the classical approach of simulated annealing is predicted to have a logarithmically slow convergence to the global minimum. We show by extensive numerical analyses that quantum annealing yields a power law convergence, thus an exponential improvement over simulated annealing. The power is larger, and thus the convergence is faster, than a prediction by an existing phenomenological theory for this problem. Performance of simulated annealing is shown to be enhanced by introducing quasi-global searches across energy barriers, leading to a power-law convergence but with a smaller power than in the quantum case and thus a slower convergence classically even with quasi-global search processes. We also reveal how diabatic quantum dynamics, quantum tunneling in particular, steers the systems toward the global minimum by a meticulous choice of annealing schedule. This latter result explicitly contrasts the role of tunneling in quantum annealing against the classical counterpart of stochastic optimization by simulated annealing.
