论文标题
封闭和开放系统的模拟量子退火的收敛条件
Convergence condition of simulated quantum annealing for closed and open systems
论文作者
论文摘要
模拟量子退火是一种通用的经典协议，用于模拟量子退火的某些方面，有时被视为量子退火的经典替代方案，可以找到经典的Ising模型的基态。我们得出了模拟量子退火的通用条件，以在给定的（通常较低的温度）下收敛到热平衡。封闭式和开放系统都得到处理。我们将模拟量子退火的经典主方程重写为假想的时间schrödinger方程，我们将其应用于渐近绝热条件的假想时间变体来推断收敛条件。该结果与封闭系统的模拟量子退火的严格合并条件有质疑，该系统源自不均匀的马尔可夫过程理论。还观察到的是定性一致性，在实时Schrödinger动力学下，封闭系统的量子退火的严格合并条件。用于模拟量子退火的经典随机过程和用于量子退火的实时量子动力学的收敛条件的这种巧合是高度非平凡的，需要进行进一步的审查。
Simulated quantum annealing is a generic classical protocol to simulate some aspects of quantum annealing and is sometimes regarded as a classical alternative to quantum annealing in finding the ground state of a classical Ising model. We derive a generic condition for simulated quantum annealing to converge to thermal equilibrium at a given, typically low, temperature. Both closed and open systems are treated. We rewrite the classical master equation for simulated quantum annealing into an imaginary-time Schrödinger equation, to which we apply the imaginary-time variant of asymptotic adiabatic condition to deduce the convergence condition. The result agrees qualitatively with a rigorous convergence condition of simulated quantum annealing for closed systems, which was derived from the theory of inhomogeneous Markov process. Also observed is qualitative agreement with a rigorous convergence condition of quantum annealing for closed systems under the real-time Schrödinger dynamics. This coincidence of convergence conditions for classical stochastic processes for simulated quantum annealing and the real-time quantum dynamics for quantum annealing is highly non-trivial and calls for further scrutiny.
