Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary.
PLoS One. 2022 Aug 30;17(8):e0273709. doi: 10.1371/journal.pone.0273709. eCollection 2022.
The Quadratic Unconstrained Binary Optimization (QUBO) problem is NP-hard. Some exact methods like the Branch-and-Bound algorithm are suitable for small problems. Some approximations like stochastic simulated annealing for discrete variables or mean-field annealing for continuous variables exist for larger ones, and quantum computers based on the quantum adiabatic annealing principle have also been developed. Here we show that the mean-field approximation of the quantum adiabatic annealing leads to equations similar to those of thermal mean-field annealing. However, a new type of sigmoid function replaces the thermal one. The new mean-field quantum adiabatic annealing can replicate the best-known cut values on some of the popular benchmark Maximum Cut problems.
二次无约束二进制优化 (QUBO) 问题是 NP 难的。一些精确方法，如分支定界算法，适用于小问题。对于较大的问题，存在一些近似方法，如用于离散变量的随机模拟退火或用于连续变量的平均场退火，并且已经开发出基于量子绝热退火原理的量子计算机。在这里，我们表明量子绝热退火的平均场近似导致与热平均场退火相似的方程。然而，一种新的 Sigmoid 函数取代了热函数。新的平均场量子绝热退火可以复制一些流行的最大切割基准问题上的最佳切割值。
