Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. This setup requires the addressed problems to be formatted as discrete quadratic functions without constraints and the variables to take binary values only. The problem of finding Nash equilibrium in two-player, non-cooperative games is a two-fold quadratic optimization problem with constraints. This problem was formatted as a single, constrained quadratic optimization in 1964 by Mangasarian and Stone. Here, we show that adding penalty terms to the quadratic function formulation of Nash equilibrium gives a quadratic unconstrained binary optimization (QUBO) formulation of this problem that can be executed on quantum annealers. Three examples are discussed to highlight the success of the formulation, and an overall, time-to-solution (hardware + software processing) speed up of seven to ten times is reported on quantum annealers developed by D-Wave System.
翻译:使用量子anneal 算法的精度来对专门硬件进行半径量量计算。 这种设置要求将所处理的问题格式化为无限制的离散二次函数和变量格式化, 只能使用二进制值。 在两个玩家、 不合作的游戏中找到 Nash 平衡的问题是一个有限制的双倍二次优化问题。 这个问题在1964年由Mangasian 和 Stone 形成为单一的、 受限制的二次优化。 在这里, 我们显示在纳什平衡的二次函数配方中添加惩罚条款, 给这个问题的二次二次优化配方提供了一种不受限制的二次优化( QUBO ), 可以在量子肾上执行 。 三个例子被讨论, 以突出配方的成功性, 整个时间到溶解( 硬软件处理) 速度高达七到十倍。 在D- Wave 系统开发的量子脉冲器上报告。