论文标题
矩阵乘法更新量子零和游戏中的更新：保护法律与复发
Matrix Multiplicative Weights Updates in Quantum Zero-Sum Games: Conservation Laws & Recurrence
论文作者
论文摘要
量子计算，尤其是量子gan的最新进展，导致对量子零和游戏理论的兴趣增加，从而将学习算法的范围扩展到了古典游戏的范围中。在本文中，我们专注于在矩阵乘法权重更新（乘法权重更新方法的概括）及其连续的模拟量子复制器动力学下的量子零和游戏中学习。当每个玩家根据量子复制器动力学选择其状态时，我们表明该系统以量子信息理论意义表现出保护定律。此外，我们表明该系统表现出繁殖性的复发，这意味着几乎所有轨道都会随意返回其最初的条件。我们的分析在古典游戏中概括了先前的结果。
Recent advances in quantum computing and in particular, the introduction of quantum GANs, have led to increased interest in quantum zero-sum game theory, extending the scope of learning algorithms for classical games into the quantum realm. In this paper, we focus on learning in quantum zero-sum games under Matrix Multiplicative Weights Update (a generalization of the multiplicative weights update method) and its continuous analogue, Quantum Replicator Dynamics. When each player selects their state according to quantum replicator dynamics, we show that the system exhibits conservation laws in a quantum-information theoretic sense. Moreover, we show that the system exhibits Poincare recurrence, meaning that almost all orbits return arbitrarily close to their initial conditions infinitely often. Our analysis generalizes previous results in the case of classical games.
