论文标题
使用量子交替的操作员Ansatz在离散的Rosenthal拥塞游戏中找到最佳的NASH平衡
Finding the optimal Nash equilibrium in a discrete Rosenthal congestion game using the Quantum Alternating Operator Ansatz
论文作者
论文摘要
本文确定了使用栅极模型量子计算机找到离散拥塞游戏的最佳NASH平衡以及最佳社会解决方案的障碍。该游戏是Rosenthal在1970年代最初提出的类型。为了找到最佳的NASH平衡，我们根据潜在功能和路径选择约束来制定一个优化问题，并使用量子交替的操作员ANSATZ解决它。我们将此公式与其前身量子近似优化算法进行比较。我们将解决方案在栅极模型量子计算机的理想化模拟器上实现，并在小型两人游戏中演示障碍性。这项工作为将来的努力提供了基础，以将量子近似优化应用于量子机学习问题，例如使用潜在功能对生成对抗网络进行有效培训。
This paper establishes the tractability of finding the optimal Nash equilibrium, as well as the optimal social solution, to a discrete congestion game using a gate-model quantum computer. The game is of the type originally posited by Rosenthal in the 1970's. To find the optimal Nash equilibrium, we formulate an optimization problem encoding based on potential functions and path selection constraints, and solve it using the Quantum Alternating Operator Ansatz. We compare this formulation to its predecessor, the Quantum Approximate Optimization Algorithm. We implement our solution on an idealized simulator of a gate-model quantum computer, and demonstrate tractability on a small two-player game. This work provides the basis for future endeavors to apply quantum approximate optimization to quantum machine learning problems, such as the efficient training of generative adversarial networks using potential functions.
