ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum process they describe. These rules can be exploited to optimize the structure of ZX-diagrams for a range of applications. However, finding an optimal sequence of transformation rules is generally an open problem. In this work, we bring together ZX-diagrams with reinforcement learning, a machine learning technique designed to discover an optimal sequence of actions in a decision-making problem and show that a trained reinforcement learning agent can significantly outperform other optimization techniques like a greedy strategy or simulated annealing. The use of graph neural networks to encode the policy of the agent enables generalization to diagrams much bigger than seen during the training phase.

翻译：ZX图是一种强大的图形化语言，用于描述量子过程，在基础量子力学、量子电路优化、张量网络模拟等领域具有广泛应用。ZX图的实用性依赖于一组局部变换规则，这些规则可在不改变所描述的底层量子过程的前提下应用于该图。利用这些规则可以针对多种应用场景优化ZX图结构。然而，寻找最优的变换规则序列通常是一个开放性问题。在本工作中，我们将ZX图与强化学习（一种旨在决策问题中发现最优动作序列的机器学习技术）相结合，并证明经过训练的强化学习智能体能够显著优于其他优化技术（如贪心策略或模拟退火）。通过使用图神经网络编码智能体的策略，实现了对远大于训练阶段所见图规模的泛化能力。