Optimizing ZX-Diagrams with Deep Reinforcement Learning
Maximilian Nägele Florian Marquardt
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.