Optimizing ZX-Diagrams with Deep Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning approach using graph neural networks to optimize ZX-diagrams, significantly outperforming traditional methods and enabling generalization to larger diagrams.

Contribution

It presents a novel application of deep reinforcement learning with graph neural networks for ZX-diagram optimization, surpassing existing techniques.

Findings

RL agent outperforms greedy, simulated annealing, and hand-crafted algorithms

Graph neural networks enable generalization to larger diagrams

Reinforcement learning significantly improves optimization quality

Abstract

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, simulated annealing, and state-of-the-art hand-crafted algorithms. 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.