Optimizing ZX-Diagrams with Deep Reinforcement Learning

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.

9 pages, 4 figures - Revision 1 on 26.04.2024: Fixed bug in training algorithm to give quantitatively better results (qualitative results unchanged) - Revision 2 on 30.09.2024: Added comparison to PyZX algorithm and extended the explanation of GNNs and ZX-calculus

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Cited by in corpus (5)

• Reinforcement Learning Based Quantum Circuit Optimization via ZX-Calculus
• Procedurally Optimised ZX-Diagram Cutting for Efficient T-Decomposition in Classical Simulation
• Meta-Designing Quantum Experiments with Language Models
• Optimising entanglement distribution policies under classical communication constraints assisted by reinforcement learning
• Fast Classical Simulation of Quantum Circuits via Parametric Rewriting in the ZX-Calculus