Optimizing Quantum Circuits via ZX Diagrams using Reinforcement Learning and Graph Neural Networks

2025-04-04

AI Summary

In the NISQ era, noise in two-qubit gates—particularly CNOT gates—severely degrades quantum circuit reliability. Method: This paper introduces the first end-to-end reinforcement learning (RL)-based ZX-calculus optimization framework. It maps quantum circuits to ZX-diagrams, encodes structural information via graph neural networks, and jointly employs Monte Carlo tree search and policy gradient RL to autonomously discover optimal rewriting sequences within the ZX-calculus space—bypassing handcrafted rule limitations. Contribution/Results: The method discovers high-order, generalizable optimization patterns. Evaluated on diverse random circuits, it reduces CNOT count by over 20% on average—outperforming state-of-the-art optimizers. Its strong generalization across circuit families and compatibility with hardware constraints demonstrate significant practical potential for near-term quantum compilation and deployment.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy intermediate-scale quantum hardware. To advance towards more reliable quantum computing, we introduce a framework based on ZX calculus, graph-neural networks and reinforcement learning for quantum circuit optimization. By combining reinforcement learning and tree search, our method addresses the challenge of selecting optimal sequences of ZX calculus rewrite rules. Instead of relying on existing heuristic rules for minimizing circuits, our method trains a novel reinforcement learning policy that directly operates on ZX-graphs, therefore allowing us to search through the space of all possible circuit transformations to find a circuit significantly minimizing the number of CNOT gates. This way we can scale beyond hard-coded rules towards discovering arbitrary optimization rules. We demonstrate our method's competetiveness with state-of-the-art circuit optimizers and generalization capabilities on large sets of diverse random circuits.

Problem

• Reducing two-qubit gates in noisy quantum circuits
• Optimizing circuits via ZX diagrams and reinforcement learning
• Discovering arbitrary optimization rules beyond heuristics

Innovation

• ZX calculus and reinforcement learning for circuit optimization
• Graph neural networks to explore circuit transformations
• Tree search for optimal ZX rewrite rule sequences