Reinforcement Learning Based Quantum Circuit Optimization via ZX-Calculus

TL;DR

This paper introduces a reinforcement learning approach using graph neural networks to optimize quantum circuits with ZX-calculus, achieving state-of-the-art results on various circuit sizes and types, and demonstrating adaptability to different optimization goals.

Contribution

It presents a novel RL method employing GNNs and ZX-calculus rules for quantum circuit optimization, outperforming existing algorithms and adaptable to diverse circuit structures.

Findings

Improves state-of-the-art for small Clifford+T circuits up to 80 qubits.

Maintains competitive computational performance on large circuits.

Enhances two-qubit gate count reduction on diverse quantum circuits.

Abstract

We propose a novel Reinforcement Learning (RL) method for optimizing quantum circuits using graph-theoretic simplification rules of ZX-diagrams. The agent, trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph Neural Networks to approximate the policy and value functions. We demonstrate the capacity of our approach by comparing it against the best performing ZX-Calculus-based algorithm for the problem in hand. After training on small Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently improves the state-of-the-art for this type of circuits, for at least up to 80-qubit and 2100 gates, whilst remaining competitive in terms of computational performance. Additionally, we illustrate the versatility of the agent by incorporating additional optimization routines on the workflow during training, improving the two-qubit gate count state-of-the-art on multiple structured quantum circuits for relevant applications of much larger dimension and different gate distributions than the circuits the agent trains on. This conveys the potential of tailoring the reward function to the specific characteristics of each application and hardware backend. Our approach is a valuable tool for the implementation of quantum algorithms in the near-term intermediate-scale range (NISQ).