AlphaClifford: Efficient Clifford Synthesis and Transpilation with Model-based RL

Abstract

Clifford circuits play a foundational role in quantum computing, particularly due to their importance in quantum error correction and fault-tolerant logical synthesis. While these circuits can be efficiently simulated and represented as symplectic matrices, standard synthesis methods-such as the Aaronson-Gottesman algorithm-often yield sub-optimal circuits with excessively high gate counts. In this work, we introduce AlphaClifford, a model-based Reinforcement Learning framework powered by Monte Carlo Tree Search, designed to efficiently synthesize Clifford circuits from the fundamental gate set composed of H, S, and CNOT. By modeling the state space through the algebraic properties of the symplectic group, AlphaClifford effectively explores this combinatorial space to minimize overall circuit cost. For unconstrained Clifford optimization, our approach achieves a consistent reduction in both total and two-qubit (CNOT) gate counts compared to state-of-the-art synthesis heuristics, despite operating with a strictly less expressive gate set. Furthermore, we demonstrate the broad applicability of our framework on two additional tasks: hardware-constrained Clifford transpilation, where we outperform existing RL-based compilers, and as a post-synthesis optimization component within a full Clifford+T logical synthesis pipeline. Our results underscore that model-based RL is highly effective at addressing the combinatorial complexities of quantum compilation, offering a scalable pathway to mitigate hardware constraints in both near-term and future fault-tolerant quantum devices.