Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning ∗

Abstract Efficient quantum compiling is essential for complex quantum algorithms realization. The Solovay–Kitaev (S–K) theorem offers a theoretical lower bound on the required operations for approaching any unitary operator. However, it is still an open question that this lower bound can be actually reached in practice. Here, we present an efficient quantum compiler which, for the first time, approaches the S–K lower bound in practical implementations, both for single-qubit and two-qubit scenarios, marking a significant milestone. Our compiler leverages deep reinforcement learning (RL) techniques to address current limitations in terms of optimality and inference time. Furthermore, we show that our compiler is versatile by demonstrating comparable performance between inverse-free basis sets, which is always the case in real quantum devices, and inverse-closed sets. Our findings also emphasize the often-neglected constant term in scaling laws, bridging the gap between theory and practice in quantum compiling. These results highlight the potential of RL-based quantum compilers, offering efficiency and practicality while contributing novel insights to quantum compiling theory.