  Efficient quantum compiling tactics greatly enhance the capability of quantum
computers to execute complicated quantum algorithms. Due to its fundamental
importance, a plethora of quantum compilers has been designed in past years.
However, there are several caveats to current protocols, which are low
optimality, high inference time, limited scalability, and lack of universality.
To compensate for these defects, here we devise an efficient and practical
quantum compiler assisted by advanced deep reinforcement learning (RL)
techniques, i.e., data generation, deep Q-learning, and AQ* search. In this
way, our protocol is compatible with various quantum machines and can be used
to compile multi-qubit operators. We systematically evaluate the performance of
our proposal in compiling quantum operators with both inverse-closed and
inverse-free universal basis sets. In the task of single-qubit operator
compiling, our proposal outperforms other RL-based quantum compilers in the
measure of compiling sequence length and inference time. Meanwhile, the output
solution is near-optimal, guaranteed by the Solovay-Kitaev theorem. Notably,
for the inverse-free universal basis set, the achieved sequence length
complexity is comparable with the inverse-based setting and dramatically
advances previous methods. These empirical results contribute to improving the
inverse-free Solovay-Kitaev theorem. In addition, for the first time, we
demonstrate how to leverage RL-based quantum compilers to accomplish two-qubit
operator compiling. The achieved results open an avenue for integrating RL with
quantum compiling to unify efficiency and practicality and thus facilitate the
exploration of quantum advantages.
