Unitary Synthesis of Clifford+T Circuits with Reinforcement Learning

This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate count, a specific gate count, or a combination of these factors. While past research has focused predominantly on continuous gate sets, synthesizing unitaries from the parameter-free Clifford+T gate set remains a challenge. Although the time complexity of this task will inevitably remain exponential in the number of qubits for general unitaries, reducing the runtime for simple problem instances still poses a significant challenge. In this study, we apply the tree-search method Gumbel AlphaZero to solve the problem for a subset of exactly synthesizable Clifford+T unitaries. Our approach can synthesize unitaries for up to five qubits generated from the set of randomized quantum circuits with up to 60 gates. Furthermore, our inference times are around 30 seconds on a single GPU on average, surpassing state-of-the-art algorithms QuantumCircuitOpt and MIN-T-SYNTH for higher qubit numbers. Our work provides a competitive baseline for synthesis algorithms to be developed in the upcoming years.