Unitary Synthesis of Clifford+T Circuits with Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning-based method using Gumbel AlphaZero to efficiently synthesize Clifford+T quantum circuits for up to five qubits, outperforming existing tools in speed and success rate.

Contribution

It applies a novel tree-search reinforcement learning approach to the challenging problem of Clifford+T unitary synthesis, demonstrating improved performance over prior methods.

Findings

Successfully synthesizes circuits for up to five qubits.

Outperforms existing tools like QuantumCircuitOpt and MIN-T-SYNTH.

Establishes a new baseline for future quantum circuit synthesis algorithms.

Abstract

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 method effectively synthesizes circuits for up to five qubits generated from randomized circuits with up to 60 gates, outperforming existing tools like QuantumCircuitOpt and MIN-T-SYNTH in terms of synthesis time for larger qubit counts. Furthermore, it surpasses Synthetiq in successfully synthesizing random, exactly synthesizable unitaries. These results establish a strong baseline for future unitary synthesis algorithms.