Learning to Synthesize Fault-Tolerant Quantum Circuits by Diagonalization

Compilation of quantum programs into circuits expressed with discrete gate sets is essential for fault-tolerant quantum computing. Optimal methods for discovering high-precision implementations of unitaries in discrete gate sets such as the Clifford+T gate set are intractable. Search-based synthesis methods, including Reinforcement Learning (RL) and simulated annealing, are promising as they empirically discover efficient implementations of low-depth unitaries. We leverage search-based methods to reduce the general unitary synthesis problem to one of synthesizing diagonal unitaries; a problem solvable efficiently in general and optimally in the single-qubit case. Relying on several improvements in deep learning architectures essential for quantum datasets, our RL-based approach demonstrates how search-based methods and mathematical decompositions can be combined to efficiently find high precision implementations of unitaries taken from an array of real quantum algorithms. On these benchmarks we observe up to an average of 94% fewer non-Clifford gates compared to the Quantum Shannon Decomposition.