Exact Unitary Synthesis with AlphaZero

Unitary synthesis translates a target unitary transformation into a quantum circuit – a sequence of quantum gates. This process is crucial for implementing algorithms with reduced circuit depth and minimal use of costly gates, such as T gates. However, developing efficient and systematic methods for the exact decomposition of unitary matrices into quantum circuits remains a challenge. In this talk, we present an AlphaZero-inspired reinforcement learning approach, based on Monte Carlo tree-search guided by a deep neural network, to achieve exact unitary synthesis with sets of discrete gates. Testing our approach across various gate sets and architectures demonstrates its strong performance in unitary synthesis, circuit simplification, and low inference times. Enabled by the flexibility of our method, we explore new quantum circuit architectures and gate sets. In particular, focusing on an architecture of three qubits coupled to a classically-controlled ancilla, we discover a new 4 T gates implementation of the Toffoli gate. We expect this approach to enable more efficient implementation of quantum algorithms, particularly in exotic quantum computing architectures.