CNOT Minimal Circuit Synthesis: A Reinforcement Learning Approach

CNOT gates are fundamental to quantum computing, as they facilitate entanglement, a crucial resource for quantum algorithms. Certain classes of quantum circuits are constructed exclusively from CNOT gates. Given their widespread use, it is imperative to minimise the number of CNOT gates employed. This problem, known as CNOT minimization, remains an open challenge, with its computational complexity yet to be fully characterized. In this work, we introduce a novel reinforcement learning approach to address this task. Instead of training multiple reinforcement learning agents for different circuit sizes, we use a single agent up to a fixed size m. Matrices of sizes different from m are preprocessed using either embedding or Gaussian striping. To assess the efficacy of our approach we trained an agent with m=8, and evaluated it on matrices of size n that ranges from 3 to 15. The results we obtained show that our method overperforms the state of the art algorithm as the value of n increases.