CNOT Minimal Circuit Synthesis: A Reinforcement Learning Approach

Abstract

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 minimisation, remains an open challenge, with its computational complexity yet to be fully characterised. 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 range 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.

References in corpus (9)

• Improved Simulation of Stabilizer Circuits
• A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
• Exact synthesis of multiqubit Clifford+T circuits
• Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits
• T-count optimization and Reed-Muller codes
• Reducing the CNOT count for Clifford+T circuits on NISQ architectures
• Gaussian Elimination versus Greedy Methods for the Synthesis of Linear Reversible Circuits
• Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial
• Decoding techniques applied to the compilation of CNOT circuits for NISQ architectures