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.

翻译：CNOT门是量子计算的基础，它们促进了量子算法关键资源——纠缠的产生。某些类别的量子电路完全由CNOT门构成。鉴于其广泛应用，最小化所用CNOT门的数量至关重要。这一被称为CNOT最小化的问题仍是一个开放挑战，其计算复杂性尚未完全明确。在本研究中，我们提出了一种新颖的强化学习方法来应对这一任务。我们使用单个智能体处理固定尺寸$m$以内的电路，而非针对不同电路尺寸训练多个强化学习智能体。对于尺寸不等于m的矩阵，我们采用嵌入或高斯条纹化进行预处理。为评估方法的有效性，我们训练了m = 8的智能体，并在尺寸n为3至15的矩阵上进行了测试。结果表明，随着n值的增加，我们的方法性能超越了当前最先进的算法。