# CNOT Minimal Circuit Synthesis: A Reinforcement Learning Approach

arXiv: https://arxiv.org/abs/2510.23304 · HTML: https://mlsanity.com/paper/2510.23304/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 5 of 5)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning](https://mlsanity.com/paper/2405.13196/) (2024)
- [qgym: A Gym for Training and Benchmarking RL-Based Quantum Compilation](https://mlsanity.com/paper/2308.02536/) (2023)
- [Optimal Layout-Aware CNOT Circuit Synthesis with Qubit Permutation](https://mlsanity.com/paper/2408.04349/) (2024)
- [Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial](https://mlsanity.com/paper/2309.11793/) (2023)

## Built on by (most cited first, 1 of 1)

- [AlphaClifford: Efficient Clifford Synthesis and Transpilation with Model-based RL](https://mlsanity.com/paper/2608.18946/) (2026)

## Abstract (arXiv)

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.