mlsanityData to 14 Oct 2026

CNOT Minimal Circuit Synthesis: A Reinforcement Learning Approach

arXiv 2510.23304 ↗First posted 27 Oct 2025cs.AIcited by 1

On the map: Deep reinforcement learning methods → Quantum reinforcement learning

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.

Key facts. Cited by 1 paper 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.

Builds on

5 of 32 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning21 May

Other references · 4

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2023qgym: A Gym for Training and Benchmarking RL-Based Quantum Compilationcited by 5
  3. 2024Optimal Layout-Aware CNOT Circuit Synthesis with Qubit Permutationcited by 4
  4. 2023Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorialcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026AlphaClifford: Efficient Clifford Synthesis and Transpilation with Model-based RLcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026AlphaCNOT: Learning CNOT Minimization with Model-Based Planning
  2. 2024A Reinforcement Learning Environment for Directed Quantum Circuit Synthesis
  3. 2025Optimizing Quantum Circuits via ZX Diagrams using Reinforcement Learning and Graph Neural Networks
  4. 2024Reinforcement Learning for Variational Quantum Circuits Design
  5. 2025Hybrid Reward-Driven Reinforcement Learning for Efficient Quantum Circuit Synthesis
  6. 2024Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimization
  7. 2025Minor Embedding for Quantum Annealing with Reinforcement Learning
  8. 2025Reinforcement Learning for Quantum Circuit Design: Using Matrix Representations