# Qubit Routing using Graph Neural Network aided Monte Carlo Tree Search

arXiv: https://arxiv.org/abs/2104.01992 · HTML: https://mlsanity.com/paper/2104.01992/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 1 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Ranked Reward: Enabling Self-Play Reinforcement Learning for Combinatorial Optimization](https://mlsanity.com/paper/1807.01672/) (2018)
- [Solving NP-Hard Problems on Graphs with Extended AlphaGo Zero](https://mlsanity.com/paper/1905.11623/) (2019)
- [On the qubit routing problem](https://mlsanity.com/paper/1902.08091/) (2019)
- [Learning Self-Game-Play Agents for Combinatorial Optimization Problems](https://mlsanity.com/paper/1903.03674/) (2019)
- [Circuit Transformations for Quantum Architectures](https://mlsanity.com/paper/1902.09102/) (2019)
- [Optimization of Quantum Circuit Mapping using Gate Transformation and Commutation](https://mlsanity.com/paper/1907.02686/) (2019)
- [Monte Carlo Tree Search for Asymmetric Trees](https://mlsanity.com/paper/1805.09218/) (2018)

## Built on by (most cited first, 9 of 9)

- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [Beyond Games: A Systematic Review of Neural Monte Carlo Tree Search Applications](https://mlsanity.com/paper/2303.08060/) (2023)
- [Quarl: A Learning-Based Quantum Circuit Optimizer](https://mlsanity.com/paper/2307.10120/) (2023)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Search](https://mlsanity.com/paper/2410.05115/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Alpha Elimination: Using Deep Reinforcement Learning to Reduce Fill-In during Sparse Matrix Decomposition](https://mlsanity.com/paper/2310.09852/) (2023)
- [Shuttling Compiler for Trapped-Ion Quantum Computers Based on Fine-Tuned Large Language Models](https://mlsanity.com/paper/2512.18021/) (2025)
- [QAP-Router: Tackling Qubit Routing as Dynamic Quadratic Assignment with Reinforcement Learning](https://mlsanity.com/paper/2605.12365/) (2026)

## Abstract (arXiv)

Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing, i.e., to transform the quantum circuit either by inserting additional SWAP gates or by reversing existing CNOT gates to satisfy the connectivity constraints of the target topology. We propose a procedure for qubit routing that is architecture agnostic and that outperforms other available routing implementations on various circuit benchmarks. The depth of the transformed quantum circuits is minimised by utilizing the Monte Carlo tree search to perform qubit routing, aided by a Graph neural network that evaluates the value function and action probabilities for each state.