# Topological Quantum Compiling with Reinforcement Learning

arXiv: https://arxiv.org/abs/2004.04743 · HTML: https://mlsanity.com/paper/2004.04743/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2020.

## Built on by (most cited first, 23 of 23)

- [Quantum circuit synthesis with diffusion models](https://mlsanity.com/paper/2311.02041/) (2023)
- [Universal Adversarial Examples and Perturbations for Quantum Classifiers](https://mlsanity.com/paper/2102.07788/) (2021)
- [Variational quantum compiling with double Q-learning](https://mlsanity.com/paper/2103.11611/) (2021)
- [Challenges for Reinforcement Learning in Quantum Circuit Design](https://mlsanity.com/paper/2312.11337/) (2023)
- [Reinforcement Learning for Variational Quantum Circuits Design](https://mlsanity.com/paper/2409.05475/) (2024)
- [Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning](https://mlsanity.com/paper/2204.06904/) (2022)
- [Entropy Regularized Reinforcement Learning Using Large Deviation Theory](https://mlsanity.com/paper/2106.03931/) (2021)
- [Towards Learning Foundation Models for Heuristic Functions to Solve Pathfinding Problems](https://mlsanity.com/paper/2406.02598/) (2024)
- [Quantum Compiling with Reinforcement Learning on a Superconducting Processor](https://mlsanity.com/paper/2406.12195/) (2024)
- [Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation](https://mlsanity.com/paper/2405.08100/) (2024)
- [A* Search Without Expansions: Learning Heuristic Functions with Deep Q-Networks](https://mlsanity.com/paper/2102.04518/) (2021)
- [Quantum continual learning of quantum data realizing knowledge backward transfer](https://mlsanity.com/paper/2203.14032/) (2022)
- [Efficient and quantum-adaptive machine learning with fermion neural networks](https://mlsanity.com/paper/2211.05793/) (2022)
- [Weighted Quantum Channel Compiling through Proximal Policy Optimization](https://mlsanity.com/paper/2111.02426/) (2021)
- [Decoding surface codes with deep reinforcement learning and probabilistic policy reuse](https://mlsanity.com/paper/2212.11890/) (2022)
- [Nonstabilizerness Estimation using Graph Neural Networks](https://mlsanity.com/paper/2511.23224/) (2025)
- [Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis](https://mlsanity.com/paper/2606.29636/) (2026)
- [A Rubik's Cube inspired approach to Clifford synthesis](https://mlsanity.com/paper/2307.08684/) (2023)
- [Compilation of product-formula Hamiltonian simulation via reinforcement learning](https://mlsanity.com/paper/2311.04285/) (2023)
- [Quantum automated learning with provable and explainable trainability](https://mlsanity.com/paper/2502.05264/) (2025)
- [The DeepXube Software Package for Solving Pathfinding Problems with Learned Heuristic Functions and Search](https://mlsanity.com/paper/2603.23873/) (2026)
- [Transpiler Autotuning with Predictive Models for Quantum Circuit Optimization](https://mlsanity.com/paper/2607.29145/) (2026)
- [Generative Replay Mitigates Sample Starvation in Quantum Architecture Search](https://mlsanity.com/paper/2609.11248/) (2026)

## Abstract (arXiv)

Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep reinforcement learning that compiles an arbitrary single-qubit gate into a sequence of elementary gates from a finite universal set. It generates near-optimal gate sequences with given accuracy and is generally applicable to various scenarios, independent of the hardware-feasible universal set and free from using ancillary qubits. For concreteness, we apply this algorithm to the case of topological compiling of Fibonacci anyons and obtain near-optimal braiding sequences for arbitrary single-qubit unitaries. Our algorithm may carry over to other challenging quantum discrete problems, thus opening up a new avenue for intriguing applications of deep learning in quantum physics.