# Automated Quantum Circuit Design with Nested Monte Carlo Tree Search

arXiv: https://arxiv.org/abs/2207.00132 · HTML: https://mlsanity.com/paper/2207.00132/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 52 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Understanding Architectures Learnt by Cell-based Neural Architecture Search](https://mlsanity.com/paper/1909.09569/) (2019)
- [Theory-Inspired Path-Regularized Differential Network Architecture Search](https://mlsanity.com/paper/2006.16537/) (2020)
- [Neural Architecture Search using Deep Neural Networks and Monte Carlo Tree Search](https://mlsanity.com/paper/1805.07440/) (2018)
- [Neural Architecture Search via Combinatorial Multi-Armed Bandit](https://mlsanity.com/paper/2101.00336/) (2021)

## Built on by (most cited first, 16 of 16)

- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)
- [Quantum Machine Learning Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2407.20147/) (2024)
- [Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search](https://mlsanity.com/paper/2502.03962/) (2025)
- [Decoding surface codes with deep reinforcement learning and probabilistic policy reuse](https://mlsanity.com/paper/2212.11890/) (2022)
- [Qubit-Wise Architecture Search Method for Variational Quantum Circuits](https://mlsanity.com/paper/2403.04268/) (2024)
- [BenchRL-QAS: Benchmarking reinforcement learning algorithms for quantum architecture search](https://mlsanity.com/paper/2507.12189/) (2025)
- [Dissecting Quantum Reinforcement Learning: A Systematic Evaluation of Key Components](https://mlsanity.com/paper/2511.17112/) (2025)
- [How to find expressible and trainable parameterized quantum circuits?](https://mlsanity.com/paper/2603.14451/) (2026)
- [Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction](https://mlsanity.com/paper/2506.11552/) (2025)
- [Replay-buffer engineering for noise-aware quantum circuit optimization](https://mlsanity.com/paper/2604.21863/) (2026)
- [Monte Carlo Search Algorithms Discovering Monte Carlo Tree Search Exploration Terms](https://mlsanity.com/paper/2404.09304/) (2024)
- [Quantum Architecture Search for Solving Quantum Machine Learning Tasks](https://mlsanity.com/paper/2509.11198/) (2025)
- [Magic-Informed Quantum Architecture Search](https://mlsanity.com/paper/2605.03932/) (2026)
- [Zero-shot Quantum Neural Architecture Search](https://mlsanity.com/paper/2605.27410/) (2026)
- [Energy Accuracy Is Not Enough: A Structure-Aware Benchmark and Evaluation Protocol for Quantum Architecture Search](https://mlsanity.com/paper/2607.04845/) (2026)

## Abstract (arXiv)

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.