# Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search

arXiv: https://arxiv.org/abs/2502.03962 · HTML: https://mlsanity.com/paper/2502.03962/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 75 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [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)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Monte Carlo Tree Search: A Review of Recent Modifications and Applications](https://mlsanity.com/paper/2103.04931/) (2021)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [Neural Architecture Search using Deep Neural Networks and Monte Carlo Tree Search](https://mlsanity.com/paper/1805.07440/) (2018)
- [Automated Quantum Circuit Design with Nested Monte Carlo Tree Search](https://mlsanity.com/paper/2207.00132/) (2022)
- [Quantum Circuit Evolution on NISQ Devices](https://mlsanity.com/paper/2012.13453/) (2020)
- [Hierarchical quantum circuit representations for neural architecture search](https://mlsanity.com/paper/2210.15073/) (2022)
- [Neural Architecture Search via Combinatorial Multi-Armed Bandit](https://mlsanity.com/paper/2101.00336/) (2021)

## Built on by (most cited first, 5 of 5)

- [Synthesis of discrete-continuous quantum circuits with multimodal diffusion models](https://mlsanity.com/paper/2506.01666/) (2025)
- [Nonstabilizerness Estimation using Graph Neural Networks](https://mlsanity.com/paper/2511.23224/) (2025)
- [A Study on Stabilizer R'enyi Entropy Estimation using Machine Learning](https://mlsanity.com/paper/2509.16799/) (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)

## Abstract (arXiv)

The performance of Variational Quantum Algorithms (VQAs) strongly depends on the choice of the parameterized quantum circuit to optimize. One of the biggest challenges in VQAs is designing quantum circuits tailored to the particular problem. This article proposes a gradient-free Monte Carlo Tree Search (MCTS) technique to automate the process of quantum circuit design. Our proposed technique introduces a novel formulation of the action space based on a sampling scheme and a progressive widening technique to explore the space dynamically. When testing our MCTS approach on the domain of random quantum circuits, MCTS approximates unstructured circuits under different values of stabilizer R'enyi entropy. It turns out that MCTS manages to approximate the benchmark quantum states independently from their degree of nonstabilizerness. Next, our technique exhibits robustness across various application domains, including quantum chemistry and systems of linear equations. Compared to previous MCTS research, our technique reduces the number of quantum circuit evaluations by a factor of 10 up to 100 while achieving equal or better results. In addition, the resulting quantum circuits exhibit up to three times fewer CNOT gates, which is important for implementation on noisy quantum hardware.