# FlowQ-Net: A Generative Framework for Automated Quantum Circuit Design

arXiv: https://arxiv.org/abs/2510.26688 · HTML: https://mlsanity.com/paper/2510.26688/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 30 Oct 2025.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Reward is enough for convex MDPs](https://mlsanity.com/paper/2106.00661/) (2021)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Generative Flow Networks as Entropy-Regularized RL](https://mlsanity.com/paper/2310.12934/) (2023)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [Learning Discrete Energy-based Models via Auxiliary-variable Local Exploration](https://mlsanity.com/paper/2011.05363/) (2020)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [PhyloGFN: Phylogenetic inference with generative flow networks](https://mlsanity.com/paper/2310.08774/) (2023)
- [A randomized quantum algorithm for statistical phase estimation](https://mlsanity.com/paper/2110.12071/) (2021)

## Built on by (most cited first, 4 of 4)

- [When Close Enough Is Not Enough: Autoregressive Drift in Quantum Circuit Synthesis](https://mlsanity.com/paper/2607.12780/) (2026)
- [Learning to Prepare Molecular Ground States with Transformer Models](https://mlsanity.com/paper/2607.22468/) (2026)
- [Generative Learning for Quantum Measurement Design](https://mlsanity.com/paper/2608.11396/) (2026)
- [Circuit Hypernetworks for Quantum-Augmented Diffusion Language Models](https://mlsanity.com/paper/2609.24657/) (2026)

## Abstract (arXiv)

Designing efficient quantum circuits is a central bottleneck to exploring the potential of quantum computing, particularly for noisy intermediate-scale quantum (NISQ) devices, where circuit efficiency and resilience to errors are paramount. The search space of gate sequences grows combinatorially, and handcrafted templates often waste scarce qubit and depth budgets. We introduce textscFlowQ-Net (Flow-based Quantum design Network), a generative framework for automated quantum circuit synthesis based on Generative Flow Networks (GFlowNets). This framework learns a stochastic policy to construct circuits sequentially, sampling them in proportion to a flexible, user-defined reward function that can encode multiple design objectives such as performance, depth, and gate count. This approach uniquely enables the generation of a diverse ensemble of high-quality circuits, moving beyond single-solution optimization. We demonstrate the efficacy of textscFlowQ-Net through an extensive set of simulations. We apply our method to Variational Quantum Algorithm (VQA) ansatz design for molecular ground state estimation, Max-Cut, and image classification, key challenges in near-term quantum computing. Circuits designed by textscFlowQ-Net achieve significant improvements, yielding circuits that are 10×-30× more compact in terms of parameters, gates, and depth compared to commonly used unitary baselines, without compromising accuracy. This trend holds even when subjected to error profiles from real-world quantum devices. Our results underline the potential of generative models as a general-purpose methodology for automated quantum circuit design, offering a promising path towards more efficient quantum algorithms and accelerating scientific discovery in the quantum domain.