# Topology-Guided Quantum GANs for Constrained Graph Generation

arXiv: https://arxiv.org/abs/2512.10582 · HTML: https://mlsanity.com/paper/2512.10582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Quantum Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/1911.00111/) (2019)
- [Noise robustness and experimental demonstration of a quantum generative adversarial network for continuous distributions](https://mlsanity.com/paper/2006.01976/) (2020)
- [Investigating Parameter-Efficiency of Hybrid QuGANs Based on Geometric Properties of Generated Sea Route Graphs](https://mlsanity.com/paper/2501.08678/) (2025)

## Abstract (arXiv)

Quantum computing (QC) promises theoretical advantages, benefiting computational problems that would not be efficiently classically simulatable. However, much of this theoretical speedup depends on the quantum circuit design solving the problem. We argue that QC literature has yet to explore more domain specific ansatz-topologies, instead of relying on generic, one-size-fits-all architectures. In this work, we show that incorporating task-specific inductive biases -- specifically geometric priors -- into quantum circuit design can enhance the performance of hybrid Quantum Generative Adversarial Networks (QuGANs) on the task of generating geometrically constrained K4 graphs. We evaluate a portfolio of entanglement topologies and loss-function designs to assess their impact on both statistical fidelity and compliance with geometric constraints, including the Triangle and Ptolemaic inequalities. Our results show that aligning circuit topology with the underlying problem structure yields substantial benefits: the Triangle-topology QuGAN achieves the highest geometric validity among quantum models and matches the performance of classical Generative Adversarial Networks (GAN). Additionally, we showcase how specific architectural choices, such as entangling gate types, variance regularization and output-scaling govern the trade-off between geometric consistency and distributional accuracy, thus emphasizing the value of structured, task-aware quantum ansatz-topologies.