Topology-Guided Quantum GANs for Constrained Graph Generation

TL;DR

This paper demonstrates that designing quantum circuit topologies with geometric priors improves the generation of constrained graphs, achieving higher geometric validity and matching classical GAN performance.

Contribution

It introduces task-specific, topology-guided quantum circuit designs for quantum GANs, enhancing geometric constraint compliance in graph generation tasks.

Findings

Topology-guided quantum GANs outperform generic designs in geometric validity.

Aligning circuit topology with problem structure improves performance.

Architectural choices influence the trade-off between geometric consistency and accuracy.

Abstract

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.