On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators

TL;DR

This paper analyzes the limitations of Quantum Generative Adversarial Networks (QGANs) with pure state generators, revealing fundamental challenges in their ability to generalize across datasets, supported by both numerical and theoretical insights.

Contribution

The paper provides a theoretical lower bound on discriminator quality for pure-state QGANs and demonstrates their limited generalization capabilities through extensive numerical testing.

Findings

QGANs tend to converge to the average training data representation.

A lower bound on discriminator fidelity is derived for pure-state generators.

Current QGAN architectures face fundamental generalization challenges.

Abstract

We investigate the capabilities of Quantum Generative Adversarial Networks (QGANs) in image generations tasks. Our analysis centers on fully quantum implementations of both the generator and discriminator. Through extensive numerical testing of current main architectures, we find that QGANs struggle to generalize across datasets, converging on merely the average representation of the training data. When the output of the generator is a pure-state, we analytically derive a lower bound for the discriminator quality given by the fidelity between the pure-state output of the generator and the target data distribution, thereby providing a theoretical explanation for the limitations observed in current models. Our findings reveal fundamental challenges in the generalization capabilities of existing quantum generative models. While our analysis focuses on QGANs, the results carry broader implications for the performance of related quantum generative models.