On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators
This work highlights fundamental generalization challenges in quantum generative models, which is incremental but important for researchers in quantum machine learning.
The paper investigates Quantum Generative Adversarial Networks (QGANs) for image generation, finding that they struggle to generalize across datasets and converge on average representations, with theoretical analysis linking this to fidelity bounds for pure-state generators.
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.