Exponential capacity scaling of classical GANs compared to hybrid latent style-based quantum GANs

TL;DR

This work investigates capacity scaling in a hybrid latent style-based QGAN where a classical discriminator and an autoencoder map high-dimensional satellite images to a 24-dimensional latent space, and a parameterized quantum circuit acts as the generator with 12 qubits across L ∈ {2,4,6,8} layers. Using SAT4 data and WGAN-GP training, the authors show that the optimal classical discriminator and classical generator capacities scale exponentially with the quantum generator capacity, while the quantum generator scales linearly, implying an exponential quantum advantage in representational efficiency. The results, validated across three random seeds and supported by both noiseless simulations and IBM hardware sampling, indicate that quantum models can achieve comparable FID performance with far fewer trainable parameters, albeit with hardware noise reducing the practical gains. This work highlights capacity scaling as a concrete metric for quantum advantage in generative modeling and points to directions in circuit design and noise-aware training to bring practical benefits closer to reality.

Abstract

Quantum generative modeling is a very active area of research in looking for practical advantage in data analysis. Quantum generative adversarial networks (QGANs) are leading candidates for quantum generative modeling and have been applied to diverse areas, from high-energy physics to image generation. The latent style-based QGAN, relying on a classical variational autoencoder to encode the input data into a latent space and then using a style-based QGAN for data generation has been proven to be efficient for image generation or drug design, hinting at the use of far less trainable parameters than their classical counterpart to achieve comparable performance, however this advantage has never been systematically studied. We present in this work the first comprehensive experimental analysis of this advantage of QGANS applied to SAT4 image generation, obtaining an exponential advantage in capacity scaling for a quantum generator in the hybrid latent style-based QGAN architecture. Careful tuning of the autoencoder is crucial to obtain stable, reliable results. Once this tuning is performed and defining training optimality as when the training is stable and the FID score is low and stable as well, the optimal capacity (or number of trainable parameters) of the classical discriminator scales exponentially with respect to the capacity of the quantum generator, and the same is true for the capacity of the classical generator. This hints toward a type of quantum advantage for quantum generative modeling.

Figures (7)

• Figure 1: Variational quantum circuit with two-qubit-$SU(4)$ gates (gray bounded boxes) for one layer. Our study will use $L=2, 4, 6, 8$ layers.
• Figure 2: High-level autoencoder schematics, showing how the convolutional encoder compresses a 28x28x3 image into a latent vector of dimension 24, and then back up to a reconstructed image.
• Figure 3: High-level GAN overview showing that for the generator we do either use a quantum generator with $L$ layers, or a classical deep neural network based generator with two layers, consisting with a width of $[N_1, N_2]$.
• Figure 4: Columns a), b) and c) each contain figures for different critic capacities $L_{1,2}$ for a run with a quantum generator of $L=6$ layers. The first line displays validation FID scores (FID), the second line displays the critic training losses (Loss D), and the third line displays the generator training losses (Loss G).
• Figure 5: Capacity scaling of the best performing discriminator (critic) $P_D$ (blue) and of the the best performing classical generator $P_{CG}$ (green) as a function of the quantum generator trainable parameters $P_{QG}$. We also display the $1\sigma$ bands of the capacity of the classical critic and generators, as well as the corresponding exponential fits of the data points (solid lines).