Quantum latent distributions in deep generative models

TL;DR

The paper addresses how latent-space design affects deep generative models and proposes quantum latent distributions, realized via photonic interference, as a means to access data distributions beyond classical pushforwards. It develops a complexity-theoretic framework, proving that under invertible Lipschitz generators, quantum latents can produce data distributions not efficiently simulable classically, and provides intuition for practical gains. The authors benchmark quantum latents on a synthetic quantum dataset and the QM9 chemistry dataset using both simulated and real photonic processors, finding that quantum interference statistics can improve generative performance, particularly for correlated, multimodal data. The findings suggest quantum processors can expand the capabilities of deep generative models by enriching the latent space with non-classical statistics, while highlighting the need for circuit-design exploration and scaling to larger architectures. Overall, the work merges theory and experiment to demonstrate a viable role for quantum latent distributions in advancing generative modeling.

Abstract

Many successful families of generative models leverage a low-dimensional latent distribution that is mapped to a data distribution. Though simple latent distributions are often used, the choice of distribution has a strong impact on model performance. Recent experiments have suggested that the probability distributions produced by quantum processors, which are typically highly correlated and classically intractable, can lead to improved performance on some datasets. However, when and why latent distributions produced by quantum processors can improve performance, and whether these improvements are connected to quantum properties of these distributions, are open questions that we investigate in this work. We show in theory that, under certain conditions, these "quantum latent distributions" enable generative models to produce data distributions that classical latent distributions cannot efficiently produce. We provide intuition as to the underlying mechanisms that could explain a performance advantage on real datasets. Based on this, we perform extensive benchmarking on a synthetic quantum dataset and the QM9 molecular dataset, using both simulated and real photonic quantum processors. We find that the statistics arising from quantum interference lead to improved generative performance compared to classical baselines, suggesting that quantum processors can play a role in expanding the capabilities of deep generative models.

Figures (7)

• Figure 1: Our work provides a theoretical and empirical study of the use of non-classical distributions produced by quantum processors in the latent space of generative models. Even on a simple dataset such as the 2D mixture of Gaussians shown here, training a simple GAN with different latent distributions yields very different results. We compare four latent distributions representing a progression from the commonly used Gaussian distribution (bottom) to a quantum distribution produced by a photonic quantum processor (top). The main failure mode is a tendency to interpolate between different modes in the data, and the model with the quantum latent distribution is least affected. Further information on this experimental setting can be found in Appendix \ref{['2dgaussians']}. In this paper, we investigate this approach from a theoretical perspective, propose some intuition to explain these results, and conduct benchmarking experiments to compare quantum distributions to relevant classical distributions in an apples-to-apples setting.
• Figure 2: An illustration of the relation between the complexity of latent distributions and that of the pushforward distributions. $\mathcal{C}$ represents classical distributions, $\mathcal{Q}$ represents non-classical distributions, and $g(\mathcal{Q})$ and $g(\mathcal{C})$ are the pushforward distributions achieved using a class of neural networks $g$ with finite complexity. When the target dataset is in the pushforward distribution of $\mathcal{C}$ (D1), a quantum distribution is not expected to provide a benefit. However, when the target dataset is not in the pushforward distribution of $\mathcal{C}$ and can be either quantum (D2) or classical (D3) the pushforward distribution of a quantum latent distribution may be closer, leading to better performance.
• Figure 3: Illustration of a loop-based boson sampling system. Here, four sequential single photons, separated by time $\tau$, are sent into a system consisting of two sequential loops with lengths such that each photon that enters the loop can interfere with a subsequent photon. Sequences of loops of different lengths ensures that a photon can interfere with a photon several time-steps behind.
• Figure 4: FCD scores during training for different latents of $d_z$=16. The mean and standard error of the mean are calculated from 20 random seeds.
• Figure 5: Examples of generated molecules using a trained model with a quantum latent distribution.

Theorems & Definitions (3)

• Remark 1
• Theorem 1
• Corollary 1