Quantum latent distributions in deep generative models

Many successful families of generative models leverage a low-dimensional latent distribution that is mapped to a data distribution. Though simple latent distributions are commonly used, it has been shown that more sophisticated distributions can improve performance. For instance, recent work has explored using the distributions produced by quantum processors and found empirical improvements. However, when latent space distributions produced by quantum processors can be expected to improve performance, and whether these improvements are reproducible, are open questions that we investigate in this work. We prove that, under certain conditions, these "quantum latent distributions" enable generative models to produce data distributions that classical latent distributions cannot efficiently produce. We also provide actionable intuitions to identify when such quantum advantages may arise in real-world settings. We perform benchmarking experiments on both a synthetic quantum dataset and the QM9 molecular dataset, using both simulated and real photonic quantum processors. Our results demonstrate that quantum latent distributions can lead to improved generative performance in GANs compared to a range of classical baselines. We also explore diffusion and flow matching models, identifying architectures compatible with quantum latent distributions. This work confirms that near-term quantum processors can expand the capabilities of deep generative models.

Exact gradients for linear optics with single photons

Though parameter shift rules have drastically improved gradient estimation methods for several types of quantum circuits, leading to improved performance in downstream tasks, so far they have not been transferable to linear optics with single photons. In this work, we derive an analytical formula for the gradients in these circuits with respect to phaseshifters via a generalized parameter shift rule, where the number of parameter shifts depends linearly on the total number of photons. Experimentally, this enables access to derivatives in photonic systems without the need for finite difference approximations. Building on this, we propose two strategies through which one can reduce the number of shifts in the expression, and hence reduce the overall sample complexity. Numerically, we show that this generalized parameter-shift rule can converge to the minimum of a cost function with fewer parameter update steps than alternative techniques. We anticipate that this method will open up new avenues to solving optimization problems with photonic systems, as well as provide new techniques for the experimental characterization and control of linear optical systems.