Sample-based training of quantum generative models

TL;DR

This paper introduces a scalable quantum generative model training method that reduces sample complexity and enables direct hardware implementation, advancing quantum machine learning capabilities.

Contribution

It extends contrastive divergence to quantum models, providing a circuit construction that achieves constant scaling with respect to the forward pass cost.

Findings

Achieves comparable accuracy to likelihood-based methods

Requires fewer samples for training

Enables direct training on quantum hardware

Abstract

Quantum computers can efficiently sample from probability distributions that are believed to be classically intractable, providing a foundation for quantum generative modeling. However, practical training of such models remains challenging, as gradient evaluation via the parameter-shift rule scales linearly with the number of parameters and requires repeated expectation-value estimation under finite-shot noise. We introduce a training framework that extends the principle of contrastive divergence to quantum models. By deriving the circuit structure and providing a general recipe for constructing it, we obtain quantum circuits that generate the samples required for parameter updates, yielding constant scaling with respect to the cost of a forward pass, analogous to backpropagation in classical neural networks. Numerical results demonstrate that it attains comparable accuracy to likelihood-based optimization while requiring substantially fewer samples. The framework thereby establishes a scalable route to training expressive quantum generative models directly on quantum hardware.