Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions

TL;DR

This paper introduces a hybrid quantum-classical generative model that uses variational quantum circuits to learn and produce continuous probability distributions, leveraging adversarial training with classical or quantum discriminators.

Contribution

It presents a novel variational quantum generator architecture combined with adversarial learning, enabling modeling of continuous distributions on near-term quantum devices.

Findings

Quantum generator successfully learns target distributions

Hybrid approach integrates quantum encoding with classical post-processing

Automatic differentiation optimizes variational circuits effectively

Abstract

We propose a hybrid quantum-classical approach to model continuous classical probability distributions using a variational quantum circuit. The architecture of the variational circuit consists of two parts: a quantum circuit employed to encode a classical random variable into a quantum state, called the quantum encoder, and a variational circuit whose parameters are optimized to mimic a target probability distribution. Samples are generated by measuring the expectation values of a set of operators chosen at the beginning of the calculation. Our quantum generator can be complemented with a classical function, such as a neural network, as part of the classical post-processing. We demonstrate the application of the quantum variational generator using a generative adversarial learning approach, where the quantum generator is trained via its interaction with a discriminator model that compares the generated samples with those coming from the real data distribution. We show that our quantum generator is able to learn target probability distributions using either a classical neural network or a variational quantum circuit as the discriminator. Our implementation takes advantage of automatic differentiation tools to perform the optimization of the variational circuits employed. The framework presented here for the design and implementation of variational quantum generators can serve as a blueprint for designing hybrid quantum-classical architectures for other machine learning tasks on near-term quantum devices.