A performance characterization of quantum generative models

TL;DR

This paper systematically compares various quantum generative models and architectures, demonstrating that quantum models can achieve comparable or superior performance with fewer parameters, especially when learning the distribution's copula.

Contribution

It provides a comprehensive comparison of quantum generative modeling techniques, architectures, and data transformations, highlighting the efficiency and effectiveness of certain quantum approaches over classical models.

Findings

Quantum models require similar or fewer parameters than classical models.

A discrete architecture learning the copula outperforms other methods.

Quantum models can require two orders of magnitude fewer parameters.

Abstract

Quantum generative modeling is a growing area of interest for industry-relevant applications. With the field still in its infancy, there are many competing techniques. This work is an attempt to systematically compare a broad range of these techniques to guide quantum computing practitioners when deciding which models and techniques to use in their applications. We compare fundamentally different architectural ansatzes of parametric quantum circuits used for quantum generative modeling: 1. A continuous architecture, which produces continuous-valued data samples, and 2. a discrete architecture, which samples on a discrete grid. We compare the performance of different data transformations: normalization by the min-max transform or by the probability integral transform. We learn the underlying probability distribution of the data sets via two popular training methods: 1. quantum circuit Born machines (QCBM), and 2. quantum generative adversarial networks (QGAN). We study their performance and trade-offs as the number of model parameters increases, with the baseline of similarly trained classical neural networks. The study is performed on six low-dimensional synthetic and two real financial data sets. Our two key findings are that: 1. For all data sets, our quantum models require similar or fewer parameters than their classical counterparts. In the extreme case, the quantum models require two of orders of magnitude less parameters. 2. We empirically find that a variant of the discrete architecture, which learns the copula of the probability distribution, outperforms all other methods.