Problem-informed Graphical Quantum Generative Learning

TL;DR

This paper introduces a problem-informed quantum generative model using Markov networks to improve training efficiency and performance in learning structured probability distributions, potentially offering quantum advantage.

Contribution

It proposes a novel quantum circuit Born machine Ansatz based on Markov networks, demonstrating improved performance over problem-agnostic models and analyzing trainability.

Findings

Outperforms previous problem-agnostic quantum generative models

Constructs benchmarks using Markov networks for structured problems

Identifies Markov networks with favorable trainability properties

Abstract

Leveraging the intrinsic probabilistic nature of quantum systems, generative quantum machine learning (QML) offers the potential to outperform classical learning models. Current generative QML algorithms mostly rely on general-purpose models that, while being very expressive, face several training challenges. One potential way to address these setbacks is by constructing problem-informed models that are capable of more efficient training on structured problems. In particular, probabilistic graphical models provide a flexible framework for representing structure in generative learning problems and can thus be exploited to incorporate inductive bias into QML algorithms. In this work, we propose a problem-informed quantum circuit Born machine Ansatz for learning the joint probability distribution of random variables, with independence relations efficiently represented by a Markov network (MN). We further demonstrate the applicability of the MN framework in constructing generative learning benchmarks and compare our model's performance to previous designs, showing that it outperforms problem-agnostic circuits. Based on a preliminary analysis of trainability, we narrow down the class of MNs to those exhibiting favourable trainability properties. Finally, we discuss the potential of our model to offer quantum advantage in the context of generative learning.