Quantum Computing for Partition Function Estimation of a Markov Random Field in a Radar Anomaly Detection Problem

TL;DR

This paper explores using quantum computing to efficiently estimate the partition function of a Markov random field in radar anomaly detection, addressing computational challenges in large-scale probabilistic models.

Contribution

It introduces a quantum algorithm for partition function estimation in MRFs within the one clean qubit model, tailored for radar applications.

Findings

Quantum algorithm shows potential for scalable partition function estimation.

Performance analysis indicates advantages over classical methods.

Applicability demonstrated in radar anomaly detection context.

Abstract

In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields (MRF) can be used to efficiently represent statistical dependencies between variables. As the number of terms in the partition function scales exponentially with the number of variables, the potential of each configuration cannot be computed exactly in a reasonable time for large instances. In this paper, we aim to take advantage of the exponential scalability of quantum computing to speed up the estimation of the partition function of a MRF representing the dependencies between operating variables of an airborne radar. For that purpose, we implement a quantum algorithm for partition function estimation in the one clean qubit model. After proposing suitable formulations, we discuss the performances and scalability of our approach in comparison to the theoretical performances of the algorithm.