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

• URL: http://arxiv.org/abs/2501.01154v1
• Date: Thu, 02 Jan 2025 09:14:14 GMT
• Title: Quantum Computing for Partition Function Estimation of a Markov Random Field in a Radar Anomaly Detection Problem
• Authors: Timothe Presles, Cyrille Enderli, Gilles Burel, El Houssain Baghious,
• Abstract summary: In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. We propose a quantum algorithm for partition function estimation in the one clean qubit model.
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• 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.

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