Factor Graphs for Quantum Information Processing

• URL: http://arxiv.org/abs/2203.12413v1
• Date: Wed, 23 Mar 2022 13:44:34 GMT
• Title: Factor Graphs for Quantum Information Processing
• Authors: Michael X. Cao
• Abstract summary: We are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs) and quantum factor graphs (QFGs)
• Score: 3.04585143845864
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: [...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs) and quantum factor graphs (QFGs). Conventionally, a factor in a factor graph represents a nonnegative real-valued local functions. Two different approaches to generalize factors in classical factor graphs yield DeFGs and QFGs, respectively. We proposed/re-proposed and analyzed generalized versions of belief-propagation algorithms for DeFGs/QFGs. As a particular application of the DeFGs, we investigate the information rate and their upper/lower bounds of classical communications over quantum channels with memory. In this study, we also propose a data-driven method for optimizing the upper/lower bounds on information rate.

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