Non-Markov quantum belief propagation

• URL: http://arxiv.org/abs/2406.06360v1
• Date: Mon, 10 Jun 2024 15:20:23 GMT
• Title: Non-Markov quantum belief propagation
• Authors: Jack Ceroni, Ian MacCormack, Guillaume Verdon,
• Abstract summary: We provide a rigorous proof of approximate convergence of sliding-window quantum belief-propagation. In particular, we confirm the hypothesis outlined in this work that the approximation error of each step in the belief-propagation algorithm decreases exponentially with the sliding-window size.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide a rigorous proof of the approximate convergence of sliding-window quantum belief-propagation as outlined heuristically in the work of Bilgin and Poulin (Ref. [1]), in the absence of the quantum Markov property. In particular, we confirm the hypothesis outlined in this work that the approximation error of each step in the belief-propagation algorithm decreases exponentially with the sliding-window size, under the assumption that the underlying state on which belief-propagation is being performed possesses a so-called thermal boundedness property: a relaxation of the Markov property required for exact convergence.

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