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arXiv · 2406.06360

Non-Markov quantum belief propagation

Jack Ceroni·Ian MacCormack·Guillaume Verdon
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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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Jack Ceroni, Ian MacCormack, Guillaume Verdon. 2024-06-10. Non-Markov quantum belief propagation. https://arxiv.org/abs/2406.06360

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