publication . Conference object . Preprint . 2015

Holographic transformation, belief propagation and loop calculus for generalized probabilistic theories

Mori, Ryuhei;
Open Access
  • Published: 17 Jan 2015
  • Publisher: IEEE
Abstract
The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is represented by an inner product of two high-dimensional vectors both of which can be decomposed to tensor products of low-dimensional vectors. On the representation, the holographic transformation is clearly understood by using adjoint linear maps. Furthermore, on the formulation using inner product, the belief propagation is naturally defined from the derivation of the loop calculus formula. As a consequence, the holographic transforma...
Subjects
free text keywords: Holography, law.invention, law, Probabilistic logic, Quantum computer, Factor graph, Tensor product, Calculus, Bipartite graph, Belief propagation, Partition function (statistical mechanics), Computer science, Computer Science - Information Theory, Condensed Matter - Statistical Mechanics, Quantum Physics
Related Organizations

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publication . Conference object . Preprint . 2015

Holographic transformation, belief propagation and loop calculus for generalized probabilistic theories

Mori, Ryuhei;