An estimate of the print contrast signal of text characters

Gudkov, A. V.; Ionov, D. V.; Shendrik, A. V.

doi:10.1007/s11018-011-9785-x

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2012

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“…There are several hard problems in graph theory (graph isomorphism, 3-colorability) for which an efficient (polynomial) solution would be highly desirable. Several authors attempted to solve problems like graph isomorphism using a physically motivated approach [11][12][13][14]. The intuition is to encode a graph into the quantum state of a system (bosons hopping on a graph [14], quantum walks [15][16][17]) and to derive properties of the underlying graph G from the associated quantum state |G .…”

Section: Introductionmentioning

confidence: 99%

Encoding graphs into quantum states: An axiomatic approach

Ionicioiu¹,

Spiller²

2012

Phys. Rev. A

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A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states), motivating us to extend this construction to other classes. We introduce an axiomatic framework for mapping graphs to quantum states of a suitable physical system. Starting from three general axioms we derived a rich structure which includes and generalizes several classes of multipartite entangled state, like graph/stabilizer states, Gaussian cluster states, quantum random networks and projected entangled pair states (PEPS). Due to its flexibility we can extend the present formalism to include directed and weighted graphs.

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