Applications of graph coloring in various fields

Thadani, Satish; Bagora, Seema; Sharma, Anand

doi:10.1016/j.matpr.2022.06.392

Cited by 6 publications

(1 citation statement)

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“…Graph coloring is one of the most studied topics of graph theory because of its applications in solving scheduling problems and compiler theory [61,62]. Coloring refers to the assignment of labels (colors) from a label set to the vertices of a graph G. This assignment defines a map C : V → L, where V is the set containing the vertices of G and L is the label set.…”

Section: The K-coloring Problemmentioning

confidence: 99%

Efficient qudit based scheme for photonic quantum computing

Karácsony,

Oroszlány,

Zimboras

2024

SciPost Phys. Core

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Linear optics is a promising alternative for the realization of quantum computation protocols due to the recent advancements in integrated photonic technology. In this context, usually qubit based quantum circuits are considered, however, photonic systems naturally allow also for d-ary, i.e., qudit based, algorithms. This work investigates qudits defined by the possible photon number states of a single photon in d > 2 optical modes. We demonstrate how to construct locally optimal non-deterministic many-qudit gates using linear optics and photon number resolving detectors, and explore the use of qudit cluster states in the context of a d-ary optimization problem. We find that the qudit cluster states require less optical modes and are encoded by a fewer number of entangled photons than the qubit cluster states with similar computational capabilities. We illustrate the benefit of our qudit scheme by applying it to the k-coloring problem.

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Section: The K-coloring Problemmentioning

confidence: 99%