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Parametric quantum search algorithm as quantum walk: a quantum simulation

Ellinas Dimosthenis, Konstantakis Christos

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Extent24 pagesen
TitleParametric quantum search algorithm as quantum walk: a quantum simulationen
CreatorEllinas Dimosthenisen
CreatorΕλληνας Δημοσθενηςel
CreatorKonstantakis Christosen
CreatorΚωνσταντακης Χρηστοςel
Content SummaryParametric quantum search algorithm (PQSA) is a form of quantum search that results by relaxing the unitarity of the original algorithm. PQSA can naturally be cast in the form of quantum walk, by means of the formalism of oracle algebra. This is due to the fact that the completely positive trace preserving search map used by PQSA, admits a unitarization (unitary dilation) a la quantum walk, at the expense of introducing auxiliary quantum coin-qubit space. The ensuing QW describes a process of spiral motion, chosen to be driven by two unitary Kraus generators, generating planar rotations of Bloch vector around an axis. The quadratic acceleration of quantum search translates into an equivalent quadratic saving of the number of coin qubits in the QW analogue. The associated to QW model Hamiltonian operator is obtained and is shown to represent a multi-particle long-range interacting quantum system that simulates parametric search. Finally, the relation of PQSA-QW simulator to the QW search algorithm is elucidated.en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Date of Item2018-10-22-
Date of Publication2016-
SubjectCP mapen
SubjectLie algebraen
SubjectQuantum searchen
SubjectQuantum simulationen
Bibliographic CitationD. Ellinas and C. Konstandakis, "Parametric quantum search algorithm as quantum walk: a quantum simulation," Rep. Math. Phys., vol. 77, no. 1, pp. 105-128, Feb. 2016. doi: 10.1016/S0034-4877(16)30008-8en