Parametric quantum search algorithm as quantum walk: a quantum simulationParametric quantum search algorithm as quantum walk: a quantum simulation Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2018-10-222016enParametric 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.http://creativecommons.org/licenses/by/4.0/Reports on Mathematical Physics771105-128 Ellinas Dimosthenis Ελληνας Δημοσθενης Konstantakis Christos Κωνσταντακης Χρηστος Elsevier CP map Lie algebra Quantum search Quantum simulation