Transitionless driving on local adiabatic quantum search algorithm

doi:10.1088/1674-1056/27/1/010308

Abstract We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transitionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term H_D ≤ ft(t) on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schrödinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of O ≤ ft(√N).

Keywords: transitionless driving local adiabatic quantum search algorithm

Received: 31 August 2017
Revised: 28 September 2017
Accepted manuscript online:

PACS:	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	03.67.Dd	(Quantum cryptography and communication security)
	03.67.Hk	(Quantum communication)

Fund: Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the National Natural Science Foundation of China (Grant Nos. 11504430 and 61502526).

Corresponding Authors: Wan-su Bao
E-mail: 2010thzz@sina.com

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Feng-guang Li(李风光), Wan-su Bao(鲍皖苏), Shuo Zhang(张硕), Xiang Wang(汪翔), He-liang Huang(黄合良), Tan Li(李坦), Bo-wen Ma(马博文) Transitionless driving on local adiabatic quantum search algorithm 2018 Chin. Phys. B 27 010308

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