Quantum search with resonances

• Published in: Physica A Vol. 360; no. 2; pp. 274 - 284
• Main Authors: Romanelli, A., Auyuanet, A., Donangelo, R.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-02-2006
• Subjects: Quantum algorithms; Quantum computation; Quantum algorithms; Quantum computation
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2005.05.101

We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to
N
, where
N is the database size. This search algorithm can be implemented using any Hamiltonian with a discrete energy spectrum through excitation of resonances between an initial and the searched state. This algorithm is robust and, as in the case of Grover's, it allows for an error
O
(
1
/
N
)
in the determination of the searched state. A discrete time version of this continuous time search algorithm is built, and the connection between the search algorithms with discrete and continuous times is established.