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Quantum search with resonances

A. Romanelli·A. Auyuanet·R. Donangelo
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Abstract

We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, 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 $O(1/\sqrt{N})$ 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.

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A. Romanelli, A. Auyuanet, R. Donangelo. 2005-05-10. Quantum search with resonances. https://doi.org/10.1016/j.physa.2005.05.101

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