Quantum search with resonances

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.

11 pages, 6 figures

References in corpus (7)

• Spatial search by quantum walk
• Quantum random walks in optical lattices
• Quantum walk on the line as an interference phenomenon
• Quantum quincunx in cavity quantum electrodynamics
• Decoherence in the quantum walk on the line
• Quantum random walk on the line as a markovian process
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Cited by in corpus (5)

• Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene
• The Grover search as a naturally occurring phenomenon
• Non adiabatic quantum search algorithms
• Quantum games via search algorithms
• Quantum Mechanical Search and Harmonic Perturbation