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arXiv:quant-ph/0502161 · Physica A Statistical Mechanics and its Applications

Quantum search with resonances

A. Romanelli, A. Auyuanet, R. Donangelo

Published Jul 28, 2005• 8 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2005.05.101

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We present an algorithm for the generalized search problem (searching k marked items among N items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity O ( N / k ) as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary “monitor” qubits, can determine k precisely, if it is unknown. The time complexity of our counting algorithm is O ( N ) , similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.
Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This paper gives a fresh perspective on the algorithm in terms of a resonance phenomenon which is implemented through classical coupled oscillators. Consider N oscillators, one of which is of a different resonant frequency. We could identify which one this is by measuring the oscillation frequency of each oscillator, a procedure that would take about N cycles. We show how, by coupling the oscillators together in a very simple way, it is possible to identify the different one in only sqrt(N) cycles. An extension of this technique to the quantum case leads to the quantum search algorithm.