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Time and frequency domain solutions in an optical analogue of Grover's search algorithm

T. W. Hijmans·T. N. Huussen·R. J. C. Spreeuw
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Abstract

We present new results on an optical implementation of Grover's quantum search algorithm. This extends previous work in which the transverse spatial mode of a light beam oscillates between a broad initial input shape and a highly localized spike, which reveals the position of the tagged item. The spike reaches its maximum intensity after $\sim\sqrt N$ round trips in a cavity equipped with two phase plates, where $N$ is the ratio of the surface area of the original beam and the area of the phase spot or tagged item. In our redesigned experiment the search space is now two-dimensional. In the time domain we demonstrate for the first time a multiple item search where the items appear directly as bright spots on the images of a gated camera. In a complementary experiment we investigate the searching cavity in the frequency domain. The oscillatory nature of the search algorithm can be seen as a splitting of cavity eigenmodes, each of which concentrates up to 50% of its power in the bright spot corresponding to the solution.

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T. W. Hijmans, T. N. Huussen, R. J. C. Spreeuw. 2006-05-22. Time and frequency domain solutions in an optical analogue of Grover's search algorithm. https://doi.org/10.1364/josab.24.000214

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