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arXiv · 0812.3694

On continuous variable quantum algorithms for oracle identification problems

Mark Adcock·Peter Hoyer·Barry C. Sanders
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Abstract

We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous representation in an infinite-dimensional Hilbert space. We apply this formalism to the Deutsch-Jozsa problem and show that, due to an uncertainty relation between the continuous representation and its Fourier-transform dual representation, the corresponding Deutsch-Jozsa algorithm is probabilistic hence forbids an exponential speed-up, contrary to a previous claim in the literature.

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Mark Adcock, Peter Hoyer, Barry C. Sanders. 2008-12-19. On continuous variable quantum algorithms for oracle identification problems. https://doi.org/10.1088/1367-2630%2F11%2F10%2F103035

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