Applications of Multi-Valued Quantum Algorithms

Details Applications of Multi-Valued Quantum Algorithms Applications of Multi-Valued Quantum Algorithms

2008-09-04

arxiv.org/abs/0809.0932v4

Physics

Quantum Physics

12 pages, 4 figures; updated version of paper for ISMVL 2007; contains new proof of multi-valued Grover algorithm time complex

Scientific paper

10.1109/ISMVL.2007.3

This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean functions in a single query, but can also find closed expressions for classes of affine logical functions in quantum oracles, accurate to a constant term. Furthermore, our multi-valued extension of the Grover algorithm for quantum database search requires fewer qudits and hence a substantially smaller memory register, as well as fewer wasted information states, to implement. We note several applications of these algorithms and their advantages over the binary cases.

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