Generalization of the Deutsch algorithm using two qudits

Jose L. Cereceda

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Generalization of the Deutsch algorithm using two qudits

Jose L. Cereceda

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Abstract

Deutsch's algorithm for two qubits (one control qubit plus one auxiliary qubit) is extended to two $d$-dimensional quantum systems or qudits for the case in which $d$ is equal to $2^n$, $n=1,2,...$ . This allows one to classify a certain oracle function by just one query, instead of the $2^{n-1}+1$ queries required by classical means. The given algorithm for two qudits also solves efficiently the Bernstein-Vazirani problem. Entanglement does not occur at any step of the computation.

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Jose L. Cereceda. 2004-09-13. Generalization of the Deutsch algorithm using two qudits. https://arxiv.org/abs/quant-ph/0407253

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