Discrimination of Unitary Transformations and Quantum Algorithms

Details Discrimination of Unitary Transformations and Quantum Algorithms Discrimination of Unitary Transformations and Quantum Algorithms

2008-11-09

arxiv.org/abs/0811.1359v1

Physics

Quantum Physics

Submitted to the proceedings of the QCMC 08 conference

Scientific paper

Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the sequence with others remaining fixed. For oracle query algorithms, the input determines the oracle unitary transformation. Such algorithms can be regarded as devices for discriminating amongst a set of unitary transformations. The question arises: "Given a set of known oracle unitary transformations, to what extent is it possible to discriminate amongst them?" We investigate this for the Deutsch-Jozsa problem. The task of discriminating amongst the admissible oracle unitary transformations results in an exhaustive collection of algorithms which can solve the problem with certainty.

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