Discrimination of unitary transformations in the Deutsch-Jozsa algorithm

Details Discrimination of unitary transformations in the Deutsch-Jozsa algorithm Discrimination of unitary transformations in the Deutsch-Jozsa algorithm

2010-02-23

arxiv.org/abs/1002.4227v1

Phys. Rev. A, 81, 052323 (2010)

Physics

Quantum Physics

7 pages, 1 figure

Scientific paper

10.1103/PhysRevA.81.052323

We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form. We also use this to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution state NMR can only succeed with greater probability than a classical algorithm when the problem size exceeds $n \sim 10^5.$

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