A General SU(2) Formulation for Quantum Searching with Certainty
arXiv:quant-ph/0112035 · doi:10.1103/PhysRevA.65.052322
Abstract
A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.
8 pages, 2 figures
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