Algebraic analysis of quantum search with pure and mixed states

Details Algebraic analysis of quantum search with pure and mixed states Algebraic analysis of quantum search with pure and mixed states

2005-04-20

arxiv.org/abs/quant-ph/0504149v1

Phys. Rev. A 71, 042320 (2005)

Physics

Quantum Physics

13 pages

Scientific paper

10.1103/PhysRevA.71.042320

An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process, which turns out to be confined to a four-dimensional subspace of the Hilbert space. This work unifies and generalizes earlier results on the time evolution of the amplitudes during the quantum search, the optimal number of iterations and the success probability. Furthermore, it enables a direct generalization to the case in which the initial state is a mixed state, providing an exact formula for the success probability.

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