Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm

Details Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm

2003-02-19

arxiv.org/abs/quant-ph/0302138v1

Phys. Rev. A 68, 062311 (2003).

Physics

Quantum Physics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevA.68.062311

We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely related algorithms in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This make it possible to implement the last two algorithms by Hamiltonian evolution on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm.

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