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

J. Roland·N. J. Cerf
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Abstract

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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J. Roland, N. J. Cerf. 2003-02-19. Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm. https://doi.org/10.1103/physreva.68.062311

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