par Roland, Jérémie ;Cerf, Nicolas
Référence Physical review. A, Atomic, Molecular, and Optical Physics, 68, 6, 062311
Publication Publié, 2003
Article révisé par les pairs
Résumé : We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover’s algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related 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 makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover’s original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover’s algorithm. © 2003 The American Physical Society.