par Roland, Jérémie ;Cerf, Nicolas
Référence Physical review. A, Atomic, Molecular, and Optical Physics, 68, 6, 062311
Publication Publié, 2003
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. |