par Roland, Jérémie 
;Cerf, Nicolas
Référence Physical review. A, Atomic, Molecular, and Optical Physics, 65, 4, 042308
Publication Publié, 2002
;Cerf, Nicolas Référence Physical review. A, Atomic, Molecular, and Optical Physics, 65, 4, 042308
Publication Publié, 2002
Article révisé par les pairs
| Résumé : | The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which tends to the solution. We apply this time-dependent Hamiltonian approach to Grover’s problem, i.e., searching a marked item in an unstructured database. We find that by adjusting the evolution rate of the Hamiltonian so as to keep the evolution adiabatic on each infinitesimal time interval, the total running time is of order [Formula Presented] where N is the number of items in the database. We thus recover the advantage of Grover’s standard algorithm as compared to a classical search, scaling as N. This is in contrast with the constant-rate adiabatic approach of Farhi et al. (e-print quant-ph/0001106), where the requirement of adiabaticity is expressed only globally, resulting in a time of order N. © 2002 The American Physical Society. |
