|
| related topics |
| {state, algorithm, problem} |
| {algorithm, log, probability} |
| {equation, function, exp} |
| {states, state, optimal} |
| {operator, operators, space} |
| {group, space, representation} |
| {classical, space, random} |
| {cos, sin, state} |
| {time, wave, function} |
| {phase, path, phys} |
| {temperature, thermal, energy} |
| {let, theorem, proof} |
| {time, decoherence, evolution} |
|
A Family of Grover's Quantum Searching Algorithms
Alberto Galindo, Miguel A. Martin-Delgado
abstract: We introduce the concepts of Grover operators and Grover kernels to
systematically analyse Grover's searching algorithms. Then, we investigate a
one-parameter family of quantum searching algorithms of Grover's type and we
show that the standard Grover's algorithm is a distinguished member of this
family. We show that all the algorithms of this class solve the searching
problem with an efficiency of order $O(\sqrt{N})$, with a coefficient which is
class-dependent. The analysis of this dependence is a test of the stability and
robustness of the algorithms. We show the stability of this constructions under
perturbations of the initial conditions and extend them upon a very general
class of Grover operators.
- oai_identifier:
- oai:arXiv.org:quant-ph/0009086
- categories:
- quant-ph cond-mat
- comments:
- REVTEX file, 6 pages, two-column, 3 eps figures; accepted in Phys.
Rev. A
- doi:
- 10.1103/PhysRevA.62.062303
- arxiv_id:
- quant-ph/0009086
- created:
- 2000-09-21
Full article ▸
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