|
| related topics |
| {algorithm, log, probability} |
| {qubit, qubits, gate} |
| {states, state, optimal} |
| {bell, inequality, local} |
|
Tradeoffs in the Quantum Search Algorithm
Lov K. Grover
abstract: Quantum search is a quantum mechanical technique for searching N
possibilities in only sqrt(N) steps. This has been proved to be the best
possible algorithm for the exhuastive search problem in the sense the number of
queries it requires cannot be reduced. However, as this paper shows, the number
of non-query operations, and thus the total number of operations, can be
reduced. The number of non-query unitary operations can be reduced by a factor
of log N/alpha*log(log N) while increasing the number of queries by a factor of
only (1+(log N)^{-alpha}). Various choices of alpha yield different variants of
the algorithm. For example, by choosing alpha to be O(log N/log(log N)), the
number of non-query unitary operations can be reduced by 40% while increasing
the number of queries by just two.
- oai_identifier:
- oai:arXiv.org:quant-ph/0201152
- categories:
- quant-ph
- comments:
- 11 pages
- doi:
- 10.1103/PhysRevA.66.052314
- arxiv_id:
- quant-ph/0201152
- created:
- 2002-01-31
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