|
| related topics |
| {state, algorithm, problem} |
| {algorithm, log, probability} |
| {equation, function, exp} |
| {energy, state, states} |
| {measurement, state, measurements} |
| {spin, pulse, spins} |
| {energy, gaussian, time} |
| {time, decoherence, evolution} |
| {cos, sin, state} |
| {level, atom, field} |
|
Quantum Mechanical Search and Harmonic Perturbation
Jie-Hong R. Jiang, Dah-Wei Chiou, Cheng-En Wu
abstract: Perturbation theory in quantum mechanics studies how quantum systems interact
with their environmental perturbations. Harmonic perturbation is a rare special
case of time-dependent perturbations in which exact analysis exists. Some
important technology advances, such as masers, lasers, nuclear magnetic
resonance, etc., originated from it. Here we add quantum computation to this
list with a theoretical demonstration. Based on harmonic perturbation, a
quantum mechanical algorithm is devised to search the ground state of a given
Hamiltonian. The intrinsic complexity of the algorithm is continuous and
parametric in both time T and energy E. More precisely, the probability of
locating a search target of a Hamiltonian in N-dimensional vector space is
shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is
optimal. As harmonic perturbation provides a different computation mechanism,
the algorithm may suggest new directions in realizing quantum computers.
- oai_identifier:
- oai:arXiv.org:quant-ph/0702007
- categories:
- quant-ph
- comments:
- 6 pages, 4 figures, revtex4
- doi:
- 10.1007/s11128-007-0062-5
- arxiv_id:
- quant-ph/0702007
- journal_ref:
- Quantum Information Processing 6(5), (Oct. 2007) 349-362
- created:
- 2007-02-01
- updated:
- 2007-09-14
Full article ▸
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