|
| related topics |
| {qubit, qubits, gate} |
| {algorithm, log, probability} |
| {group, space, representation} |
| {time, systems, information} |
| {information, entropy, channel} |
| {entanglement, phys, rev} |
| {classical, space, random} |
| {theory, mechanics, state} |
| {state, algorithm, problem} |
| {measurement, state, measurements} |
| {state, states, coherent} |
| {particle, mechanics, theory} |
| {trap, ion, state} |
|
Quantum Algorithms: Entanglement Enhanced Information Processing
Artur Ekert, Richard Jozsa
abstract: We discuss the fundamental role of entanglement as the essential nonclassical
feature providing the computational speed-up in the known quantum algorithms.
We review the construction of the Fourier transform on an Abelian group and the
principles underlying the fast Fourier transform algorithm. We describe the
implementation of the FFT algorithm for the group of integers modulo 2^n in the
quantum context, showing how the group-theoretic formalism leads to the
standard quantum network and identifying the property of entanglement that
gives rise to the exponential speedup (compared to the classical FFT). Finally
we outline the use of the Fourier transform in extracting periodicities, which
underlies its utility in the known quantum algorithms.
- oai_identifier:
- oai:arXiv.org:quant-ph/9803072
- categories:
- quant-ph
- comments:
- 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc.
(Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum
Computation: Theory and Experiment'', held in November 1997
- doi:
- 10.1098/rsta.1998.0248
- arxiv_id:
- quant-ph/9803072
- created:
- 1998-03-26
Full article ▸
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