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| related topics |
| {classical, space, random} |
| {algorithm, log, probability} |
| {operator, operators, space} |
| {wave, scattering, interference} |
| {photon, photons, single} |
| {state, algorithm, problem} |
| {equation, function, exp} |
| {cos, sin, state} |
| {state, phys, rev} |
| {let, theorem, proof} |
| {states, state, optimal} |
| {field, particle, equation} |
|
Quantum walks based on an interferometric analogy
Mark Hillery, Janos Bergou, Edgar Feldman
abstract: There are presently two models for quantum walks on graphs. The "coined" walk
uses discrete time steps, and contains, besides the particle making the walk, a
second quantum system, the coin, that determines the direction in which the
particle will move. The continuous walk operates with continuous time. Here a
third model for a quantum walk is proposed, which is based on an analogy to
optical interferometers. It is a discrete-time model, and the unitary operator
that advances the walk one step depends only on the local structure of the
graph on which the walk is taking place. No quantum coin is introduced. This
type of walk allows us to introduce elements, such as phase shifters, that have
no counterpart in classical random walks. Walks on the line and cycle are
discussed in some detail, and a probability current for these walks is
introduced. The relation to the coined quantum walk is also discussed. The
paper concludes by showing how to define these walks for a general graph.
- oai_identifier:
- oai:arXiv.org:quant-ph/0302161
- categories:
- quant-ph
- comments:
- Latex,18 pages, 5 figures
- doi:
- 10.1103/PhysRevA.68.032314
- arxiv_id:
- quant-ph/0302161
- created:
- 2003-02-20
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