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Lattice Quantum Algorithm for the Schrödinger Wave Equation in 2+1 Dimensions with a Demonstration by Modeling Soliton Instabilities.
- Source :
-
Quantum Information Processing . Dec2005, Vol. 4 Issue 6, p457-469. 13p. 3 Graphs. - Publication Year :
- 2005
-
Abstract
- A lattice-based quantum algorithm is presented to model the non-linear Schrödinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit–qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. The model is tested on the transverse modulation instability of a one dimensional soliton wave train, both in its linear and non-linear stages. In the integrable cases where analytical solutions are available, the numerical predictions are in excellent agreement with the theory. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LATTICE dynamics
*QUANTUM theory
*ALGORITHMS
*WAVE equation
*WAVELENGTHS
*SOLITONS
Subjects
Details
- Language :
- English
- ISSN :
- 15700755
- Volume :
- 4
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Quantum Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 20179858
- Full Text :
- https://doi.org/10.1007/s11128-005-0008-8