Lattice Quantum Algorithm for the Schrödinger Wave Equation in 2+1 Dimensions with a Demonstration by Modeling Soliton Instabilities

Lattice Quantum Algorithm for the Schrödinger Wave Equation in 2+1 Dimensions with a... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Lattice Quantum Algorithm for the Schrödinger Wave Equation in 2+1 Dimensions with a Demonstration by Modeling Soliton Instabilities

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Publisher
Springer US
Copyright
Copyright © 2006 by Springer Science+Business Media, Inc.
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-005-0008-8
Publisher site
See Article on Publisher Site

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 24, 2006

References

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