Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media
Abstract
To obtain stable vortex structures in three-dimensional (3D) nonlinear optics, Efremidis et al. (2007) have introduced a generalized Nonlinear Schrodinger equation (NLS) in which the transverse quantum vortex components are stabilized by a longitudinal bright soliton: i.e., the elliptic operator ∇2 is replaced by its hyperbolic counterpart . A new 3D mesoscopic qubit unitary lattice algorithm is developed for this generalized NLS. One introduces 2 qubits for each lattice site and entangles them with a local unitary collision operator. This entanglement is then spread throughout the lattice by nearest neighbor streaming. These interwined operators lead to an extremely well parallelized code on classical supcomputers while their unitary structure will permit encoding onto a quantum computer. Somewhat unexpectedly, the hyperbolic operator can be realized from variations in the collision operator, without introducing variations in the streaming operator. The initial line vortices are generated by Pade asymptotics. The energy constraint is conserved to 10 digit accuracy.
- Authors:
-
- Old Dominion Univ., Norfolk, VA (United States)
- College of William and Mary, Williamsburg, VA (United States)
- Rogers State Univ., Claremore, OK (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Univ. of Hawaii at Manoa, Honolulu, HI (United States)
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
- OSTI Identifier:
- 1609000
- Alternate Identifier(s):
- OSTI ID: 1547566
- Grant/Contract Number:
- FC02-01ER54648; FG02-91ER54109; #DE-FG02-91ER-54109
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Communications in Nonlinear Science and Numerical Simulation
- Additional Journal Information:
- Journal Volume: 75; Journal ID: ISSN 1007-5704
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 3D solitons; Gross-Pitaevskii equation; unitary qubit lattice algorithm; nonlinear optics
Citation Formats
Vahala, Linda, Vahala, George, Soe, Min, Ram, Abhay, and Yepez, Jeffrey. Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media. United States: N. p., 2019.
Web. doi:10.1016/j.cnsns.2019.03.016.
Vahala, Linda, Vahala, George, Soe, Min, Ram, Abhay, & Yepez, Jeffrey. Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media. United States. https://doi.org/10.1016/j.cnsns.2019.03.016
Vahala, Linda, Vahala, George, Soe, Min, Ram, Abhay, and Yepez, Jeffrey. Sat .
"Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media". United States. https://doi.org/10.1016/j.cnsns.2019.03.016. https://www.osti.gov/servlets/purl/1609000.
@article{osti_1609000,
title = {Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media},
author = {Vahala, Linda and Vahala, George and Soe, Min and Ram, Abhay and Yepez, Jeffrey},
abstractNote = {To obtain stable vortex structures in three-dimensional (3D) nonlinear optics, Efremidis et al. (2007) have introduced a generalized Nonlinear Schrodinger equation (NLS) in which the transverse quantum vortex components are stabilized by a longitudinal bright soliton: i.e., the elliptic operator ∇2 is replaced by its hyperbolic counterpart ∇⊥2-∂2/∂z2. A new 3D mesoscopic qubit unitary lattice algorithm is developed for this generalized NLS. One introduces 2 qubits for each lattice site and entangles them with a local unitary collision operator. This entanglement is then spread throughout the lattice by nearest neighbor streaming. These interwined operators lead to an extremely well parallelized code on classical supcomputers while their unitary structure will permit encoding onto a quantum computer. Somewhat unexpectedly, the hyperbolic operator can be realized from variations in the collision operator, without introducing variations in the streaming operator. The initial line vortices are generated by Pade asymptotics. The energy constraint is conserved to 10 digit accuracy.},
doi = {10.1016/j.cnsns.2019.03.016},
journal = {Communications in Nonlinear Science and Numerical Simulation},
number = ,
volume = 75,
place = {United States},
year = {Sat Mar 30 00:00:00 EDT 2019},
month = {Sat Mar 30 00:00:00 EDT 2019}
}
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Works referenced in this record:
C programs for solving the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap
journal, September 2012
- Vudragović, Dušan; Vidanović, Ivana; Balaž, Antun
- Computer Physics Communications, Vol. 183, Issue 9
Stability of periodic waves of finite amplitude on the surface of a deep fluid
journal, January 1972
- Zakharov, V. E.
- Journal of Applied Mechanics and Technical Physics, Vol. 9, Issue 2
Langmuir solitons in magnetized plasmas
journal, November 1978
- Dysthe, K. B.; Mj lhus, E.; P. cseli, H. L.
- Plasma Physics, Vol. 20, Issue 11
On Davydov's alpha-helix solitons
journal, July 1981
- Hyman, J. M.; McLaughlin, D. W.; Scott, A. C.
- Physica D: Nonlinear Phenomena, Vol. 3, Issue 1-2
Three-Dimensional Vortex Solitons in Self-Defocusing Media
journal, March 2007
- Efremidis, Nikolaos K.; Hizanidis, Kyriakos; Malomed, Boris A.
- Physical Review Letters, Vol. 98, Issue 11
Bright temporal solitonlike pulses in self-defocusing AlGaAs waveguides near 800 nm
journal, January 1996
- Dumais, P.; Aitchison, J. S.; Villeneuve, A.
- Optics Letters, Vol. 21, Issue 4
Snake Instability of a Spatiotemporal Bright Soliton Stripe
journal, February 2004
- Gorza, S. -P.; Roig, N.; Emplit, Ph.
- Physical Review Letters, Vol. 92, Issue 8
Lattice-Gas Quantum Computation
journal, December 1998
- Yepez, Jeffrey
- International Journal of Modern Physics C, Vol. 09, Issue 08
Quantum computation for physical modeling
journal, July 2002
- Yepez, Jeffrey
- Computer Physics Communications, Vol. 146, Issue 3
Quantum lattice gas representation of some classical solitons
journal, April 2003
- Vahala, George; Yepez, Jeffrey; Vahala, Linda
- Physics Letters A, Vol. 310, Issue 2-3
Quantum lattice representations for vector solitons in external potentials
journal, March 2006
- Vahala, George; Vahala, Linda; Yepez, Jeffrey
- Physica A: Statistical Mechanics and its Applications, Vol. 362, Issue 1
Superfluid Turbulence from Quantum Kelvin Wave to Classical Kolmogorov Cascades
journal, August 2009
- Yepez, Jeffrey; Vahala, George; Vahala, Linda
- Physical Review Letters, Vol. 103, Issue 8
Unitary quantum lattice gas algorithm generated from the Dirac collision operator for 1D soliton–soliton collisions
journal, January 2015
- Oganesov, Armen; Vahala, George; Vahala, Linda
- Radiation Effects and Defects in Solids, Vol. 170, Issue 1
Effect of Fourier transform on the streaming in quantum lattice gas algorithms
journal, February 2018
- Oganesov, Armen; Vahala, George; Vahala, Linda
- Radiation Effects and Defects in Solids, Vol. 173, Issue 3-4
Padé approximations of solitary wave solutions of the Gross–Pitaevskii equation
journal, January 2004
- Berloff, Natalia G.
- Journal of Physics A: Mathematical and General, Vol. 37, Issue 5