Computing with Solitons: A Review and Prospectus

Jakubowski, Mariusz; Steiglitz, K.; Squier, Richard K.

doi:10.1007/978-1-4471-0129-1_10

Cited by 34 publications

(36 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, we only list the indexes (i, j) of nonzero elements. Y = {(1, 2), (1, 44), (2, 3), (2, 119), (3,4), (4, 5), (4, 58), (5,6), (6, 7), (7, 8), (7,89), (8,9), (9, 10), (10,11), (10,15), (11,12), (12,13), Figure 8: Graph representation for the subsystem Λ A of a non-stationary localisation with velocity 1/5, it is the same mobile localisation calculated with a de Bruijn diagram showed in Fig. 7.…”

Section: Subsystem Diagramsmentioning

confidence: 99%

Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs

Mart́ınez

Adamatzky

Chen

et al. 2017

Emergence, Complexity and Computation

View full text Add to dashboard Cite

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders. * Chapter published in the book Swarm Dynamics as a Complex Network, Springer, (Ivan Zelinka and Guanrong Chen Eds.), chapter 12, pages 241-264, 2017.

show abstract

Section: Subsystem Diagramsmentioning

confidence: 99%

Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs

Mart́ınez

Adamatzky

Chen

et al. 2017

Emergence, Complexity and Computation

View full text Add to dashboard Cite

show abstract

“…[2] Significantr esults haveb eeno btainedi nc ollision-basedc omputingw iths olitons, [3][4][5][6] includingc onstructiono ff unctionally completes etso f logic gates, [7] information transferb etween colliding solitons, [8] computationv ia phase coding, [1] quantum computingv ia the entanglement of solitons in theF renkel-Kontorova model. [9] Gliders in cellular automataare discretephenomenological analogieso fs olitons.…”

Section: Introductionmentioning

confidence: 99%

Computing in Verotoxin

Adamatzky

2017

ChemPhysChem

View full text Add to dashboard Cite

We develop an excitable automata model of a protein verotoxin and demonstrate that logic gates and circuits are realised in the model via interacting patterns of excitation. By sampling potential input pairs of nodes, we calculate frequencies of logic gates which occurred in the verotoxin model for various parameters of node excitation rules. We show that overall the gates can be arranged in the following hierarchy of descending frequencies: AND>OR>AND‐NOT>XOR. We demonstrate realisations of one‐bit half‐adder and controlled‐not gates and estimate memory capacity of the verotoxin molecule.

show abstract

“…The NLS equation is pivotal in non-linear optics, (1) plasma physics (2) as well as in ideas for information transfer in optical computers. (3,4) In 1+1 dimensions, both the focusing and defocusing NLS equations are exactly integrable and exhibit soliton solutions. Here, we develop and test a quantum lattice representation of the (focusing) NLS equation in 2+1 dimensions i∂ t ψ + ∂ xx ψ + ∂ yy ψ + 2|ψ| 2 ψ = 0.…”

Section: Introductionmentioning

confidence: 99%

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

Yepez

Vahala

2006

Quantum Inf Process

View full text Add to dashboard Cite

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.KEY WORDS: Non-linear Schrödinger wave equation; quantum algorithm; soliton dynamics; non-linear quantum mechanical instability; quantum computing; computational physics.

show abstract

Computing with Solitons: A Review and Prospectus

Cited by 34 publications

References 27 publications

Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs

Simple Networks on Complex Cellular Automata: From de Bruijn Diagrams to Jump-Graphs

Computing in Verotoxin

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

Contact Info

Product

Resources

About