Result: Quantum Walks on the Line with Phase Parameters : Foundations of Computer Science - Mathematical Foundations and Applications of Computer Science and Algorithms

Title:
Quantum Walks on the Line with Phase Parameters : Foundations of Computer Science - Mathematical Foundations and Applications of Computer Science and Algorithms
Authors:
VILLAGRA, Marcos, NAKANISHI, Masaki, YAMASHITA, Shigeru, NAKASHIMA, Yasuhiko
Source:
IEICE transactions on information and systems. 95(3):722-730
Publisher Information:
Oxford: Oxford University Press, 2012.
Publication Year:
2012
Physical Description:
print, 23 ref
Original Material:
INIST-CNRS
Subject Terms:
Electronics, Electronique, Computer science, Informatique, Telecommunications, Télécommunications, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Generalites, General, Physiques classique et quantique: mécanique et champs, Classical and quantum physics: mechanics and fields, Information quantique, Quantum information, Calcul quantique, Quantum computation, Analyse Fourier, Fourier analysis, Approche probabiliste, Probabilistic approach, Enfoque probabilista, Approximation asymptotique, Asymptotic approximation, Aproximación asintótica, Calcul quantique, Quantum computing, En ligne, On line, En línea, Equation forme close, Closed form equation, Ecuación forma cerrada, Loi probabilité, Probability distribution, Ley probabilidad, Marche aléatoire, Random walk, Modèle marche aléatoire, Random walk model, Modelo marcha aleatoria, Méthode approchée, Approximate method, Método aproximado, Méthode combinatoire, Combinatorial method, Método combinatorio, Opérateur, Operator, Operador, Temps discret, Discrete time, Tiempo discreto, Traitement en ligne, On line processing, Tratamiento en línea, 0367L, asymptotic approximation, quantum computation, quantum walks, random walks
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma-shi, 630― 0192, Japan
Faculty of Education, Art and Science, Yamagata University, Yamagata-shi, 990―8560, Japan
Department of Computer Science, Ritsumeikan University, Kusatsu-shi, 525―8577, Japan
ISSN:
0916-8532
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=25577215
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Theoretical physics
Accession Number:
edscal.25577215
Database:
PASCAL Archive

Further Information

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step toward this objective, the following question is being addressed: Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps? This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin operator (Hadamard operator) for walks on the line. Even considering only walks on lines, generalizing these computations to a general S U(2) coin operator is a complex task. The main contribution is a closed-form formula for the amplitudes of the state of the walk (which includes the question above) for a general symmetric S U(2) operator for walks on the line. To this end, a coin operator with parameters that alters the phase of the state of the walk is defined. Then, closed-form solutions are computed by means of Fourier analysis and asymptotic approximation methods. We also present some basic properties of the walk which can be deducted using weak convergence theorems for quantum walks. In particular, the support of the induced probability distribution of the walk is calculated. Then, it is shown how changing the parameters in the coin operator affects the resulting probability distribution.