On the digraph of a unitary matrix

SIAM Journal on Matrix Analysis and Applications

Volumn 25, Issue 1, 2004, Pages 295-300

  Severini, Simone ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Digraphs; Quantum random walks; Unitary matrices

Indexed keywords

EID: 1342267534     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479802410293     Document Type: Article

References (12)

1. [ABNVW01] A. AMBAINIS, E. BACH, A. NAYAK, A. VISHWANATH, AND J. WATROUS, One-dimensional quantum walks, in Proceedings of the 33rd ACM Symposium on Theory of Computing, ACM, New York, 2001, pp. 50-59.
2. [AKV01] A. AMBAINIS, J. KEMPE, AND U. VAZIRANI, Quantum walks on graphs, in Proceedings of the 33rd ACM Symposium on Theory of Computing, ACM, New York, 2001, pp. 60-69.
3. [BR91] R. A. BRUALDI AND H. J. RYSER, Combinatorial Matrix Theory, Encyclopedia of Mathematics and Its Applications 39, Cambridge University Press, Cambridge, UK, 1991.
4. [CvL91] P. J. CAMERON AND J. H. VAN LINT, Designs, Graphs, Codes and Their Links, London Mathematical Society Student Texts 22, Cambridge University Press, Cambridge, UK, 1991.
5. [GZ98] P. M. GIBSON AND G.-H. ZHANG, Combinatorially orthogonal matrices and related graphs, Linear Algebra Appl., 282 (1998), pp. 83-95.
6. [GZe88] G. GRÖSSINGER AND A. ZEILINGER, Quantum cellular automata, Complex Systems, 2 (1988), pp. 197-208.
7. [G88] S. GUDDER, Quantum Probability, Academic Press, New York, 1988.
8. [L93] L. LOVÁSZ, Random walks on graphs: A survey, in Combinatorics, Paul Erdös is Eighty, Vol. 2, Bolyai Soc. Math. Stud. 2, János Bolyai Math. Soc., Budapest, 1996, pp. 353-397.
9. [M96] D. MEYER, From quantum cellular automata to quantum lattice gases, J. Statist. Phys., 85 (1996), pp. 551-574.
10. [P96] E. PRISNER, Line graphs and generalizations: A survey, in Surveys in Graph Theory, Congr. Numer. 116, G. Chartrand and M. Jacobson, eds., University of Manitoba, Winnipeg, Manitoba, Canada, 1996, pp. 193-230.
11. [T99] A. TERRAS, Fourier Analysis on Finite Groups and Applications, London Mathematical Society Student Texts 43, Cambridge University Press, Cambridge, UK, 1999.
12. [T84] W. T. TUTTE, Graph Theory, Encyclopedia of Mathematics and Its Applications 21, Cambridge University Press, Cambridge, UK, 1984.