1. Perfect state transfer on quotient graphs
- Author
-
Michael Landry, Jessica Fuller, Michael C. Opperman, Eric Fredette, A. Tollefson, Christino Tamon, and R. Bachman
- Subjects
Nuclear and High Energy Physics ,General Physics and Astronomy ,FOS: Physical sciences ,0102 computer and information sciences ,01 natural sciences ,Quotient graph ,Theoretical Computer Science ,Combinatorics ,symbols.namesake ,Chordal graph ,Trivially perfect graph ,0103 physical sciences ,Perfect graph theorem ,Quantum walk ,010306 general physics ,Mathematical Physics ,Quotient ,Mathematics ,Discrete mathematics ,Quantum Physics ,Strong perfect graph theorem ,Statistical and Nonlinear Physics ,Cartesian product ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,symbols ,Quantum Physics (quant-ph) - Abstract
We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph $G$ has perfect state transfer if and only if its quotient $G/\pi$, under any equitable partition $\pi$, has perfect state transfer, we exhibit graphs with perfect state transfer between two vertices but which lack automorphism swapping them. This answers a question of Godsil (Discrete Mathematics 312(1):129-147, 2011). We also show that the Cartesian product of quotient graphs $\Box_{k} G_{k}/\pi_{k}$ is isomorphic to the quotient graph $\Box_{k} G_{k}/\pi$, for some equitable partition $\pi$. This provides an algebraic description of a construction due to Feder (Physical Review Letters 97, 180502, 2006) which is based on many-boson quantum walk., Comment: 20 pages, 10 figures
- Published
- 2011