PERFECT STATE TRANSFER ON QUOTIENT GRAPHS

被引：0

作者：

Bachman, Rachel ^{[2
]}

Predette, Eric ^{[2
]}

Fuller, Jessica ^{[3
]}

Landry, Michael ^{[4
]}

Opperman, Michael ^{[2
]}

Tamon, Christino ^{[1
]}

Tollefson, Andrew ^{[5
]}

机构：

[1] Clarkson Univ, Dept Comp Sci, Potsdam, NY 13699 USA

[2] Clarkson Univ, Dept Math, Potsdam, NY 13699 USA

[3] Seton Hall Univ, Dept Math & Comp Sci, S Orange, NJ 07079 USA

[4] Univ Calif Berkeley, Dept Math, Berkeley, CA 94704 USA

[5] Univ Nevada, Dept Math, Reno, NV 89557 USA

来源：

QUANTUM INFORMATION & COMPUTATION | 2012年 / 12卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Quantum walk; perfect state transfer; quotient graphs; equitable partitions; QUANTUM WALKS;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph C 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 a square(k)G(k)/pi(k) is isomorphic to the quotient, graph square(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.

引用

页码：293 / 313

页数：21

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