Continuous-Time Quantum Walk

time

8.83

graph

11

start

1

A continuous-time quantum walk (CTQW) on a graph

G=(V,E)

, where

V

is the set of vertices (nodes) and

E

is the set of edges connecting the nodes, is defined as follows: Let

A

be the

|V|×|V|

adjacency matrix of

G

. The continuous-time quantum walk on the graph

G

is then defined by the unitary matrix

U(t)=

-At

e

, where

i

is the imaginary unit and

t∈

. The probability

p

of a walk starting at vertex

u

ending up at vertex

v

at time

t

is given by

2

〈u|U(t)|v〉

. The size and color of vertex

v

represent

p

when the system is measured.