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Continuous-Time Quantum Walk

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8.83
graph
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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.
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