Friday, October 1, 2010 3:30 pm
-
4:30 pm
EDT (GMT -04:00)
State Transfer on Graphs
| Speaker: | Chris Godsil |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics & Computer Building (MC) 5158 |
Abstract:
If A is the adjacency matrix of a graph X, then the matrix
| H(t) := exp(iAt) |
is
the
transition
matrix
of
a
so-called
continuous
quantum
walk
on X.
In
this
context
we
say
that
we
have perfect
state
transfer from
a
vertex u to
a
vertex v at
time
τ
if
the uv-entry
of H(τ)
has
absolute
value
1.
One
fundamental
problem
is
to
characterize
the
pairs
of
vertices
where
perfect
state
transfer
occurs.
In
all
cases
where
it
does,
there
is
an
automorphism
of
order
two
of X that
swaps u and v,
but
it
is
not
clear
whether
this
condition
is
necessary.
My
talk
will
provide
an
introduction
to
this
problem,
and
to
some
recent
work
in
the
area.