Tuesday, June 21, 2016 4:00 pm
-
4:30 pm
EDT (GMT -04:00)
Title: Spectra of Discrete Quantum Walks
| Speaker: | Harmony Zhan |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
Due
to
the
extra
coin
register,
the
relation
between
the
spectrum
of
a
discrete
quantum
walk
and
the
spectrum
of
the
underlying
graph
$X$
is
in
general
unclear.
However,
in
the
model
where
the
transition
matrix
$U$
is
a
product
of
two
reflections,
the
eigenvalues
and
eigenvectors
of
$U$
are
completely
determined
by
those
of
$X$.
In
fact,
$U$
is
closely
related
to
the
directed
line
graph
of
$X$.
We
will
derive
the
spectral
decomposition
of
$U$
and
use
it
to
construct
a
family
of
circulant
graphs
that
admit
perfect
state
transfer.