Title: Quantum walks on regular graphs
| Speaker: | Krystal Guo |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
A
quantum
walk
is
a
quantum
process
on
a
graph,
which
can
be
used
to
implement
a
universal
model
of
quantum
computation.
In
this
talk,
we
will
discuss
discrete-time
quantum
walks.
Emms,
Hancock,
Severini
and
Wilson
proposed
a
graph
isomorphism
routine
for
the
class
of
strongly
regular
graphs,
based
on
the
spectrum
of
a
matrix
related
to
the
discrete-time
quantum
walk.
We
give
counterexamples
to
this
conjecture.
Another
matrix
related
to
the
discrete-time
quantum
walk
has
been
independently
studied
as
the
Bass-Hashimoto
edge
adjacency
operator,
in
the
context
of
the
Ihara
zeta
function
of
graphs.
We
find
its
spectrum
for
the
class
of
regular
graphs.
We
will
also
discuss
a
result
about
the
cycle
space
of
line
digraphs
of
graphs,
which
is
motivated
by
the
previous
problems.