[quantum-info] *TWO* PIQuDos seminar this week(W&Th)

[Isaac Kim]

We have two PIQuDos seminar this week.

On Dec 16 at 4PM in the Time room, we have Michael Jarret.

Title: Spectral graph theory applied to simulated stoquastic adiabatic
optimization

Abstract: Quantum adiabatic optimization (QAO) slowly varies an initial
Hamiltonian with an easy-to-prepare ground-state to a final Hamiltonian
whose ground-state encodes the solution to some optimization problem.
Currently, little is known about the performance of QAO relative to
classical optimization algorithms as we still lack strong analytic tools
for analyzing its performance. In this talk, I will unify the problem of
bounding the runtime of one such class of Hamiltonians -- so-called
stoquastic Hamiltonians -- with questions about functions on graphs, heat
diffusion, and classical sub-stochastic processes. I will introduce new
tools for bounding the spectral gap of stoquastic Hamiltonians and, by
exploiting heat diffusion, show that one of these techniques also provides
an optimal and previously unknown gap bound for particular classes of
graphs. Using this intuition and combining heat diffusion with classical
sub-stochastic processes, I will offer a classical adiabatic algorithm that
exhibits behavior typically considered "quantum", such as tunneling.


On Dec 17 at 11AM in the Time room, we have Shawn Cui.

Title: Topological quantum computation and compilation

Abstract:Topological quantum computation is a fault tolerant protocol for
quantum computing using non-abelian topological phases of matter.
Information is encoded in states of multi-quasiparticle
excitations(anyons), and quantum gates are realized by braiding of anyons.
The mathematical foundation of anyon systems is described by unitary
modular tensor categories. We will show one can encode a qutrit in four
anyons in the SU(2)_4 anyon system, and universal qutrit computation is
achieved by braiding of anyons and one projective measurement which checks
whether the total charge of two anyons is trivial. We will also give an
algorithm to approximate an arbitrary quantum gate with the ones from the
anyon system. The algorithm produces more efficient circuits than the
Solovay-Kitaev algorithm.
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