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

Isaac Kim ikim at perimeterinstitute.ca
Wed Dec 16 11:27:51 EST 2015


Reminder: There is a talk today at 4PM in the Time room by 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 Tue, Dec 15, 2015 at 8:02 AM, Isaac Kim <ikim at perimeterinstitute.ca>
wrote:

> 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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