[quantum-info] PiQuDos seminar Wednesday Nov 2 - David Poulin

Daniel Brod dbrod at perimeterinstitute.ca
Mon Oct 31 09:01:13 EDT 2016


Dear all

Please join us on Wednesday, Nov 2 at 4pm in the Time room for a quantum
information seminar by David Poulin.

***
Title: Fault-tolerant quantum error correction with non-abelian anyons

Abstract: Non-abelian anyons have drawn much interest due to their
suspected existence in two-dimensional condensed matter systems and for
their potential applications in quantum computation. In particular, a
quantum computation can in principle be realized by braiding and fusing
certain non-abelian anyons. These operations are expected to be
intrinsically robust due to their topological nature. Provided the system
is kept at a temperature T lower than the spectral gap, the density of
thermal excitations is suppressed by an exponential Boltzman factor. In
contrast to the topological protection however, this thermal protection is
not scalable: thermal excitations do appear at constant density for any
non-zero temperature and so their presence is unavoidable as the size of
the computation increases. Thermally activated anyons can corrupt the
encoded data by braiding or fusing with the computational anyons.

In the present work, we generalize a fault-tolerant scheme introduced by
Harrington for the toric-code to the setting of non-cyclic modular anyons.
We prove that the quantum information encoded in the fusion space of a
non-abelian anyon system can be preserved for arbitrarily long times with
poly-log overhead. In particular, our model accounts for noise processes
which lead to the creation of anyon pairs from the vacuum, anyon diffusion,
anyon fusion as well as errors in topological charge measurements.
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