One of the primary
barriers to continued experimental advances in quantum computing is the
basic problem of "quantum error correction". The difficulties arise
from a need to control and maintain features of open
quantum systems as they evolve in time. Recently a unified
approach to quantum error correction was introduced -- called "operator
quantum error correction" -- that has enabled the study of
error-correcting subsystems for arbitrary quantum operations. As
special cases the approach includes standard error-correcting
(subspace) codes and "noiseless" (or "decoherence-free") subspaces and
subsystems.
I will begin this talk with a brief introduction to some
relevant mathematical aspects, such as completely positive maps. Then
I'll discuss the basic framework and results for operator quantum error
correction, focusing on a recently developed structure theory for
noiseless subsystems. Time permitting, I will also discuss a
generalized notion of noiseless subsystems that captures all
error-correcting subsystems.
This talk is based on joint works with Raymond Laflamme,
David Poulin, Maia Lesosky, Man-Duen Choi, and Robert Spekkens.
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For those considering coming from Dublin, there is a commuter train to
Maynooth which is leaving Dublin-Pearse Street Station at 14:15pm and
arriving to Maynooth at 14:57 pm. More information about how to reach
NUI Maynooth is available at
http://www.nuim.ie/location/.