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Quasi-Topological Quantum Error Correction Codes

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Existing proposals for topological quantum computation have encountered

difficulties in recent years in the form of several ``obstructing'' results.

These are not actually no-go theorems but they do present some serious

obstacles. A further aggravation is the fact that the known topological

error correction codes only really work well in spatial dimensions higher

than three. In this talk I will present a method for modifying a higher

dimensional topological error correction code into one that can be embedded

into two (or three) dimensions. These projected codes retain at least some

of their higher-dimensional topological properties. The resulting subsystem

codes are not discrete analogs of TQFTs and as such they evade the usual

obstruction results. Instead they obey a discrete analog of a conformal

symmetry. Nevertheless, there are real systems which have these features,

and if time permits I'll discuss some of these. Many of them exhibit

strange low temperature behaviours that might even be helpful for

establishing finite temperature fault tolerance thresholds.

This research is still very much a work in progress... As such it has

numerous loose ends and open questions for further investigation. These

constructions could also be of interest to quantum condensed matter

theorists and may even be of interest to people who like weird-and-wonderful

spin models in general.