A talk that I will have given:
Urs Schreiber$\;$ on joint work with $\;$ Hisham Sati:
Knots for Quantum Computation from Defect Branes
talk at
Workshop on Topological Methods in Mathematical Physics
Erice, 02 Sep 2022
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Abstract. Already 25 years ago, Kitaev proposed that intrinsically fault-tolerant quantum computation should be possible by knotting the worldlines of defect points in effectively 2-dimensional quantum materials akin to graphene. Meanwhile, there have been striking advances (a) in the theoretical understanding of such quantum materials, in terms of topological K-theory and (b) in the practical construction of toy quantum computers – but the “topological quantum gates” proposed by Kitaev have remained somewhat elusive, both practically but also theoretically. Recently we have shown that a previously neglected sector of topological K-theory in its fully-fledged twisted equivariant differential refinement does reflect exactly those topological quantum gates that are thought to be practically realizable – namely the “$SU(2)$-anyon braid quantum gates”. This insight was drawn from the study of “defect branes” in string theory and points to a non-perturbative enhancement of what is known as "holographic" condensed matter theory. I will give a gentle exposition and motivation of these results.
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