Protected gates for topological quantum field theories (Prof. R. König)
11:30 - 14:00
Prof. Robert König, TUM, München
Herbert Walther Lecture Hall
MPQ, Theory Division
We give restrictions on locality-preserving unitary automorphisms U, which are protected gates, for 2-dimensional topologically ordered systems.
For generic anyon models, we show that such unitaries only generate a
finite group, and hence do not provide universality. For non-abelian
models, we find that such automorphisms are very limited: for example,
there is no non-trivial gate for Fibonacci anyons. More generally,
systems with computationally universal braiding have no such gates. For
Ising anyons, protected gates are elements of the Pauli group.
results are derived by relating such automorphisms to symmetries of the
underlying anyon model: protected gates realize automorphisms of the
Verlinde algebra. We additionally use the compatibility with basis
changes to characterize the logical action.
This is joint work with M.
Beverland, O. Buerschaper, F. Pastawski, J. Preskill and S. Sijher.