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Topological phases have been extensively investigated in both theory and experiment in the condensed matter physics and ultracold atoms. This rapidly developing field has brought about a lot of new co...
Models for topological quantum computation are based on braiding and fusing anyons (quasi- particles of fractional statistics) in (2+1)-D. The anyons that can exist in a physical theory are determine...
We describe the hashing technique to obtain a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements ofa universal basis. The hashing exploits ...
Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperkähler manifold. They conjectured that this theory has an associated TQFT, with vector spaces given by certai...
We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrica...
Quantum phase transitions that take place between two distinct topological phases remain an unexplored area for the applicability of the fidelity approach. Here, we apply this method to spin systems i...

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