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Meeting 12.2: Topological quantum computing IV

We show that if an extended unitary TQFT supports a quantum representation of a braid group with image that is dense inside of the unitary group of an appropriate state space, then the TQFT can be…

From  Eric Samperton 16 plays 0  

Meeting 10.2: Topological quantum computing I

Continuing to follow Kitaev, we consider the toric code as the ground state space of a Hamiltonian constructed from the vertex and plaquette operators. The other eigenspaces of this Hamiltonian are…

From  Eric Samperton 67 plays 0  

Meeting 3.1: More on knots, and building knot diagrams from braid words

We combinatorialize tame knots using stick presentations, then form knot diagrams by taking regular projections onto a plane. I explain two ways to convert a word in the generators of Artin's…

From  Eric Samperton 28 plays 0