Search for tag: "tqft"

Meeting 14.1: Computational complexity of TQFT invariants

I give lightening overview of what is known about the computational complexity of TQFT invariants like the Jones polynomial.

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From  Eric Samperton 89 plays 0  

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…

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From  Eric Samperton 24 plays 0  

Meeting 11.2: Topological quantum computing III

We discuss extended (2+1)-dimensional TQFTs, and show how the structure of an extended TQFT allows us to localize the state spaces of surfaces by cutting them up into subsurfaces.

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From  Eric Samperton 30 plays 0  

Meeting 11.1: Topological quantum computing II

We mostly say more about (2+1)-dimensional unitary TQFTs. In particular, we define the quantum representations of mapping class groups of surfaces determined by a TQFT. We also begin to show one…

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From  Eric Samperton 36 plays 0  

Meeting 10.1: From TQFT to TQC, Part 1

I begin a probably-too-zoomed-out overview of the historical development of ideas that begin with topological quantum field theory (TQFT) and lead to topological quantum computation (TQC). A list of…

From  Eric Samperton 48 plays 0