Topological Quantum Programming in TED-K
summary
Describes a concrete programming scheme that encodes SU(2) anyon wavefunctions (Majorana/Ising and Fibonacci) as twisted equivariant differential K-cohomology classes and implements their braid gates as path-lifting in cohesive HoTT. Claims the bundle of conformal blocks is expressible in a few lines of dependent-homotopy-type code so that braid representations become transport/executions, and a prototype type-checker via Agda-flat can both verify programs and classically simulate the intended topological q-bit dynamics.
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chapters (16)
- 0:00Topological quantum programming intro
- 0:24Why topological quantum computation matters
- 1:09Anion braiding for quantum gates
- 2:36SU2 WZW model in quantum programming
- 3:59Dependently typed languages for TQP
- 5:00Homotopy type theory foundations
- 8:12Braid groups and quantum gates
- 10:39Three key observations on TQP
- 11:42Conformal block bundles in type theory
- 13:27Implementing conformal blocks in HoTT
- 16:39TQP language in ACTA
- 17:01Evaluating topological quantum circuits
- 17:43Twisted differential K-theory
- 19:28Cohesive HoTT for physics
- 20:53Future directions in quantum programming
- 21:15Q&A
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