Foliated Quantum Codes, with a chance of Anyonic Time

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Raussendorf introduced a powerful model of fault tolerant measurement based quantum computation, which can be understood as a layering (or “foliation”) of a multiplicity of Kitaev’s toric code. I will discuss our generalisation of Raussendorf’s construction to an arbitrary CSS code. We call this a Foliated Quantum Code. Decoding this foliated construction is not necessarily straightforward, so I will discuss an example in which we foliate a family of finite-rate quantum turbo codes, and present the results of numerical simulations of the decoder performance.

If I have time, I will discuss some ongoing work (with Gavin Brennan) on relational time applied to topological quantum field theories, in particular, how anyonic systems with essentially trivial dynamics can still exhibit correlations that track “time".