Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes

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Constructs Floquet codes from colour-code hyperbolic tilings and a fine-grained semi-hyperbolic family, yielding weight-two checks and degree‑three connectivity that decode with minimum‑weight perfect matching. Claims semi‑hyperbolic instances give √n distance scaling via fine‑graining and, under an EM3 pair‑measurement noise model, show up to ~48× improvement over planar honeycomb codes (over 100× vs surface‑code compilations) and a teraquop footprint as low as 32 physical qubits per logical qubit at 0.1% noise. Includes a 16‑qubit Bolza instance encoding four logical qubits and proposes biplanar/modular implementations.

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" chapters (17)

1. 0:00Hyperbolic Floquet codes intro
2. 1:29LDPC codes in quantum error correction
3. 3:37Hyperbolic surface code challenges
4. 5:44Hyperbolic codes with Floquet circuits
5. 7:08Floquet codes overview
6. 11:26Hyperbolic Floquet code construction
7. 13:54Distance in hyperbolic Floquet codes
8. 15:30Bolza Floquet code example
9. 16:55Logarithmic distance limitations
10. 18:01Semi-hyperbolic Floquet codes
11. 20:13Honeycomb vs hyperbolic codes
12. 21:44Noise model simulations
13. 24:17Hardware hyperbolic connectivity
14. 27:11Recent LDPC code work
15. 28:19Future directions and gates
16. 29:25Conclusion
17. 30:07Q&A on distances