Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes

Explore the construction and performance of hyperbolic and semi-hyperbolic Floquet codes in this 38-minute talk by Oscar Higgott from Google, presented at the Simons Institute's "Advances in Quantum Coding Theory" series. Delve into the creation of Floquet code families derived from colour code tilings of closed hyperbolic surfaces, featuring weight-two check operators, finite encoding rates, and efficient decoding through minimum-weight perfect matching. Examine the development of semi-hyperbolic Floquet codes with enhanced distance scaling, obtained through a fine-graining procedure. Analyze the efficiency of these codes compared to planar honeycomb and surface codes under various noise models, including direct two-qubit measurements and circuit-level depolarizing noise. Discover the potential for significant improvements in qubit efficiency, with semi-hyperbolic Floquet codes demonstrating up to 48x better performance than planar honeycomb codes and over 100x better than certain surface code implementations. Learn about the teraquop footprint reduction to just 32 physical qubits per logical qubit at 0.1% noise strength. Conclude with an analysis of small-scale implementations suitable for near-term experiments, including a Floquet code based on the Bolza surface that encodes four logical qubits into 16 physical qubits.