Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes

• URL: http://arxiv.org/abs/2308.03750v1
• Date: Mon, 7 Aug 2023 17:54:45 GMT
• Title: Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Authors: Oscar Higgott and Nikolas P. Breuckmann
• Abstract summary: We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces. We also construct semi-hyperbolic Floquet codes, which have improved distance scaling.
• Score: 5.33024001730262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces. These codes have weight-two check operators, a finite encoding rate and can be decoded efficiently with minimum-weight perfect matching. We also construct semi-hyperbolic Floquet codes, which have improved distance scaling, and are obtained via a fine-graining procedure. Using a circuit-based noise model that assumes direct two-qubit measurements, we show that semi-hyperbolic Floquet codes can be $48\times$ more efficient than planar honeycomb codes and therefore over $100\times$ more efficient than alternative compilations of the surface code to two-qubit measurements, even at physical error rates of $0.3\%$ to $1\%$. We further demonstrate that semi-hyperbolic Floquet codes can have a teraquop footprint of only 32 physical qubits per logical qubit at a noise strength of $0.1\%$. For standard circuit-level depolarising noise at $p=0.1\%$, we find a $30\times$ improvement over planar honeycomb codes and a $5.6\times$ improvement over surface codes. Finally, we analyse small instances that are amenable to near-term experiments, including a 16-qubit Floquet code derived from the Bolza surface.

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