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Paper 1

Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes

Oscar Higgott, Nikolas P. Breuckmann

Year

2023

Journal

arXiv preprint

DOI

arXiv:2308.03750

arXiv

2308.03750

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 Floquet code derived from the Bolza surface that encodes four logical qubits into 16 physical qubits.

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Paper 2

ADaPT: Adaptive-window Decoding for Practical fault-Tolerance

Tina Oberoi, Joshua Viszlai, Frederic T. Chong

Year

2026

Journal

arXiv preprint

DOI

arXiv:2605.01149

arXiv

2605.01149

Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through parallelization and reducing reaction time via speculation on window boundaries. However, these methods use a fixed window size d, paying a fixed decoding time overhead for each window. In practice, we find this overhead of a fixed window size unnecessary in many cases due to the sparsity of average-case errors in QEC. Leveraging this insight, in this paper we propose an adaptive window decoding technique based on decoder confidence. This technique reduces the overhead in decoding time thus reducing reaction time without compromising on logical error rates. We benchmark adaptive window decoding across different codes and hardware inspired noise models. Our results show that this adaptive technique reaches the target error rate while maintaining a low decoding time overhead across different codes, and under different noise models.

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