Related papers: Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

URL: http://arxiv.org/abs/2602.22906v1
Date: Thu, 26 Feb 2026 11:51:08 GMT
Title: Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing
Authors: Aygul Azatovna Galimova,
Abstract summary: We construct hyperbolic and semi-hyperbolic Floquet codes from $8,3$, $10,3$, and $12,3$ tessellations.<n>The $10,3$ and $12,3$ families are new to hyperbolic Floquet codes.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Tailoring error correcting codes to the structure of the physical noise can reduce the overhead of fault-tolerant quantum computation. Hyperbolic Floquet codes use only weight-2 measurements and can be implemented directly on hardware with native pair measurements. We construct hyperbolic and semi-hyperbolic Floquet codes from $\{8,3\}$, $\{10,3\}$, and $\{12,3\}$ tessellations via the Wythoff kaleidoscopic construction with the Low-Index Normal Subgroups (LINS) algorithm. The $\{10,3\}$ and $\{12,3\}$ families are new to hyperbolic Floquet codes. We evaluate these codes under four noise models: phenomenological, ancilla Entangling Measurement (EM3), Single-step Depolarizing EM3 (SDEM3), and erasure. Under phenomenological noise, specific-logical threshold crossings occur near $p_e \approx 0.3$--$0.5\%$ for $\{8,3\}$ ($k=6$--$56$) and $0.15$--$0.2\%$ for $\{10,3\}$ ($k=12$--$146$). EM3 ancilla noise yields a threshold of ${\sim}1.5\%$ for all three families. SDEM3 is a depolarizing noise model motivated by Majorana tetron architectures; fine-grained codes achieve thresholds of ${\sim}1.0$--$1.2\%$ for all three families. The erasure model captures detected photon loss on spin-optical links; fine-grained codes achieve erasure thresholds of ${\sim}8.5$--$9\%$ for $\{8,3\}$, ${\sim}7$--$8\%$ for $\{10,3\}$, and ${\sim}6.5$--$8\%$ for $\{12,3\}$. Photon loss is the dominant error source in photon-mediated quantum computing. Under the full three-parameter SPOQC-2 noise model, the $\{8,3\}$ codes achieve a 2D fault-tolerant area $2.2\times$ that of the surface code compiled to pair measurements while encoding $k = 10$ logical qubits. In a companion paper, we evaluate the same code families in a distributed setting.

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