arXiv subjects

Aygul Azatovna Galimova

Publications and source records attributed to Aygul Azatovna Galimova.

4 recordsLinked to original sources

arXiv2026

Erasure Thresholds for Hyperbolic and Semi-Hyperbolic Surface Codes

We extend the circuit-level erasure noise model and Wang et al.\ quadratic expansion fitting of Chang et al.\ from planar surface codes to hyperbolic CSS surface codes. Under Chang et al.'s noise models, the $\{8,3\}$ Bolza fine-grained family threshold reaches $3.6\%$ under the general-Pauli models (which coincide at temporal resolution $η= 1$) and $4.7\%$ under the tailored spatially perfect model at $R_e = 1$ (pure erasure). The corresponding erasure-to-Pauli ratios ($5.0\times$ and $6.5\times$) match the surface code values to within $5\%$. Per-observable crossing-point analysis at $R_e = 1$ (Models 1--3) independently yields an erasure-to-Pauli ratio of $5.3\times$. These results establish that the erasure advantage extends to hyperbolic codes.

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arXiv2026

Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

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. Under ancilla-based Entangling Measurement (EM3) noise, all three families achieve a threshold of ${\sim}1.5\%$. With a native pair-measurement depolarizing model (SDEM3), thresholds are ${\sim}1.0$--$1.2\%$. For heralded photon loss, the $\{8,3\}$ family achieves ${\sim}8.5$--$9\%$, exceeding the planar honeycomb threshold of ${\sim}6.3\%$. In the multi-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. We present the first photon loss and SPOQC-2 thresholds for hyperbolic Floquet codes.

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arXiv2026

Independent Trivariate Bicycle Codes

We introduce six independent trivariate bicycle (ITB) codes, which extend the bivariate bicycle framework of Bravyi et al.\ to three cyclic dimensions. Using asymmetric polynomial pairs on three-dimensional tori, we construct four codes including a $[[140,6,14]]$ code with $kd^2/n = 8.40$. In the code-capacity setting, the $[[140,6,14]]$ code achieves a pseudothreshold of $8.0\%$ and $kd^2/n = 8.40$, exceeding the best multivariate bicycle code of Voss et al.\ ($7.9\%$, $kd^2/n = 2.67$). With circuit-level depolarizing noise, pseudothresholds reach $0.59\%$ for $[[140,6,14]]$ and $0.53\%$ for $[[84,6,10]]$. On the SI1000 superconducting noise model, the $[[140,6,14]]$ code achieves a per-round per-observable rate of $5.6 \times 10^{-5}$ at $p = 0.20\%$. We additionally present two self-dual codes with weight-8 stabilizers: $[[54,14,5]]$ ($kd^2/n = 6.48$) and $[[128,20,8]]$ ($kd^2/n = 10.0$). These results expand the design space of algebraic quantum LDPC codes and demonstrate that the third cyclic dimension yields competitive candidates for practical fault-tolerant implementations.

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arXiv2026

Distributed Hyperbolic Floquet Codes under Depolarizing and Erasure Noise

Distributing qubits across quantum processing units (QPUs) connected by shared entanglement enables scaling beyond monolithic architectures. Hyperbolic Floquet codes use only weight-2 measurements and are good candidates for distributed quantum error correcting codes. 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 and distribute them across QPUs via spectral bisection. The $\{10,3\}$ and $\{12,3\}$ families are new to hyperbolic Floquet codes. We simulate these distributed codes under four noise models: depolarizing, SDEM3, correlated EM3, and erasure. With depolarizing noise ($p_{\text{local}} = 0.03\%$), fine-grained codes achieve non-local pseudo-thresholds up to 3.0\% for $\{8,3\}$, 3.0\% for $\{10,3\}$, and 1.75\% for $\{12,3\}$. Correlated EM3 yields pseudo-thresholds up to 0.75\% for $\{8,3\}$, 0.75\% for $\{10,3\}$, and 0.50\% for $\{12,3\}$; crossing-based thresholds from same-$k$ families are ${\sim}1.75$--$2.9\%$ across all tessellations. Using the SDEM3 model, fine-grained codes achieve distributed pseudo-thresholds of 1.75\% for $\{8,3\}$, 1.25\% for $\{10,3\}$, and 1.00\% for $\{12,3\}$. Under erasure noise motivated by spin-optical architectures, thresholds at 1\% local loss are 35--40\% for $\{8,3\}$, 30--35\% for $\{10,3\}$, and 25--30\% for $\{12,3\}$.

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