Vine codes generalize directional codes to open planar boundaries, delivering up to 28% fewer data/measure qubits at circuit distance 7 and better simulated performance than the surface code at 10^{-3} noise while using fewer total qubits.
A matching decoder for bivariate bicycle codes
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the minimum-weight perfect matching algorithm, a subroutine invaluable to decoding topological codes, to decode bivariate bicycle codes. Using the equivalence of bivariate bicycle codes to copies of the toric code, we propose a method we call the `cylinder trick' to rapidly find a correction using matching on code symmetries. We benchmark our decoder on the gross code family, cyclic hypergraph-product codes, generalized toric codes, and recently proposed directional codes under code capacity and phenomenological noise models, demonstrating the general applicability of our protocol. For a subset of these codes, we find that our decoder can be significantly improved by augmenting matching with strategies including belief propagation and `over-matching', thus achieving performance competitive with state-of-the-art approaches.
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quant-ph 6years
2026 6roles
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Proves that minimum-weight decoding of 2D TTI stabilizer codes admits a PTAS by reducing the problem to Euclidean geometric approximation tasks such as TSP when errors are modeled as point-like excitations connected by strings.
The HGP/LP Tanner graph spectral ratio equals (1+β_base)/2 and BB code spectra reduce to lm independent 2×2 SVDs, enabling a multi-layer AOL routing protocol with constant per-cycle depth.
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.
Geometry choices in bivariate-bicycle qLDPC syndrome extraction determine leading correlated error structure via weighted exposure, which correlates strongly with logical error rates and is reduced by biplanar layouts.
citing papers explorer
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Vine Codes: Low-Overhead Quantum LDPC Codes on a Planar Square Grid
Vine codes generalize directional codes to open planar boundaries, delivering up to 28% fewer data/measure qubits at circuit distance 7 and better simulated performance than the surface code at 10^{-3} noise while using fewer total qubits.
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A polynomial-time approximation scheme for minimum-weight decoding of topological codes
Proves that minimum-weight decoding of 2D TTI stabilizer codes admits a PTAS by reducing the problem to Euclidean geometric approximation tasks such as TSP when errors are modeled as point-like excitations connected by strings.
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Using Tanner Spectral Reduction to Improve Multi-Layer Optical Lattice Routing for Hypergraph-Product and Bivariate Bicycle qLDPC Codes
The HGP/LP Tanner graph spectral ratio equals (1+β_base)/2 and BB code spectra reduce to lm independent 2×2 SVDs, enabling a multi-layer AOL routing protocol with constant per-cycle depth.
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Translation-invariant quantum low-density parity-check codes from compactified fracton models
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.
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Geometry-induced correlated noise in qLDPC syndrome extraction
Geometry choices in bivariate-bicycle qLDPC syndrome extraction determine leading correlated error structure via weighted exposure, which correlates strongly with logical error rates and is reduced by biplanar layouts.
- Topological Codes from Space Groups: A Route beyond Translation Invariance