Cylindrical and M""obius Quantum Codes for Asymmetric Pauli Errors

2025-02-26

AI Summary

Conventional surface codes exhibit suboptimal fault-tolerance under asymmetric Pauli noise—where phase-flip errors dominate bit-flip errors—due to their symmetric stabilizer structure. Method: This work introduces two novel CSS topological quantum codes—the cylindrical code (fully planar) and the Möbius code (quasi-planar with low nonlocality)—unifiedly constructed for the first time via fiber-bundle formalism and algebraic chain complexes. Contribution/Results: We derive rigorous upper bounds on logical error rates, surpassing the performance ceiling of surface codes under asymmetric noise. Under minimum-weight perfect matching (MWPM) decoding, both codes achieve significantly lower logical error rates than the surface code across a broad range of asymmetry ratios. Numerical simulations confirm their enhanced error-correction capability and structural adaptability in highly asymmetric noise environments, establishing a new framework for noise-tailored topological code design.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric errors are critical to mitigating the impact of such impairments. To this aim, several asymmetric quantum codes have been proposed. These include variants of surface codes like the XZZX and ZZZY surface codes, tailored to preserve quantum information in the presence of error asymmetries. In this work, we propose two classes of Calderbank, Shor and Steane (CSS) topological codes, referred to as cylindrical and M""obius codes, particular cases of the fiber bundle family. Cylindrical codes maintain a fully planar structure, while M""obius codes are quasi-planar, with minimal non-local qubit interactions. We construct these codes employing the algebraic chain complexes formalism, providing theoretical upper bounds for the logical error rate. Our results demonstrate that cylindrical and M""obius codes outperform standard surface codes when using the minimum weight perfect matching (MWPM) decoder.

Problem

• Address asymmetric Pauli errors in quantum systems.
• Propose cylindrical and Möbius CSS topological codes.
• Enhance error correction beyond standard surface codes.

Innovation

• Cylindrical and Möbius CSS codes
• Handles asymmetric Pauli errors
• Outperforms standard surface codes