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Anyon Theory and Topological Frustration of High-Efficiency Quantum LDPC Codes by Chen, Keyang; Liu, Yuanting; Zhang, Yiming; Liang, Zijian; Chen, Yu-An; Liu, Ke; Song, Hao is a scholarly article available to read on EtoBox.

What is Anyon Theory and Topological Frustration of High-Efficiency Quantum LDPC Codes about?

Quantum low-density parity-check (QLDPC) codes present a promising route to low-overhead fault-tolerant quantum computation, yet systematic strategies for their exploration remain underdeveloped. In this work, we establish a topological framework for studying the bivariate-bicycle codes, a prominent class of QLDPC codes tailored for real-world quantum hardware. Our framework enables the investigation of these codes through universal properties of topological orders. Besides providing efficient characterizations for demonstrations using Gr\"obner bases, we also introduce a novel algebraic-geometric approach based on the Bernstein--Khovanskii--Kushnirenko theorem, allowing us to analytically determine how the topological order varies with the generic choice of bivariate-bicycle codes under toric layouts. Novel phenomena are unveiled, including topological frustration, where ground-state degeneracy on a torus deviates from the total anyon number, and quasi-fractonic mobility, where anyon movement violates energy conservation. We demonstrate their inherent link to symmetry-enriched topological orders and offer an efficient method for searching for finite-size codes. Furthermore, we ext

Author

Chen, Keyang; Liu, Yuanting; Zhang, Yiming; Liang, Zijian; Chen, Yu-An; Liu, Ke; Song, Hao

Published

2025

Language

EN