aiqbench analysis
This paper introduces a novel family of CSS quantum codes derived from Low-Density Generator Matrix (LDGM) structures, specifically optimized for fault-tolerant computation through controlled stabilizer weights and iterative decoding. By leveraging discrete Density Evolution to tune performance in depolarizing channels, the research offers a flexible design framework that enhances error correction capabilities without relying on standard low-density parity-check approaches. These advancements directly address critical challenges in scaling quantum hardware by improving code efficiency and stability under noise.
LDGM-Based Quantum Codes for Fault-Tolerant Quantum Computation
arXiv:2607.15159v2 Announce Type: replace Abstract: We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.
Abstract:We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.
Quantum Physics (quant-ph); Information Theory (cs.IT)
arXiv:2607.15159 [quant-ph]
(or arXiv:2607.15159v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.15159 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 232 words
