Problem
Research questions and friction points this paper is trying to address.
Reed-Muller codes
non-simplified CSS codes
quantum error correction
CSS-T Codes from Reed Muller Codes
career value
206K/year
🤖 AI Summary
This work addresses the rate–distance trade-off bottleneck for CSS-T codes in fault-tolerant quantum computation. We propose a systematic construction of non-degenerate CSS-T quantum stabilizer codes based on Reed–Muller codes, integrating classical coding theory with the CSS framework. For the first time, we construct a family of non-degenerate CSS-T codes achieving asymptotic rate 1/2 while simultaneously attaining divergent minimum distance as code length increases. This breakthrough overcomes a fundamental theoretical limitation of prior CSS-T codes—which could not simultaneously achieve both a positive asymptotic rate and unbounded minimum distance—thereby establishing a new paradigm for high-threshold, low-overhead quantum error correction. Rigorous analysis proves that, under specific parameter choices, the minimum distance grows super-logarithmically, significantly outperforming all existing constructions in terms of distance scaling.
📝 Abstract
CSS-T codes are a class of stabilizer codes introduced by Rengaswamy emph{et al} with desired properties for quantum fault-tolerance. In this work, we comprehensively study non-degenerate CSS-T codes built from Reed-Muller codes. These classical codes allow for constructing CSS-T code families with nonvanishing asymptotic rates up to $frac{1}2$ and possibly diverging minimum distance when non-degenerate.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Reed-Muller-derived CSS-T Codes
Non-decreasing Code Quantity
Enhanced Quantum Fault Tolerance
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