Breaking the bicycle frame: Coset-based quantum LDPC codes

• URL: http://arxiv.org/abs/2606.17268v1
• Date: Mon, 15 Jun 2026 20:20:57 GMT
• Title: Breaking the bicycle frame: Coset-based quantum LDPC codes
• Abstract summary: Generalizing the construction of two-block group algebra (2BGA) codes, we introduce a family of two-block quantum LDPC codes.<n>We identify several new quantum LDPC codes, including weight-6 codes with parameters $[48,8,6]]$, $[96,8,10]]$, and $[224,12,16]]$.<n>Our codes, when decoded using BP-OSD, perform competitively with BB codes, achieving thresholds of $approx0.65%$ for the weight-6 family and $approx0.35%$ for the weight-8 family.
• Score: 65.96089068176079
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generalizing the construction of two-block group algebra (2BGA) codes, we introduce a family of two-block quantum LDPC codes constructed using the action of a group on the cosets of its subgroup. This replaces the regular group actions of the earlier two-block constructions and significantly expands the search space, yielding new quantum LDPC codes outside the 2BGA family. Through a computer search, we identify several new quantum LDPC codes, including weight-6 codes with parameters $[[48,8,6]]$, $[[96,8,10]]$, and $[[224,12,16]]$, as well as weight-8 codes with parameters $[[84,16,8]]$, $[[112,16,10]]$, $[[128,16,12]]$, and $[[168,16,15]]$. Furthermore, we introduce a maximally packed syndrome extraction schedule of depth $w+2$, including initialization and measurement steps, for any code with a maximum stabilizer weight of $w$ from our family. Under a standard circuit-level noise model, our codes, when decoded using BP-OSD, perform competitively with BB codes, achieving thresholds of $\approx0.65\%$ for the weight-6 family and $\approx0.35\%$ for the weight-8 family. Finally, we introduce a group-theoretic framework to generate sequences of graph-based covers of 2BGA codes, recovering and extending recent results on code constructions of this type.

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