Quantum Tanner Codes at Moderate Blocklength

• URL: http://arxiv.org/abs/2608.12509v1
• Date: Wed, 12 Aug 2026 18:37:15 GMT
• Title: Quantum Tanner Codes at Moderate Blocklength
• Abstract summary: We present explicit constructions of quantum Tanner (QT) codes with good rate and distance.<n>The code instances presented have check weights ranging from $9$ to $20$.<n>We also provide QuantumExpanders.jl, an open-source Julia library for constructing QT codes and explicit constructions of Ramanujan graphs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present explicit constructions of quantum Tanner (QT) codes with good rate and distance, obtained through two complementary approaches: the left-right Cayley complex (LRCC) description and the "lifting" perspective, in which a seed Calderbank-Shor-Steane (CSS) code is lifted by commuting left-right regular actions of a finite group $\mathcal{G}$. Through an extensive search over non-abelian groups from GAP's SmallGrp library, we investigate the moderate-blocklength regime ($n \in [500,1000]$) and identify several new code instances with distance upper bounds exceeding $20$. These include $[[480,8,(\leq 21,\leq 21)]]$, $[[504,4,(\leq 36,\leq 27)]]$, $[[672,4,(\leq 48,\leq 28)]]$, $[[720,6,(\leq 30,\leq 30)]]$, and $[[864,8,(\leq 39,\leq 31)]]$, with these bounds obtained using up to $350$ million trials of sQetch, a randomized distance estimator. The code instances presented have check weights ranging from $9$ to $20$. Using the Tesseract decoder, we estimate pseudo-thresholds of $3.6\%$-$4.6\%$ under phenomenological noise and $0.14\%$-$0.27\%$ under circuit-level noise, comparable to prior results at shorter code lengths. We also provide QuantumExpanders.jl, an open-source Julia library for constructing QT codes and explicit constructions of Ramanujan graphs.

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