2026/08/01 by Shanxiang Lyu
Computer Science · Mathematics · Physics and Astronomy · #cs.IT #math.IT #quant-ph
arxiv created 2026/08/01 · arxiv updated 2026/08/04
We construct an explicit symplectic realization of the Barnes-Wall lattice that yields a family of multimode Gottesman-Kitaev-Preskill (GKP) codes with encoding rate R = (1)/(2)log2 N and a deterministic O(Nlog2 N) bounded-distance decoder. The recursive generator Gm+1 = (\beginsmallmatrix Gm & 0 Gm & Rm Gm \endsmallmatrix) with Rm = I + Ω simultaneously guarantees symplectic integrality for valid quantum stabilizers and preserves the exact Barnes-Wall decoding structure through a chain of isometric isomorphisms. The code distance is constant at Δ2 = 1 (in units of 2π), representing an explicit distance--rate tradeoff in which logarithmic encoding efficiency is achieved at the cost of non-scaling protection. This construction provides a deterministic, space-efficient paradigm for GKP error correction in platforms supporting non-local modular connectivity.