Local Quantum Codes from Subdivided Manifolds

2023/03/12 by Elia Portnoy, Portnoy, Elia · 6 citations
Computer Science · Engineering · #Computability, Logic, AI Algorithms #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2303.06755

openalex publication_date 2023/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n ≥ 3, we demonstrate the existence of quantum codes which are local in dimension n with V qubits, distance V^(n-1)/(n), and dimension V^(n-2)/(n), up to a polylog(V) factor. The distance is optimal up to the polylog factor. The dimension is also optimal for this distance up to the polylog factor. The proof combines the existence of asymptotically good quantum codes, a procedure to build a manifold from a code by Freedman-Hastings, and a quantitative embedding theorem by Gromov-Guth.

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