2021/02/19 by M. B. Hastings, Hastings, M. B. · 7 citations
Computer Science · #Error Correcting Code Techniques #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2102.10030
openalex publication_date 2021/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a general procedure for weight reducing quantum codes. This corrects a previous work\citeowr, and introduces a new technique that we call "coning" to effectively induce high weight stabilizers in an LDPC code. As one application, any LDPC code (with arbitrary O(1) stabilizer weights) may be turned into a code where all stabilizers have weight at most 5 at the cost of at most a constant factor increase in number of physical qubits and constant factor reduction in distance. Also, by applying this technique to a quantum code whose X-stabilizers are derived from a classical log-weight random code and whose Z-stabilizers have linear weight, we construct an LDPC quantum code with distance Ω(N2/3) and Ω(N2/3) logical qubits.