2008/02/05 by Stephen S. Bullock, Dianne P. O'Leary, Dianne P. O’Leary +2 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Data Storage Technologies #Coding theory and cryptography #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.0802.0626
12 pages, two algorithms, one figure, to be submitted to QIC
arxiv created 2008/02/05 · openalex publication_date 2008/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This manuscript introduces various notions of k-locality of stabilizer codes inherited from the associated stabilizer groups. A choice of generators for the group leads to a Hamiltonian with the code in its groundspace, while a Hamiltonian holding the code in its groundspace might be called effective if its locality is less than that of a natural choice of generators (or any choice). This paper establishes some conditions under which effective Hamiltonians for stabilizer codes do not exist. Our results simplify in the cases of Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations.