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Local Bounds on Effective Hamiltonians for Stabilizer Codes



Stephen Bullock, Dianne M. O'Leary


This paper introduces various notion 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. An application to topological orders on a surface bounds k by the minimum valence of the cell structure and its dual.
Quantum Information & Computation


adiabatic quantum computing, Calderbank-Shor-Steane codes, stabilizer codes


Bullock, S. and O'Leary, D. (2009), Local Bounds on Effective Hamiltonians for Stabilizer Codes, Quantum Information & Computation, [online], (Accessed April 21, 2024)
Created January 22, 2009, Updated February 19, 2017