Bullock, S.
and O'Leary, D.
(2009),
Local Bounds on Effective Hamiltonians for Stabilizer Codes, Quantum Information & Computation, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51274
(Accessed February 11, 2025)
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Local Bounds on Effective Hamiltonians for Stabilizer Codes
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Abstract
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.Citation
Quantum Information & Computation
Volume
9
Pub Type
Journals
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Keywords
adiabatic quantum computing, Calderbank-Shor-Steane codes, stabilizer codes
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Created January 22, 2009, Updated February 19, 2017