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Publication Citation: Local Bounds on Effective Hamiltonians for Stabilizer Codes

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Author(s): Stephen Bullock; Dianne M. O'Leary;
Title: Local Bounds on Effective Hamiltonians for Stabilizer Codes
Published: January 22, 2009
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
Pages: pp. 487 - 499
Keywords: adiabatic quantum computing,Calderbank-Shor-Steane codes,stabilizer codes
Research Areas: Math
PDF version: PDF Document Click here to retrieve PDF version of paper (280KB)