Bounds on Effective Hamiltonians for Stabilizer Codes

Details Bounds on Effective Hamiltonians for Stabilizer Codes Bounds on Effective Hamiltonians for Stabilizer Codes

2008-02-05

arxiv.org/abs/0802.0626v1

Physics

Quantum Physics

12 pages, two algorithms, one figure, to be submitted to QIC

Scientific paper

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.

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