Bounds on Effective Hamiltonians for Stabilizer Codes
Quantum Physics
2008-02-06 v1
Abstract
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.
Cite
@article{arxiv.0802.0626,
title = {Bounds on Effective Hamiltonians for Stabilizer Codes},
author = {Stephen S. Bullock and Dianne P. O'Leary},
journal= {arXiv preprint arXiv:0802.0626},
year = {2008}
}
Comments
12 pages, two algorithms, one figure, to be submitted to QIC