Symmetry protection of measurement-based quantum computation in ground states
Abstract
The two-dimensional cluster state, a universal resource for measurement-based quantum computation, is also the gapped ground state of a short-ranged Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian. We prove that, provided the perturbation is sufficiently small and respects a certain symmetry, the perturbed ground state remains a universal resource. We do this by characterising the operation of an adaptive measurement protocol throughout a suitable symmetry-protected quantum phase, relying on generic properties of the phase rather than any analytic control over the ground state.
Keywords
Cite
@article{arxiv.1207.4805,
title = {Symmetry protection of measurement-based quantum computation in ground states},
author = {Dominic V. Else and Stephen D. Bartlett and Andrew C. Doherty},
journal= {arXiv preprint arXiv:1207.4805},
year = {2012}
}
Comments
20 pages plus appendices, 11 figures, comments very welcome; v2 minor corrections and additional references; v3 published version with minor corrections