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arXiv · 1207.4805

Symmetry protection of measurement-based quantum computation in ground states

Dominic V. Else·Stephen D. Bartlett·Andrew C. Doherty
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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.

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Dominic V. Else, Stephen D. Bartlett, Andrew C. Doherty. 2012-11-11. Symmetry protection of measurement-based quantum computation in ground states. https://doi.org/10.1088/1367-2630%2F14%2F11%2F113016

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