Symmetry protection of measurement-based quantum computation in ground states

TL;DR

This paper demonstrates that the ground state of a symmetry-protected Hamiltonian remains a universal resource for measurement-based quantum computation under small, symmetry-preserving perturbations, ensuring robustness of quantum computational resources.

Contribution

It proves the robustness of measurement-based quantum computation in ground states against small symmetry-preserving perturbations, using phase properties rather than explicit ground state control.

Findings

Perturbed ground states remain universal resources under certain conditions.

Symmetry protection ensures stability of quantum computational phases.

Adaptive measurement protocols are effective throughout the symmetry-protected phase.

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.