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.

20 pages plus appendices, 11 figures, comments very welcome; v2 minor corrections and additional references; v3 published version with minor corrections

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Cited by in corpus (4)

• Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• MERA for Spin Chains with Continuously Varying Criticality
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter