Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation

• URL: http://arxiv.org/abs/2310.10561v3
• Date: Fri, 5 Jan 2024 21:40:31 GMT
• Title: Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation
• Authors: Zhuohao Liu, Emma C. Johnson, and David L. Feder
• Abstract summary: All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order. This work considers two families of one-dimensional qubit states to answer this question in the negative.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-onsite symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry.

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