Browsing by Author "Liu, Zhuohao"

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    Symmetry Protected Topological Order As A Requirement for Measurement-Based Quantum Gate Teleportation
    (2025-01-20) Liu, Zhuohao; Feder, David; Sanders, Barry; Barclay, Paul; Salahub, Dennis
    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 unable to deterministically teleport gates and which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit. 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.