Qudit quantum computation on matrix product states with global symmetry

Abstract

Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the 1D qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order.

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• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Qubit-qudit entanglement transfer in defect centers with high-spin nuclei
• Resource-efficient entanglement detection in high-dimensional states via two-qubit witnesses
• Measurement-based quantum computing with qudit stabilizer states
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• A quantum number theory
• Qudit Noisy Stabilizer Formalism