Symmetry-protected phases for measurement-based quantum computation

Abstract

Ground states of spin lattices can serve as a resource for measurement-based quantum computation. Ideally, the ability to perform quantum gates via measurements on such states would be insensitive to small variations in the Hamiltonian. Here, we describe a class of symmetry-protected topological orders in one-dimensional systems, any one of which ensures the perfect operation of the identity gate. As a result, measurement-based quantum gates can be a robust property of an entire phase in a quantum spin lattice, when protected by an appropriate symmetry.

5 pages, 1 figure, comments welcome; v2 fixed minor typographic errors; v3 published version

References in corpus (8)

• Matrix product states represent ground states faithfully
• String order and symmetries in quantum spin lattices
• Measurement-based quantum computation beyond the one-way model
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Quantum computation on the edge of a symmetry-protected topological order
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum computational capability of a 2D valence bond solid phase
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems

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