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Symmetry-protected topological ordered phases and their use for quantum computation

Akimasa Miyake, University of New Mexico

(Session 4 : Thursday from 4:30pm - 5:00pm)

Collective phenomena, like superconductivity and magnetism, are usually robust features of quantum many-body systems. They only depend on a few key parameters of a system Hamiltonian, and often symmetries are sufficient enough to characterize different (quantum) phases associated with different collective behaviors. Through remarkable progress at the crossover between quantum information and quantum many-body physics, it gets more and more clear that certain strongly-correlated ground states could be harnessed for quantum information processing, based on their underlying entanglement structure and thus inherent complexity. For example, some concrete models of topological orders are most known by the application to quantum error correction. Here we address a question: "to what extent computational usefulness of quantum many-body ground states would be determined ubiquitously by symmetries, without the system Hamiltonian specified in detail?" Our approach may be also applicable to how quantum state preparation and verification can be made without detailed knowledge about the system, in the context of quantum simulation. This is a joint work with Jacob Miller.