Identifying phases of matter that are universal for quantum computation

          @misc{ pirsa_PIRSA:08050044,
            doi = {10.48660/08050044},
            url = {https://pirsa.org/08050044},
            author = {Bartlett, Stephen},
            keywords = {Quantum Information},
            language = {en},
            title = {Identifying phases of matter that are universal for quantum computation},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {may},
            note = {PIRSA:08050044 see, \url{https://pirsa.org}}
          }
          

Abstract

A recent breakthrough in quantum computing has been the realization that quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state - for example, the ground state of an interacting many-body system. It would be unfortunate, however, if the usefulness of a ground state for quantum computation was critically dependent on the details of the system\'s Hamiltonian; a much more powerful result would be the existence of a robust ordered phase which is characterized by the ability to perform measurement-based quantum computation (MBQC). To identify such phases, we propose to use nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits. We investigate a simple spin-lattice system based on the cluster-state model for MBQC, and demonstrate that it possesses a zero temperature phase transition between a disordered phase and an ordered \'cluster phase\' in which it is possible to perform a universal set of quantum gates.