PIRSA:08050044 Scientific Series Quantum Information

DOI10.48660/08050044

Series: Quantum Information

Bartlett, S. (2008). Identifying phases of matter that are universal for quantum computation. Perimeter Institute. https://pirsa.org/08050044

Bartlett, Stephen. Identifying phases of matter that are universal for quantum computation. Perimeter Institute, May. 28, 2008, https://pirsa.org/08050044 

@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.

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