Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal quantum computational resource.

@article{Wei2011AffleckKennedyLiebTasakiSO,
  title={Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal quantum computational resource.},
  author={Tzu-Chieh Wei and Ian Affleck and Robert Raussendorf},
  journal={Physical review letters},
  year={2011},
  volume={106 7},
  pages={
          070501
        }
}
Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal resource for measurement-based quantum computation. 

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References

SHOWING 1-10 OF 38 REFERENCES
Quantum computation and quantum information
  • T. Paul
  • Mathematics, Computer Science
  • Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers dealExpand
Stabilizer Codes and Quantum Error Correction
TLDR
An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed. Expand
Random graph dynamics
1. Overview 2. Erdos-Renyi random graphs 3. Fixed degree distributions 4. Power laws 5. Small worlds 6. Random walks 7. CHKNS model.
Nature
  • R. Rosenfeld
  • Medicine
  • Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009
TLDR
I am writing with a simple plea to balance the voluminous articles about treatment in your journal with a modicum of information about nature and caring effects to rekindle the perception of physicians as healers, not only treaters, who relish the gifts of nature, and foster the humanistic aspect of medicine that has thrived for millennia. Expand
Phys
  • Rev. Lett. 59, 799 (1987); I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Comm. Math. Phys. 115, 477
  • 1988
Phys
  • Rev. A 82, 052309
  • 2010
J. Phys. A: Math. Theor
  • J. Phys. A: Math. Theor
  • 2010
Nature Phys
  • Nature Phys
  • 2010
Phys
  • Rev. Lett. 105, 040501
  • 2010
Phys
  • Rev. Lett. 105, 020502
  • 2010
...
1
2
3
4
...