Bose-Hubbard model for universal quantum walk-based computation

  title={Bose-Hubbard model for universal quantum walk-based computation},
  author={Michael S. Underwood and David L. Feder},
  journal={Physical Review A},
We present a novel scheme for universal quantum computation based on spinless interacting bosonic quantum walkers on a piecewise-constant graph, described by the two-dimensional Bose-Hubbard model. Arbitrary X and Z rotations are constructed, as well as an entangling two-qubit CPHASE gate and a SWAP gate. Quantum information is encoded in the positions of the walkers on the graph, as in previous quantum walk-based proposals for universal quantum computation, though in contrast to prior schemes… 

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Nature 415
  • 39
  • 2002
and M
  • Szegedy, in Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
  • 2005
  • Rev. Lett. 102, 180501
  • 2009
  • Rev. A 81, 042330
  • 2010
  • Rev. Lett. 90, 147901
  • 2003
  • J. Quant. Inf. 1, 507
  • 2003
  • Rev. A 85, 022307
  • 2012