• DOI:10.1103/PhysRevA.85.052314
• Corpus ID: 118322995

Bose-Hubbard model for universal quantum walk-based computation

@article{Underwood2012BoseHubbardMF,
  title={Bose-Hubbard model for universal quantum walk-based computation},
  author={Michael S. Underwood and David L. Feder},
  journal={Physical Review A},
  year={2012},
  volume={85}
}

• M. Underwood, D. Feder
• Published 26 April 2012
• Physics
• 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 this proposal requires a number of vertices only linear in the number of encoded qubits. It allows single-qubit measurements to be performed in a straightforward manner with localized operators, and can make use of existing quantum error correcting codes either directly within the universal gate set provided, or by extending the lattice to a third dimension. We present an intuitive example of a logical encoding to implement the seven-qubit Steane code. Finally, an implementation in terms of ultracold atoms in optical lattices is suggested.