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arXiv · 1204.6021

Bose-Hubbard model for universal quantum walk-based computation

Michael S. Underwood·David L. Feder
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Abstract

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.

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Michael S. Underwood, David L. Feder. 2012-04-26. Bose-Hubbard model for universal quantum walk-based computation. https://doi.org/10.1103/physreva.85.052314

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