Bose-Hubbard model for universal quantum walk-based computation

Understand

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.