Bose-Hubbard model for universal quantum walk-based computation

TL;DR

This paper proposes a new universal quantum computation scheme using bosonic quantum walkers on a graph, leveraging the Bose-Hubbard model, with efficient encoding, gates, and potential implementation in optical lattices.

Contribution

It introduces a scalable, graph-based quantum computing method using bosonic walkers with efficient encoding and gate construction, compatible with error correction.

Findings

Linear vertex requirement in qubit encoding

Implementation of universal gates including CPHASE and SWAP

Potential realization with ultracold atoms in optical lattices

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.