Quantum search with interacting Bose-Einstein condensates

TL;DR

This paper studies how nonlinearity in interacting Bose-Einstein condensates affects quantum search efficiency, finding that the search time scales similarly to linear cases, suggesting condensates as potential quantum search platforms.

Contribution

It demonstrates that nonlinear interactions in Bose-Einstein condensates do not alter the fundamental scaling of quantum search algorithms on complete graphs.

Findings

Search time scales as √N, similar to linear quantum walk.

Interacting BECs can implement quantum search algorithms.

Nonlinearity affects the overall constant but not the scaling.

Abstract

One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a graph containing a marked site. In many physical implementations, however, one might expect to have multiple particles. In interacting bosonic systems at zero temperature, the dynamics is well-described by a discrete nonlinear Schrodinger equation. We investigate the role of nonlinearity in determining the efficiency of the spatial search algorithm within the quantum walk model, for the complete graph. The analytical calculations reveal that the nonlinear search time scales with size of the search space N like the square root of N, equivalent to the linear case though with a different overall constant. The results indicate that interacting Bose-Einstein condensates at zero temperature could be natural systems for the implementation of the quantum search algorithm.