Quantum search by the nonlinear Schrodinger equation with a generalized cubic-quintic nonlinearity

Continuous-time quantum walks, a quantum analog to the continuous-time

Markov chain, allow the efficient solution to some spatial search problems. At

low temperatures and a high number of atoms, two- and three-body interac-

tions cause Bose-Einstein condensates to evolve according to an effective, non-

linear Schr ¨odinger equation. These effective nonlinearities can be exploited to

solve a search problem faster than the linear case. This speedup comes at the

cost of increased precision needed in the timing of the search, as well as a lower

bound on the number of bosonic walkers necessary to observe this speedup.

We will present our work analyzing the computational speedups afforded by

continuous-time quantum walks with effective nonlinearities for search prob-

lems with multiple correct answers.