2013/03/31 by Mahdi Ebrahimi Kahou, David L. Feder
Computer Science · Physics and Astronomy · #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Theoretical physics #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.1103/physreva.88.032310
published as Phys. Rev. A 88, 032310 (2013) · 12 pages, 6 figures; introduction and background sections overhauled; new section added addressing the impact of errors
arxiv created 2013/08/22 · openalex publication_date 2013/09/11 · arxiv updated 2013/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Schr"odinger 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 the size of the search space N like √(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 implementation of the quantum search algorithm.