2005/07/31 by Johan Åberg, David Kult, Erik Sjöqvist
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.72.042317
published as Phys. Rev. A 72, 042317 (2005) · Material added, journal reference added
openalex publication_date 2005/10/18 · arxiv created 2005/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Phys. Rev. A 71, 060312(R) (2005), the robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian was examined. We expand this analysis to include the case of the global adiabatic quantum search. As in the case of the local search the asymptotic time complexity for the global search is the same as for the ideal closed case, as long as the Hamiltonian dynamics is present. In the case of pure decoherence, where the environment monitors the search Hamiltonian, we find that the time complexity of the global quantum adiabatic search scales like N3∕2, where N is the list length. We moreover extend the analysis to include success probabilities p<1 and prove bounds on the run time with the same scaling as in the conditions for the p\ensuremath→1 limit. We supplement the analytical results by numerical simulations of the global and local search.