The quantum adiabatic search with decoherence in the instantaneous energy eigenbasis

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dc.creatorÅberg, Johan
dc.creatorKult, David
dc.creatorSjöqvist, Erik
dc.date2005-07-01
dc.date2005-10-20
dc.date.accessioned2026-07-07T06:43:35Z
dc.date.available2026-07-07T06:43:35Z
dc.descriptionIn Phys. Rev. A {\bf 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 $N^{3/2}$, 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 $p\to 1$ limit. We supplement the analytical results by numerical simulations of the global and local search.
dc.descriptionMaterial added, journal reference added
dc.identifierhttps://arxiv.org/abs/quant-ph/0507010
dc.identifierhttp://arxiv.org/abs/quant-ph/0507010
dc.identifierPhys. Rev. A 72, 042317 (2005)
dc.identifierdoi:10.1103/PhysRevA.72.042317
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102466
dc.subjectQuantum Physics
dc.titleThe quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
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