Transitionless driving on adiabatic search algorithm

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.

Original languageEnglish
Article number224108
JournalJournal of Chemical Physics
Volume141
Issue number22
DOIs
Publication statusPublished - 1 Jan 2014

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Hamiltonians
decay
transition probabilities
Trajectories
trajectories
scaling

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Transitionless driving on adiabatic search algorithm. / Oh, Sangchul; Kais, Sabre.

In: Journal of Chemical Physics, Vol. 141, No. 22, 224108, 01.01.2014.

Research output: Contribution to journalArticle

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