2008/08/31 by Daniel A. Lidar, D. A. Lidar, A. T. Rezakhani +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.3236685
published as J. Math. Phys 50, 102106 (2009) · 22 pages, 2 figures. Supersedes arXiv:0804.0604. v2: some corrections, new remarks, and a new subsection on the adiabatic theorem for open systems. v3: additional corrections
arxiv created 2009/03/11 · openalex publication_date 2009/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.