Physics – Quantum Physics
Scientific paper
2008-08-20
J. Math. Phys 50, 102106 (2009)
Physics
Quantum Physics
22 pages, 2 figures. Supersedes arXiv:0804.0604. v2: some corrections, new remarks, and a new subsection on the adiabatic theo
Scientific paper
10.1063/1.3236685
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 non-degenerate 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.
Hamma Alioscia
Lidar Daniel A.
Rezakhani Ali T.
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