منابع مشابه
Consistency of the Adiabatic Theorem
The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic the...
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The consistency of quantum adiabatic theorem has been doubted recently. It is shown in the present paper, that the difference between the adiabatic solution and the exact solution to the Schrödinger equation with a slowly changing driving Hamiltonian is small; while the difference between their time derivatives is not small. This explains why substituting the adiabatic solution back into Schröd...
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We prove the adiabatic theorem for quantum evolution without the traditional gap condition. We show that the theorem holds essentially in all cases where it can be formulated. In particular, our result implies that the adiabatic theorem holds also for eigenvalues embedded in the continuous spectrum. If there is information on the Hölder continuity of the spectral measure, then one can also esti...
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ژورنال
عنوان ژورنال: Quantum Information Processing
سال: 2004
ISSN: 1570-0755,1573-1332
DOI: 10.1007/s11128-004-7712-7