In the four series papers published recently on Science China-Physics, Mechanics & Astronomy (2013(7), 2014(2), 2014(11) and 2014(10), respectively), the mathematical versions of quantum adiabatic theorem for conventional and PT-symmetric quantum systems have been set up and qualitative estimations of the errors between the adiabatic approximate solution and the exact solution have been obtained, which establish an important foundation of adiabatic quantum computation.
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