  The success of adiabatic quantum computation (AQC) depends crucially on the
ability to maintain the quantum computer in the ground state of the evolution
Hamiltonian. The computation process has to be sufficiently slow as restricted
by the minimal energy gap. However, at finite temperatures, it might need to be
fast enough to avoid thermal excitations. The question is, how fast does it
need to be? The structure of evolution Hamiltonians for AQC is generally too
complicated for answering this question. Here we model an adiabatic quantum
computer as a (parametrically driven) harmonic oscillator. The advantages of
this model are (1) it offers high flexibility for quantitative analysis on the
thermal effect, (2) the results qualitatively agree with previous numerical
calculation, and (3) it could be experimentally verified with quantum
electronic circuits.
