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Solid state devices for quantum bit computation (qubits) are not perfect isolated two-level systems, since additional higher energy levels always exist.
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In Fig. 2 the intrinsic leakage comes back to the same value almost periodically in time because we are consider the dynamics in the ideal case, neglecting the effect of the environment. The solution of the time dependent Schrodinger equation always gives almost periodic oscillations of the populations of the eigenstates. At longer time scales, the effect of the environment will start to be important, and then the leakage ℒ ( τ ) {\cal L}(\tau) should increase with time. This effect is taken into account later in Fig. 9 in Sec. VI, in an approximate semiclassical treatment of noise effects
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