Error rate of a charge qubit coupled to an acoustic phonon reservoir

We analyze decoherence of an electron in a double dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.