  Decoherence of a flux qubit due to inelastic scattering of thermal phonons by
the qubit is studied. The computed decoherence rates contain no unknown
constants and are expressed entirely in terms of measurable parameters of the
qubit. The answer depends strongly on the size of the qubit as compared to the
wavelength of phonons of frequency corresponding to the tunnel splitting of the
qubit. Thermal phonons set the upper limit on the operating temperature of a
small qubit at around 10-20 K. For large qubits acoustic decoherence due to one
phonon processes should be taken into account at any temperature when a high
quality factor is desired.
