Acoustic decoherence of flux qubits
  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. 
Jaroslav Albert and Eugene M. Chudnovsky