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 $f=\Delta ∕(2\pi \hslash )$, with $\Delta$ being the tunnel splitting of the qubit. Thermal phonons set the upper limit on the operating temperature of a small qubit at around $10–20\mathrm{K}$. In the mK range the scattering of thermal phonons by the flux qubit must not be among factors contributing to the decoherence.

• Received 11 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.144502