  We study theoretically the phonon-induced relaxation and decoherence
processes in the hybrid qubit in silicon. Hybrid qubit behaves as a charge
qubit when the detuning is close to zero and as spin qubit for large detuning
values. It is realized starting from an electrostatically defined double
quantum dot where three electrons are confined and manipulated through only
electrical tuning. By employing a three-level effective model for the qubit and
describing the environment bath as a series of harmonic oscillators in the
thermal equilibrium states, we extract the relaxation and decoherence times as
a function of the bath spectral density and of the bath temperature using the
Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly
affected by the physics of the valley, i.e. the conduction band minima, so we
also included the contribution of the valley excitations in our analysis. Our
results offer fundamental information on the system decoherence properties when
the unavoidable interaction with the environment is included and temperature
effects are considered.
