  The spin dynamics of radical-triplet system (RTS) has been calculated by
using the Lindblad formalism within the theory of open quantum system. The
single-radical-triplet system (SRTS) is considered here for single-qubit
quantum gate operations while double-radical-triplet system (DRTS) for
two-qubit operations. The environment effects taken into account include the
spin-lattice relaxation of the triplet exciton and radical spin-$\frac{1}{2}$,
the inter-system crossing process that induces the transition from singlet
excited state to the triplet ground state, and the rather slow relaxation
process from the triplet ground state back down to the singlet ground state.
These calculations shown that the line shape broadening is strongly related to
the exchange interaction between triplet and exciton, which can be understood
as a spontaneous magnetic field created by the triplet renormalises the
original spin-$\frac{1}{2}$ electron spin resonance spectra. This work will
provide key information about the spin dynamics for building
optically-controlled molecular quantum gate out of radical-bearing molecules.
Moreover, this has generated the further theoretical question on how the
mixture of fermion and boson behaves.
