Nonlinear Liouville equation, project Green function and stabilizing quantum computing

Using the kinetic equation of subdynamics and the principle of maximal entropy we derive a type of nonlinear Liouville equation (NLE) for project/open quantum systems. The NLE can describe projected (or reduced) density operator, which allows to establish formalism of project Green functions (PGF) for project/open quantum system. We found that PGF can be related to Green function (GF) by the similarity operators in subdynamics. There are parallel structure and relations between PGF and GF. Finally, we demonstrated how to decrease/cancel decoherence using PGF to stabilize quantum logic operations for silicon-based or photonic quantum computing systems.