Irreversible Liouville equation and nonperturbative approach in quantum computing

Having analyzed the role of time-ordering boundary conditions in deriving irreversible kinetic equation a general irreversible Liouville equation is proposed. By this equation a variety of irreversible kinetic equations, such as a stochastic diffusion equation, a irreversible project Liouville equation can be constructed. We also develop a nonperturbative method to solve the eigenvalue problem for this equation. Application in controlling decoherence for quantum computing is also studied.