  A formulation for performing quantum computing in a projected subspace is
presented, based on the subdynamical kinetic equation (SKE) for an open quantum
system. The eigenvectors of the kinetic equation are shown to remain invariant
before and after interaction with the environment. However, the eigenvalues in
the projected subspace exhibit a type of phase shift to the evolutionary
states. This phase shift does not destroy the decoherence-free (DF) property of
the subspace because the associated fidelity is 1. This permits a universal
formalism to be presented - the eigenprojectors of the free part of the
Hamiltonian for the system and bath may be used to construct a DF projected
subspace based on the SKE. To eliminate possible phase or unitary errors
induced by the change in the eigenvalues, a cancellation technique is proposed,
using the adjustment of the coupling time, and applied to a two qubit computing
system. A general criteria for constructing a DF projected subspace from the
SKE is discussed. Finally, a proposal for using triangulation to realize a
decoherence-free subsystem based on SKE is presented. The concrete formulation
for a two-qubit model is given exactly. Our approach is novel and general, and
appears applicable to any type of decoherence. Key Words: Quantum Computing,
Decoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-k
