Finding decoherence-free subspaces numerically

For a particular subspace or subsystem, if the quantum information is preserved by a noise with exact symmetry then it is known as a decoherence free subspace or subsystem (DFS). A numerical method was proposed to identify such a DFS by Wang, Byrd and Jacobs (Phys. Rev. A 87, 012338 (2013)). An algebraic form that gives the structure of the DFS is decomposed into simple components and these components are then further decomposed into irreducible components. These irreducible components are then used to find a unitary transform that leaves the algebraic form invariant under such a transformation. We applied the same numerical method to find DFS's with more than 1 qubit. If a particular noise process is given then this numerical method could be used to find the subspace or subsystem that is not affected by the noise or is the least affected by the noise. The latter is known as a minimal-noise subspace or subsystem (MNS).