Robustness of decoherence-free subspaces for quantum computation

Abstract

It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)]\nthat within the framework of the semigroup Markovian master equation,\ndecoherence-free (DF) subspaces exist which are stable to first order in time\nto a perturbation. Here this result is extended to the non-Markovian regime and\ngeneralized. In particular, it is shown that within both the semigroup and the\nnon-Markovian operator sum representation, DF subspaces are stable to all\norders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal\nfor quantum memory applications. For quantum computation, however, the\nstability result does not extend beyond the first order. Thus, to perform\nrobust quantum computation in DF subspaces, they must be supplemented with\nquantum error correcting codes.\n