A general introduction to the issue of decoherence in quantum computing and the remarkable idea of quantum error correction is first given. Then we introduce a spin-boson model to study the decoherence of a quantum computer in an environment which is inherently non-Markovian and spatially correlated. Generalizing from this exactly solvable case, we derive the non-unitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. Our results demonstrate that effects of correlation can be systematically reduced by suitable changes in the error correction codes.

Duke University