  Quantum error correction is a solution to preserve the fidelity of quantum
information encoded in physical systems subject to noise. However, unfavorable
correlated errors could be induced even for non-interacting qubits through the
environment (bath), when they are "packed" together. The question is, to what
extent can we treat the noise induced by the bath as independent? In the
context of the spin-boson model, we show that, under some reasonable
constraints, the independent noise approximation could be valid. On the other
hand, in the strongly correlated limit, we show how the method of decoherence
free subspace can be made applicable. Combining these two methods makes
fault-tolerant quantum computation promising in fighting against correlated
errors.
