Sufficient condition on noise correlations for scalable quantum   computing
  I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum computations can be executed reliably provided that noise terms acting collectively on k system qubits are sufficiently weak, and decay sufficiently rapidly with increasing k and with increasing spatial separation of the qubits. 
John Preskill
quant-ph cond-mat.other