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I study the effectiveness of fault-tolerant quantum computation againstcorrelated Hamiltonian noise, and derive a sufficient condition forscalability. Arbitrarily long quantum computations can be executed reliablyprovided that noise terms acting collectively on k system qubits aresufficiently weak, and decay sufficiently rapidly with increasing k and withincreasing spatial separation of the qubits.

Sufficient condition on noise correlations for scalable quantum computing