Sufficient condition on noise correlations for scalable quantum computing
John P. Preskill · Quantum Information and Computation · 2013
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.