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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.
Comment: 18 pages, 8 figures. Rapporteur talk at the 25th Solvay Conference on Physics ("The Theory of the Quantum World"), 19-22 October 2011. (v2): References added
Comment: 41 pages, CALT-68-1787
Comment: 18 pages, harvmac, CALT-68-1819
Comment: 8 pages, 5 figures, REVTeX and epsf
Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor corrections
Comment: 24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor corrections
Comment: 58 pages with 7 PostScript figures, LaTeX, uses sprocl.sty and psfig, to appear in "Introduction to Quantum Computation," edited by H.-K. Lo, S. Popescu, and T. P. Spiller
Comment: 7 pages, references added
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