A scalable, high-speed measurement-based quantum computer using trapped ions

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Scaling with N N can be improved by long-distance gates to 3000 ​ N 2 3000N^{2} , or even O ⁡ ( N ​ ln ⁡ N ) O(N\ln{N}) (see Table 1 in A. G. Fowler et al. 2004 ). 3000 ​ N 2 3000N^{2} scaling requires 250 ns gates for a 5 minute factorization of the RSA640 number. Further improvements are possible by parallelizing the algorithm but with tradeoffs (see R. Van Meter et al

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