Abstract
We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates.Under a generic model of random noise for(controlled)rotation gates,we prove that the algorithm does not factor integers of the form pq when the noise exceeds a vanishingly small level in terms of n-the number of bits of the integer to be factored,where p and q are from a well-defined set of primes of positive density.We further prove that with probability 1-o(1)over random prime pairs(p,q),Shor's factoring algorithm does not factor numbers of the form pq,with the same level of random noise present.
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