<F4.08e+05> C. H. Bennett, E. Bernstein, G. Brassard, and U.<F4.039e+05> Vazirani,<F4.112e+05> Strengths and weaknesses of quantum<F4.039e+05> computing, SIAM J. Comput., 26 (1997), pp. 1376-1389.  Home/Search   Document Not in Database   Summary   Related Articles

....Turing machines are more powerful than classical probabilistic Turing machines (in the unrelativized setting) unless there is a major breakthrough in complexity theory. It is natural to ask whether QTMs can solve every problem in NP in polynomial time. Bennett, Bernstein, Brassard, and Vazirani [9] give evidence showing the limitations of QTMs. They show that relative to an oracle chosen uniformly at random, with probability 1, the class NP cannot be solved on a QTM in time o(2 n 2 ) They also show that relative to a permutation oracle chosen uniformly at random, with probability 1, the ....

....the start cell. So, using only polynomial space, we can step through all of these configurations computing a running sum of the their squared magnitudes. Following Valiant s suggestion [43] the upper bound can be further improved to P #P . This proof can be simplified by using a theorem from [9] that shows how any BQP machine can be turned into a clean version M that on input x produces a final superposition with almost all of its weight on x; M(x) where M(x) is a 1 if M accepts x and a 0 otherwise. This means we need only estimate the amplitude of this one configuration in the final ....

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<F4.08e+05> C. H. Bennett, E. Bernstein, G. Brassard, and U.<F4.039e+05> Vazirani,<F4.112e+05> Strengths and weaknesses of quantum<F4.039e+05> computing, SIAM J. Comput., 26 (1997), pp. 1376-1389.

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