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This is still a theoretical problem, not one solvable by building a faster computer



You're right that part of the problem is, indeed, theoretical (it remains to be shown that BPP ≠ BQP, even if it is widely believed to be true), but part of the problem is also physical (we need to build a model of BQP---i.e. a quantum computer---to show that there is a physically realizable model of it).




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