We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over Z p can be efficiently approximated by transforming over Z q for any q in a large range. Our result places no restrictions on the superposition to be transformed, generalizing previous applications. In addition, our proof easily generalizes to multi-dimensional transforms for any constant number of dimensions
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