CSE 599d - Quantum Computing The Quantum Fourier Transform and Jordan’s Algorithm
نویسنده
چکیده
There are many motivations for the discrete Fourier transform. Those of you in computer science have probably encountered them first in signal processing and perhaps further in cool theory results like switching lemmas. Those of you in physics have definitely encountered the continuous fourier transform, most likely first in quantum theory where we learn that the fourier transform goes between the momentum and position representations of a wave function. Suppose that we have a vector f of N complex numbers, fk, k ∈ {0, 1, . . . , N − 1}. Then the discrete Fourier transform (DFT) is a map from these N complex numbers to N complex numbers, the Fourier transformed coefficients f̃j , given by
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