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now these phases were restricted to ±1. More general phases come about if
the Fourier transform is implemented. In this section, we introduced the idea
of using the H gate on the output to produce interfering amplitudes. This is
just a special case of the quantum Fourier transform, as we will see in the
next section.
8.4 Quantum Fourier Transform and Applications
The Fourier transform, a mathematical tool named after the 18th century
French mathematician Joseph Fourier, is an invaluable tool in engineering
and the sciences. No technical education is complete without a firm grasp
of this technique and its uses. The simplest way