Broadly speaking, can we say that quantum circuits are like Fourier Transform/Decomposition?
We use qbit like waves, tune it with quantum gates, to find answer.
https://ars.els-cdn.com/content/image/3-s2.0-B978075067444750042X-f05-16-9780750674447.gif
https://www.sciencedirect.com/topics/engineering/fourier-decomposition
https://youtu.be/spUNpyF58BY?t=106
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1$\begingroup$ Some circuits use QFT (for example Shor's algorithm, some implementation of adders, phase estimation etc.), however, not all. $\endgroup$– Martin VeselyCommented Oct 4, 2020 at 6:32
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1$\begingroup$ I would rather think of quantum circuit as a unitary operator. It is true that DFT is a unitary operator and hence it can be decompose into a quantum circuit, it is not true that all quantum circuits have to be DFT like operator. $\endgroup$– KAJ226Commented Oct 4, 2020 at 9:51
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A quantum circuit is a sequence of initialization, resets, and quantum gates - typically a quantum circuit ends in measurements. When you reuse a quantum circuit - it precedes another quantum circuit.
So in this case of QFT the implementation is over the amplitudes of a wavefunction. (Note this is different in many ways when compared to FFT that transforms a signal - input is time domain and the output is frequency domain). There are quantum circuit with no semblance of QFT - it could be energy levels when used to produce the maximized value of the objective function and so on.
Here is a good textbook to start with https://qiskit.org/textbook/ch-algorithms/defining-quantum-circuits.html
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$\begingroup$ github.com/Qiskit/textbook/blob/main/notebooks/ch-algorithms/… $\endgroup$– abhi-raoCommented Apr 14 at 23:36