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.




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    $\begingroup$ Some circuits use QFT (for example Shor's algorithm, some implementation of adders, phase estimation etc.), however, not all. $\endgroup$ – Martin Vesely Oct 4 '20 at 6:32
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    $\begingroup$ 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. $\endgroup$ – KAJ226 Oct 4 '20 at 9:51

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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