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Derivation of QFT product formula

If the quantum fourier transform is defined as follows: $$ U_{FT} |x\rangle = \frac{1}{2^{n/2}} \sum^{2^n-1}_{y=0} e^{2\pi i x y / 2^n} | y \rangle. $$ We can rewrite the exponential term as: $$ e^{2\ …
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Why is the trace of the outer product of two states equal to the inner product of the two st...

Why is it that, given two quantum states $|\psi_1\rangle$, $|\psi_2\rangle$, $$\mathrm{Tr}(|\psi_1\rangle\langle\psi_2|) = \langle\psi_2|\psi_1\rangle \quad $$ I went through the equation with the qub …
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