Quantum Fourier Transform: <j|QFT_N|k> = omega^{jk}/sqrt(N) with omega = exp(2*pi*i/N)

Layer 1 — Physicsin the quantum-computing subtree

Quantum Fourier Transform framework. Setup: given an n-qubit register (N = 2^n basis states) the QFT is the unitary map QFT_N |k> = (1/sqrt(N)) * sum_{j=0}^{N-1} omega^{jk} |j>, with omega = exp(2*pi*i/N) the primitive N-th root of unity.…

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