Quantum Computing: The Walsh-Hadamard Matrix — Backbone of Grover's Diffusion Operator

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Grover's algorithm on a 3‑qubit system searches for |101⟩ using two optimal iterations, tracking exact amplitudes. The diffusion operator applies H⊗3 twice per cycle, and the full 8×8 Walsh‑Hadamard matrix is derived from first‑principles sign rules.
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