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

Originally published on malcolmlow.net In the Grover's Algorithm — Inversion About the Mean walkthrough, the diffusion operator applies H⊗³ twice per iteration. Every single step is governed by a sign table called the Hadamard Reference . That table is not a lookup shortcut — it is the 8×8 Walsh-Hadamard Transform matrix written out in full. This post derives it from scratch: one qubit, then two, then all three, arriving at the complete matrix and the rule behind every sign in it. 1 · The Circui