QFT, Shor, Hadamard and everything

I made explorations in Qunatum Computing last year. An awesome world of pure nature. I drew the following diagrams as I progressed through my experiments. These drawings are meant to throw light from a different perspective, and providing new visualizations for the concepts.

The Awesome Hadamard Gate

Probably the single most important tool in Quantum Computing. A different way to look at this is, as a mechanism to teleport between computational basis and Forurier basis, which is amazing. The nature provides two mutually complimentary and fundamental ways to quantify things - the frequency and the amplitude. One can be derived from the rate of change in the other. That's the crux of Fourier Transform in general (from signal processing).

Hadamard Phase

I have created this GeoGebra notebook to explore effect of phase difference interactively.

Hadamard Interference

The color coding of the arrows the phase difference (orange color for negative or pi phase).

Cyclic CZ gates (Fully connected QFT)

Not quite QFT (see next diagram), but this helps to understand the phase rotations across the qubits.

Quantum Fourier Transform

Swap Gates for Mult

Shor Algorithm for Integer Factoring

I drew this to visualize the four stages in the algorithm. This shows very simple view of what's happening