🌀 3D Quantum Fourier Transform — |j⟩ → QFT|j⟩ in Volumetric Space
The same exact QFT amplitude formula as the 2D original on a 3-qubit register (N = 8) — every output state has equal magnitude 1/√8, only its phase θ = ±2πjk/8 changes — now laid out as eight orbiting phase towers in true 3D space, next to a live 3D gate-circuit diagram of the Hadamard/controlled-phase/swap decomposition that produces it.
This is the 3D companion to the Quantum Fourier Transform simulator. It computes the identical amplitudes as the 2D original — QFT|j⟩ = (1/√8)·Σk e2πijk/8|k⟩ for the forward transform, with the conjugate exponent e−2πijk/8 for the inverse — for a fixed 3-qubit register (N = 8 basis states). Every output tower has the same height (magnitude 1/√8); only its colour and the small phasor arrow on top, both driven by the exact phase θk, differ between towers. Behind the ring, a Three.js gate-circuit diagram lays out the standard Hadamard / controlled-R₂ / controlled-R₃ / swap decomposition that produces this transform, spread across three physical qubit rails in genuine 3D space instead of a flat schematic.
3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install