Three-qubit quantum Fourier transform (references arXiv:2607.13641)

Primitive: quantum Fourier transform. This card builds a three-qubit QFT from Hadamards, controlled-phase rotations (decomposed into rz and cx gates) and a final swap, the textbook transform that sits at the core of the referenced work.

The referenced paper, The potential of quantum computers for Particle Image Velocimetry (arXiv:2607.13641), presents QuPIV, a quantum algorithm that uses multidimensional quantum Fourier transforms to replace the classical FFT-based cross-correlation step of Particle Image Velocimetry. Per its abstract, the end-to-end algorithm includes a novel state preparation, a modified amplitude amplification enhanced by a contracted ground-state projector to reduce gate count, and an output-extraction stage, with numerical studies on synthetic and experimental data justifying the approach.

This Provenova card does not reproduce QuPIV or any of its numerical results. It is a deterministic, noiseless statevector simulation of a standalone three-qubit QFT circuit, run on Provenova's simulator; it does not include the state preparation, amplitude amplification, or velocimetry pipeline of the paper, and no hardware is involved. Applied to the |000> input the QFT produces a uniform magnitude distribution over all eight computational-basis outcomes (each probability 1/8), the expected textbook behaviour, with the transform's content carried in the relative phases tracked by the simulator's statevector. This card references the paper as the inspiration for the primitive and does not imply any endorsement by its authors.