The Quantum Fourier Transform

The QFT is an exponentially compact Fourier transform - the core primitive Kronos would use to read energies out of a material's Hamiltonian.

The concept

The QFT maps |x> to a superposition whose phases encode x's frequencies, in O(n^2) gates on n qubits. It does not hand you all Fourier coefficients - it exposes periodic structure that measurement can extract.

How Kronos uses it

Inside phase estimation, the QFT converts the phase a material Hamiltonian imprints during time evolution into a measurable energy - the step that turns a quantum simulation into a usable ground-state number for candidate fusion materials.

Honest note

High-resolution phase estimation on real molecules requires error correction, ~mid-2030s.