# QC2.7 Quantum Fourier Transform (QFT)

This skill introduces the Quantum Fourier Transform (QFT) as a key quantum algorithmic tool for processing and analysing quantum states in the frequency domain. Learners study how QFT maps computational basis states to superpositions with well-defined phases, and how it is implemented using a sequence of single- and two-qubit gates. Emphasis is placed on executing the QFT circuit and interpreting the resulting amplitudes.

## Requirements

* [[skill-tree:qc:1:3:b]]
* [[skill-tree:qc:2:1:b]]

## Learning Outcomes

* Describe the purpose and mathematical action of the Quantum Fourier Transform.
* Explain how the QFT maps computational basis states to phase-encoded superpositions.
* Execute the QFT circuit step by step for a small number of qubits.
* Calculate and interpret the output amplitudes of the transformed state.