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.

• QC1.3 Multi-Qubit Systems and the Gate Model of Quantum Computation
• QC2.1 Phase Kickback and Controlled Operations

• 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.