This skill introduces Quantum Phase Estimation (QPE) as a fundamental quantum algorithm for estimating the phase associated with an eigenvalue of a unitary operator. Learners study how the Quantum Fourier Transform (QFT) is combined with controlled unitary operations and phase kickback to estimate the phase associated with an eigenstate. Emphasis is placed on executing the algorithm for small examples and interpreting the measured output.

• QC1.3 Multi-Qubit Systems and the Gate Model of Quantum Computation
• QC2.1 Phase Kickback and Controlled Operations
• QC2.7 Quantum Fourier Transform (QFT)

• Describe the goal of Quantum Phase Estimation and its relevance to quantum algorithms.
• Explain how phase kickback and the Quantum Fourier Transform are used to estimate the eigenvalues (or eigenphases) of a unitary operator.
• Execute the Quantum Phase Estimation algorithm step by step for a simple unitary and eigenstate.
• Calculate and interpret the measurement outcomes to determine the estimated phase.