Reasoning About Quantum Algorithms: Phase Estimation, Amplitude Amplification, and More

Designing or evaluating a quantum algorithm requires fluency with a small set of building blocks. Phase estimation, amplitude amplification, and the Quantum Fourier Transform recur across many algorithms, and recognizing them is the difference between reading a paper passively and understanding it deeply. This course walks through those building blocks and how they combine. You will work through written reasoning exercises that mirror how researchers and practitioners actually approach quantum algorithm design. The emphasis is on developing intuition you can apply to new algorithms you encounter. What you'll learn: - Apply the Quantum Fourier Transform as a building block in factoring and period-finding - Use phase estimation as a general technique for extracting eigenvalues from unitary operators - Reason about amplitude amplification as a generalization of Grover-style search - Combine building blocks to understand algorithms for hidden subgroup problems - Read how variational quantum algorithms blend classical optimization with quantum circuits - Recognize the assumptions and limitations behind speedup claims in recent quantum literature The course progresses from the Quantum Fourier Transform through phase estimation, amplitude amplification, hidden subgroup approaches, and variational algorithms. A capstone written exercise asks you to walk through a chosen quantum algorithm and identify its building blocks and assumptions. This course is designed for committed beginners with basic linear algebra and the foundational quantum computing concepts. It is approachable for students of computer science, mathematics, and physics. No prior algorithm design experience is required. The course treats quantum algorithm reasoning as a craft you can develop through structured practice.