Quantum Algorithms · Mithilesh Kumar
Quantum Algorithms
From computational techniques to complete algorithms
A quantum algorithm is not a superposition followed by hope. It is a construction: specify what the input gives you, encode the property you need into amplitudes or phases, arrange interference so that the property becomes a measurement outcome, and account for every resource. This course builds that craft one technique at a time.
Begin reading Continue where you left off →Prerequisites and approach
The course continues Quantum Computing. It assumes amplitudes, unitary circuits, measurement, reversible oracles, phase kickback, and amplitude amplification as developed there, but no further mathematics or physics. Norms, spectra, Hamiltonians, singular values, and polynomial approximation are built from worked examples at the point where an algorithm needs them.
The chapters are organized by technique rather than by famous algorithm. Named algorithms such as Bernstein–Vazirani, phase estimation, Shor’s factoring, amplitude estimation, element distinctness, quantum signal processing, Trotter simulation, the variational eigensolver, QAOA, and measurement-based computation appear as applications or compositions of those techniques. Each technique is carried from a small circuit you can verify by hand to a statement about general input sizes, with its assumptions, costs, and limits.
How to use this course
Each subsection develops one step of an argument, lists the terms it defines, often includes a circuit or plot, and ends with three problems: a check of the central idea, a calculation applying it, and a challenge that probes a limit or a tempting mistake. Every problem has a worked solution behind “Show solution”. Each chapter opens with a reading guide and closes with exercises that have hints.
Small examples motivate general results; they do not prove them. When a chapter relies on a theorem whose proof lies beyond it, the text says so and links to the source. The study guide suggests routes through the material and the glossary collects definitions.