Quantum Computing: Lecture Notes
Ronald de Wolf (CWI / QuSoft)
Free, self-contained and rigorous, with exercises. Widely used as the standard course text in Europe and the best single free replacement for a paid textbook.
Intermediate · 5 resources
Deutsch–Jozsa & Bernstein–Vazirani
The teaching algorithms: contrived problems where a quantum computer needs one oracle query and a classical computer needs many, built entirely out of Hadamards and phase kickback.
Learn first:Multi-qubit states & tensor products
Why it matters
They are the smallest complete examples of quantum interference doing useful work, and phase kickback — the trick they teach — reappears in Grover, Shor and phase estimation.
After this you will be able to
- Explain phase kickback
- Derive the Deutsch–Jozsa speedup by hand
- Recognise the same pattern inside larger algorithms
Start here
3 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
Lecture Notes on Quantum Algorithms
Andrew Childs (University of Maryland)
The algorithms course. Hidden subgroup problems, quantum walks, Hamiltonian simulation and query complexity, all treated properly. Dense, and worth every hour.
Basics of Quantum Information
IBM Quantum Learning (John Watrous)
A rigorous but genuinely well-taught course by John Watrous covering single systems, multiple systems, quantum circuits and the core protocols. The cleanest bridge from intuition to real notation.
Also covering this
2 more resources
Qiskit Textbook (archived)
Qiskit community
The legendary original Qiskit Textbook, now archived in favour of IBM Quantum Learning. The notebooks still run and its algorithm chapters remain some of the clearest explanations written.
Quantum Katas
Microsoft
Self-paced programming exercises with automatic verification, in the style of code katas. Superposition, measurement, oracles, Grover and teleportation, each as a set of puzzles you must actually solve.
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This unlocks
Topics that list Deutsch–Jozsa & Bernstein–Vazirani as a prerequisite.