A fast quantum mechanical algorithm for database search
Lov Grover (1996)
Six pages, and readable in an evening once you know basic circuit notation. A good first primary source because the whole argument fits in your head at once.
Intermediate · 9 resources
Grover's algorithm
Finds a marked item among N possibilities in about sqrt(N) queries instead of N, by repeatedly reflecting the state to pump amplitude onto the answer.
Learn first:Deutsch–Jozsa & Bernstein–Vazirani
Why it matters
It is the most broadly applicable quantum algorithm — anything you can phrase as search inherits the speedup — and the quadratic (not exponential) size of that speedup is a lesson in calibrated expectations.
After this you will be able to
- Explain the oracle and diffusion steps geometrically
- Work out the optimal number of iterations
- Implement Grover for a small search space
Start here
3 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
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.
IBM's free structured course platform and the successor to the old Qiskit Textbook. Mixes written lessons, videos and runnable notebooks, and takes you from 'what is a qubit' to running jobs on real hardware.
Also covering this
6 more resources
A free, complete undergraduate textbook with worked exercises. Uniquely, it teaches classical computing alongside quantum, so the comparison is always concrete rather than hand-waved.
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.
Coding tutorials, seminar talks and the complete recordings of the Qiskit Global Summer Schools — which are effectively free graduate-level lecture series on algorithms and error correction.
Quantum Algorithm Zoo
Stephen Jordan
A comprehensive catalogue of every known quantum algorithm with its speedup and primary references. The definitive answer to "has anyone found a quantum algorithm for X?"
Quantum Computing UK tutorials
Quantum Computing UK
Short, complete, copy-pasteable Qiskit tutorials for individual algorithms and protocols. Useful when you want one working example of a specific thing rather than a whole course.
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 Grover's algorithm as a prerequisite.