The paper that created the field as a funded discipline. Read it after you understand phase estimation — it is more approachable than its reputation suggests.
Intermediate · 7 resources
Shor's algorithm
Factors large integers in polynomial time by reducing factoring to finding the period of a modular exponentiation function, which the QFT does efficiently.
Learn first:Quantum phase estimation
Why it matters
It is the reason governments fund quantum computing: it breaks RSA and elliptic-curve cryptography. It is also a beautiful lesson in reduction — most of Shor is classical number theory.
After this you will be able to
- Explain the reduction from factoring to period finding
- Identify which parts are classical and which are quantum
- Discuss realistic resource estimates for breaking RSA-2048
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.
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Craig Gidney & Martin Ekerå (2019)
The resource-estimate paper everyone cites when asked "when will RSA break?". A masterclass in turning an asymptotic algorithm into concrete hardware requirements.
Also covering this
4 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 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 Computation and Quantum Information
Nielsen & Chuang (Cambridge University Press)
Universally called "Mike & Ike" and still the field's reference text after two decades. Comprehensive rather than gentle — use it as the book you look things up in, not the one you read cover to cover 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.
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Topics that list Shor's algorithm as a prerequisite.