How does Shor's algorithm factor integers?

Shor's algorithm is a quantum algorithm developed by Peter Shor in 1994 to find the prime factors of an integer. On a quantum computer, it runs in polynomial time, demonstrating a superpolynomial speedup compared to the best known classical algorithms like the general number field sieve. It achieves this by transforming the factoring problem into a period-finding problem.

What we know

• Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. [1, 2]
• The algorithm was developed in 1994 by American mathematician Peter Shor. [2]
• On a quantum computer, Shor's algorithm runs in polynomial time with respect to the input size. [2]
• Both the discrete logarithm algorithm and the factoring algorithm are instances of the period-finding problem. [2]

Where to go next

• whoWho was Peter Shor?
• how it workedHow does quantum error correction affect quantum computers?
• compared withWhat is the general number field sieve?
• the bigger pictureWhat is the P versus NP problem?
• how we knowWhat is the hidden subgroup problem?
• an unexpected connectionHow do Fibonacci numbers appear in nature and computer science?Although number theory underlies both quantum factoring algorithms and Fibonacci sequences, Fibonacci numbers unexpectedly show up in biological growth patterns like plant leaves as well as data structures.

Sources

• [1]Shor's algorithm (Wikidata Q940334) · CC0 1.0
• [2]Shor's algorithm · CC BY-SA 4.0
• [3]P versus NP problem · CC BY-SA 4.0
• [4]NP (complexity) · CC BY-SA 4.0
• [5]Fibonacci sequence · CC BY-SA 4.0