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algorithms
advanced

Shor's Algorithm

Definition

A quantum algorithm for integer factorization that runs in polynomial time O((log N)³), exponentially faster than the best known classical algorithm. It threatens RSA encryption.

AI Explanation

Examples

  • • Factoring 15 = 3 × 5 was first demonstrated on a quantum computer in 2001.
  • • Breaking RSA-2048 would require ~4096 logical qubits (millions of physical qubits with error correction).

Visual

Flowchart showing: classical reduction to period finding → quantum Fourier transform → classical post-processing to extract factors.

Related Concepts

Quantum Fourier Transform
RSA
Post-Quantum Cryptography
Period Finding

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