Factoring 51 and 85 with 8 qubits
Related Experiment Video
Updated: May 6, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Michael R Geller1, Zhongyuan Zhou
1Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA.
Abstract:
We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85, 771, 1285, 4369, … have the simplifying property that the order of a modulo N for every base a coprime to N is a power of 2, significantly reducing the usual phase estimation precision requirement. Prime factorization of 51 and 85 can be demonstrated with only 8 qubits and a modular exponentiation circuit consisting of no more than four CNOT gates.
Related Concept Videos
Synthetic Disvision of Polynomials
Quantum Numbers
Long Division of Polynomials
Compacting Factor test
The procedure begins by placing concrete into the upper hopper without any compaction. Once filled, the bottom door of this hopper is opened,...
Factorial Design
Rationalizing Substitutions

