Factoring 51 and 85 with 8 qubits

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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 28, 2013
Accession Number
AD1076821

Entities

People

  • Michael R. Geller
  • Zhongyuan Zhou

Organizations

  • University of Georgia

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Algorithms
  • Composite Materials
  • Computers
  • Demonstrations
  • Failure Mode And Effect Analysis
  • Intelligence Community (United States)
  • Ion Traps
  • Magnetic Resonance
  • Nuclear Magnetic Resonance
  • Probability
  • Probability Distributions
  • Quantum Algorithms
  • Quantum Circuits
  • Quantum Computers
  • Quantum Computing
  • Quantum Information Science
  • Shor'S Algorithm

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Quantum Computing