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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Oversimplifying quantum factoring.

John A Smolin1, Graeme Smith, Alexander Vargo

  • 1IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA. smolin@alum.mit.edu

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|July 13, 2013
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Summary
This summary is machine-generated.

Shor's quantum factoring algorithm can be simplified for all composite numbers, making experiments easier. Valid implementations must avoid using the factors being sought for accurate results.

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Area of Science:

  • Quantum computing
  • Number theory
  • Algorithm analysis

Background:

  • Shor's quantum factoring algorithm offers exponential speedup over classical methods.
  • Prior experimental setups relied on pre-determined factors, limiting practical application.

Purpose of the Study:

  • To demonstrate a universal simplification for Shor's algorithm applicable to all composite numbers.
  • To re-evaluate the experimental difficulty of quantum factoring.

Main Methods:

  • Developed a theoretical framework showing all composite numbers allow algorithm simplification.
  • Proposed a circuit model equivalent to coin flipping for factoring experiments.

Main Results:

  • Identified a simplification applicable to any composite number, independent of its factors.
  • Demonstrated that experimental difficulty correlates with chosen simplification level, not number size.

Conclusions:

  • Experimental complexity of Shor's algorithm is not solely dependent on the magnitude of the number being factored.
  • Future valid experimental implementations should not presuppose knowledge of the factors.
  • The proposed simplification offers a more practical approach to experimental quantum factoring.