Efficient algorithms for NMR quantum computers with small qubits

  • Authors:

  • Noboru Kunihiro;Shigeru Yamashita

  • Affiliations:

  • The University of Electro-communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan;Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara 631-0101, Japan

  • Venue:
  • New Generation Computing - Quantum computing
  • Year:
  • 2003

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Abstract

The security of the RSA cryptosystems is based on the difficulty of factoring a large composite integer. In 1994, Shor showed that factoring a large composite is executable in polynomial time if we use a quantum Turing machine. Since this algorithm is complicated, straightforward implementations seem impractical judging from current technologies. In this paper, we propose simple and efficient algorithms for factoring and discrete logarithm problem based on NMR quantum computers. Our algorithms are easier to implement if we consider NMR quantum computers with small qubits.