Advertisement

Changing the Gate Order for Optimal LNN Conversion

  • Atsushi Matsuo
  • Shigeru Yamashita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7165)

Abstract

While several physical realization schemes have been proposed for future quantum information processing, most known facts suggest that quantum information processing should have intrinsic limitations; physically realizable operations would be only interaction between neighbor qubits. To use only such physically realizable operations, we need to convert a general quantum circuit into one for an so-called Linear Nearest Neighbor (LNN) architecture where any gates should be operated between only adjacent qubits. Thus, there has been much attention to develop efficient methods to design quantum circuits for an LNN architecture. Most of the existing researches do not consider changing the gate order of the original circuit, and thus the result may not be optimal. In this paper, we propose a method to convert a quantum circuit into one for an LNN architecture with the smallest number of SWAP gates. Our method improves the previous result for Approximate Quantum Fourier Transform (AQFT) by the state-of-the-art design method.

Keywords

Quantum Circuit Linear Nearest Neighbor Adjacent Transposition Graph 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
  2. 2.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ross, M., Oskin, M.: Quantum computing. Commun. ACM 51(7), 12–13 (2008)CrossRefGoogle Scholar
  4. 4.
    Fowler, A.G., Devitt, S.J., Hollenberg, L.C.: Implementation of shor’s algorithm on a linear nearest neighbour qubit array. Quantum Information and Computation 4(4), 4:237–4:251 (2004)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Takahashi, Y., Kunihiro, N., Ohta, K.: The quantum fourier transform on a linear nearest neighbor architecture. Quantum Information and Computation 7(4), 383–391 (2007)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Kutin, S.A.: Shor’s algorithm on a nearest-neighbor machine. Technical report, Asian Conference on Quantum Information Science (2007)Google Scholar
  7. 7.
    Choi, B.S., Meter, R.V.: Effects of interaction distance on quantum addition circuits. ArXiv e-prints (September 2008)Google Scholar
  8. 8.
    Fowler, A.G., Hill, C.D., Hollenberg, L.C.L.: Quantum-error correction on linear-nearest-neighbor qubit arrays. Phys. Rev. A 69(4), 042314 (2004)CrossRefGoogle Scholar
  9. 9.
    Hirata, Y., Nakanishi, M., Yamashita, S., Nakashima, Y.: An efficient coversion o quantum circuits to a linear nearest neighbor architecture. Qnantum Information and Computation 11(1), 142–166 (2011)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Saeedi, M., Wille, R., Drechsler, R.: Synthesis of quantum circuits for linear nearest neighbor architectures. Quantum Information Processing, 1–23 (2010), 10.1007/s11128-010-0201-2Google Scholar
  11. 11.
    Wille, R., Große, D., Teuber, L., Dueck, G.W., Drechsler, R.: RevLib: An online resource for reversible functions and reversible circuits. In: International Symposium on Multiple Valued Logic, pp. 220–225 (May 2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Atsushi Matsuo
    • 1
  • Shigeru Yamashita
    • 1
  1. 1.Graduate School of Science and EngineeringRitsumeikan UniversityKusatsuJapan

Personalised recommendations