Skip to main content
SpringerLink
Log in

Existence of the Exact CNOT on a Quantum Computer with the Exchange Interaction

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

We prove the existence of the exact CNOT gate on aquantum computer with the nearest-neighbor exchange interaction in the serial operation mode. Its existence has been an open problem, though a concrete sequence of exchange operations, which is approximately locally equivalent to the exact CNOT, has already been found. We found the exact values of time parameters (exchange rates between qubits) by using computer algebraic techniques such as Gröbner bases and resultants. These techniques have been widely used for finding rigorous solutions of simultaneous algebraic equations, and here are applied to finding quantum gates on the decoherence-free subsystem for the first time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • M.A. Nielsen I.L. Chuang (2000) Quantum Computation and Quantum Information Cambridge University Press Cambridge UK

    Google Scholar 

  • D. Bacon J. Kempe D.P. DiVincenzo D.A. Lidar K.B. Whaley (2000) Phys. Rev. Lett. 85 1758 Occurrence Handle10.1103/PhysRevLett.85.1758 Occurrence Handle1:CAS:528:DC%2BD3cXlslGntbY%3D Occurrence Handle10970607

    Article  CAS  PubMed  Google Scholar 

  • J. Kempe D. Bacon D.A. Lidar K.B. Whaley (2001) Phys Rev A 63 042307

    Google Scholar 

  • J. Kempe D. Bacon D.P. DiVincenzo K.B. Whaley (2001) Quant. Inf. Comput. 1 241

    Google Scholar 

  • J. Kempe K.B. Whaley (2002) Phys Rev A 65 052330

    Google Scholar 

  • D.Bacon (2003). Ph.D thesis, UC Berkeley

  • D. A. Lidar and K. B. Whaley, Irreversible Quantum Dynamics, F. Benatti, R. Floreanini (eds.) (Springer Lecture Notes in Physics vol. 622, Berlin, 2003), p.83.

  • D.P. DiVincenzo D. Bacon J. Kempe S. Burkard K.B. Whaley (2000) Nature 408 339 Occurrence Handle10.1038/35042541 Occurrence Handle1:CAS:528:DC%2BD3cXosVeksLw%3D Occurrence Handle11099036

    Article  CAS  PubMed  Google Scholar 

  • M. Hsieh J. Kempe S. Myrgren K. B. Whaley (2003) Quant. Inf. Proc. 2 289 Occurrence Handle10.1023/B:QINP.0000020084.53422.8e Occurrence HandleMR2063922

    Article  MathSciNet  Google Scholar 

  • E.S. Myrgren K.B. Whaley (2003) Quant. Inf. Proc. 2 309 Occurrence Handle10.1023/B:QINP.0000022724.32019.7c

    Article  Google Scholar 

  • D. Cox J. Little D. O’Shea (1992) Ideals, Varieties, and Algorithms Springer-Verlag New York

    Google Scholar 

  • D. Cox J. Little D. O’Shea (1998) Using Algebraic Geometry Springer-Verlag New York

    Google Scholar 

  • http://www.maplesoft.com/

  • http://www.math.kobe-u.ac.jp/Asir/

  • T. Becker V. Weispfenning (1993) Gröbner Bases Springer-Verlag New York

    Google Scholar 

  • Y. Makhlin (2002) Quant. inf. Proc. 1 243 Occurrence Handle10.1023/A:1022144002391

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NTT Communication Science Laboratories, NTT Corporation, 3-1, Morinosato Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan

    Y. Kawano, H. Sekigawa & K. Shirayanagi

  2. Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    K. Kimura

  3. Department of Mathematics, Kobe University, Nada-ku, Kobe, 657-8501, Japan

    M. Noro

  4. Graduate School of Engineering Science, Osaka University, Toyonaka-shi, Osaka, 560-8531, Japan

    M. Kitagawa

  5. NTT Communication Science Laboratories, NTT Corporation, 3-1, Morinosato Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan

    M. Kitagawa

  6. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579, Japan

    M. Ozawa

  7. Japan Science and Technology Agency, Japan

    M. Kitagawa & M. Ozawa

Authors
  1. Y. Kawano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Kimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Sekigawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Noro
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. Shirayanagi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Kitagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. M. Ozawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

PACS: 02.70.Wz, 03.65.Yz, 03.67.Lx

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kawano, Y., Kimura, K., Sekigawa, H. et al. Existence of the Exact CNOT on a Quantum Computer with the Exchange Interaction. Quantum Inf Process 4, 65–85 (2005). https://doi.org/10.1007/s11128-005-4480-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-005-4480-y

Keywords

Search

Navigation