Skip to main content
SpringerLink
Log in

Quantum computing via the Bethe ansatz

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang–Baxter equation) and acts as a parametric two-body quantum gate. We conclude by comparing quantum computing via the factorisable scattering with topological quantum computing.

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

  1. Deutsch D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400(1818), 97–117 (1985)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Deutsch D.: Quantum computational networks. Proc. R. Soc. Lond. A 425(1868), 73–90 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. DiVincenzo D.P.: Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015–1022 (1995)

    Article  ADS  Google Scholar 

  4. Barenco A.: A universal two-bit gate for quantum computation. Proc. Royal Soc. Lond. A Math. Phys. Sci. 449(1937), 679–683 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Barenco A. et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)

    Article  ADS  Google Scholar 

  6. Sutherland B.: Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems. World Scientific, Singapore (2004)

    MATH  Google Scholar 

  7. McGuire J.B.: Study of exactly soluble one-dimensional N-body problems. J. Math. Phys. 5, 622 (1964)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Yang C.N.: Some exact results for the many body problems in one dimension with repulsive delta function interaction. Phys. Rev. Lett. 19, 1312–1314 (1967)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Yang C.N.: S matrix for the one-dimensional N-body problem with repilsive or attractive δ-function interaction. Phys. Rev. 168, 1920–1923 (1968)

    Article  ADS  Google Scholar 

  10. Zhang Y., Kauffman L.H., Ge M.L.: Universal quantum gate, Yang–Baxterization and Hamiltonian. Int. J. Quantum Inf. 4, 669–678 (2005)

    Article  MathSciNet  Google Scholar 

  11. Zhang Y., Kauffman L.H., Ge M.L.: Yang–Baxterizations, universal quantum gates and Hamiltonians. Quantum Inf. Process. 4, 159–197 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang Y., Kauffman L.H., Werner R.F.: Permutation and its partial transpose. Int. J. Quantum Inf. 5, 469–507 (2007)

    Article  MATH  Google Scholar 

  13. Zhang Y., Ge M.L.: GHZ states, almost-complex structure and Yang–Baxter equation. Quantum Inf. Process. 6, 363–379 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rowell E.C. et al.: Extraspecial two-groups, generalized Yang–Baxter equations and braiding quantum gates. Quantum Inf. Comput. 10(7&8), 0685–0702 (2010)

    MathSciNet  Google Scholar 

  15. Zhang, Y.: Quantum error correction code in the Hamiltonian formulation. arXiv:0801.2561v1, v2, v3

  16. Bose, S., Korepin, V.: Quantum gates between flying qubits via spin-independent scattering. arXiv:1106.2329

  17. Cordourier-Maruri G. et al.: Implementing quantum gates through scattering between a static and a flying qubit. Phys. Rev. A 82, 052313 (2010)

    Article  ADS  Google Scholar 

  18. Loss D., DiVincenzo D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

    Article  ADS  Google Scholar 

  19. DiVincenzo D.P. et al.: Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)

    Article  ADS  Google Scholar 

  20. Kitaev A.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zhuopu Zhonghu Computing Company, Wuhan, 430080, People’s Republic of China

    Yong Zhang

Authors
  1. Yong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Y. Quantum computing via the Bethe ansatz. Quantum Inf Process 11, 585–590 (2012). https://doi.org/10.1007/s11128-011-0268-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-011-0268-4

Keywords

Search

Navigation