Quantum Information Processing

, Volume 11, Issue 2, pp 585–590 | Cite as

Quantum computing via the Bethe ansatz



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.


Quantum computing The Bethe ansatz The Yang–Baxter equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Deutsch D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400(1818), 97–117 (1985)MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Deutsch D.: Quantum computational networks. Proc. R. Soc. Lond. A 425(1868), 73–90 (1989)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    DiVincenzo D.P.: Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015–1022 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    Barenco A.: A universal two-bit gate for quantum computation. Proc. Royal Soc. Lond. A Math. Phys. Sci. 449(1937), 679–683 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Barenco A. et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    Sutherland B.: Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems. World Scientific, Singapore (2004)MATHGoogle Scholar
  7. 7.
    McGuire J.B.: Study of exactly soluble one-dimensional N-body problems. J. Math. Phys. 5, 622 (1964)MathSciNetADSMATHCrossRefGoogle Scholar
  8. 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)MathSciNetADSMATHCrossRefGoogle Scholar
  9. 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)ADSCrossRefGoogle Scholar
  10. 10.
    Zhang Y., Kauffman L.H., Ge M.L.: Universal quantum gate, Yang–Baxterization and Hamiltonian. Int. J. Quantum Inf. 4, 669–678 (2005)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhang Y., Kauffman L.H., Ge M.L.: Yang–Baxterizations, universal quantum gates and Hamiltonians. Quantum Inf. Process. 4, 159–197 (2005)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Zhang Y., Kauffman L.H., Werner R.F.: Permutation and its partial transpose. Int. J. Quantum Inf. 5, 469–507 (2007)MATHCrossRefGoogle Scholar
  13. 13.
    Zhang Y., Ge M.L.: GHZ states, almost-complex structure and Yang–Baxter equation. Quantum Inf. Process. 6, 363–379 (2007)MathSciNetMATHCrossRefGoogle Scholar
  14. 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)MathSciNetGoogle Scholar
  15. 15.
    Zhang, Y.: Quantum error correction code in the Hamiltonian formulation. arXiv:0801.2561v1, v2, v3Google Scholar
  16. 16.
    Bose, S., Korepin, V.: Quantum gates between flying qubits via spin-independent scattering. arXiv:1106.2329Google Scholar
  17. 17.
    Cordourier-Maruri G. et al.: Implementing quantum gates through scattering between a static and a flying qubit. Phys. Rev. A 82, 052313 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    Loss D., DiVincenzo D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    DiVincenzo D.P. et al.: Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)ADSCrossRefGoogle Scholar
  20. 20.
    Kitaev A.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2 (2003)MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Zhuopu Zhonghu Computing CompanyWuhanPeople’s Republic of China

Personalised recommendations