Quantum Information Processing

, Volume 12, Issue 1, pp 631–639 | Cite as

Integrable quantum computation

  • Yong Zhang


Integrable quantum computation is defined as quantum computing via the integrable condition, in which two-qubit gates are either nontrivial unitary solutions of the Yang–Baxter equation or the Swap gate (permutation). To make the definition clear, in this article, we explore the physics underlying the quantum circuit model, and then present a unified description on both quantum computing via the Bethe ansatz and quantum computing via the Yang–Baxter equation.


Quantum computing Bethe ansatz The Yang–Baxter equation 


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  1. 1.
    Deutsch D.: Quantum computational networks. Proc. R. Soc. Lond. A. 425(1868), 73–90 (1989)MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information, pp. 203–204. Cambridge University Press, Cambridge (2000) 2011MATHGoogle Scholar
  3. 3.
    Zhang Y.: Quantum computing via the Bethe ansatz. Quantum Inf. Process. 11(2), 585–590 (2012)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Sutherland B.: Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems. World Scientific, Singapore (2004)MATHGoogle Scholar
  5. 5.
    DiVincenzo D.P.: Two-bit gates are universal for quantum computation. Phys. Rev. A. 51, 1015–1022 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    Preskill, J.: Online Lecture Notes on Quantum Computation, Chap. 6 on Quantum Computing, pp. 21–22.
  7. 7.
    Zhang Y., Kauffman L.H., Ge M.L.: Yang–Baxterizations, universal quantum gates and Hamiltonians. Quantum Inf. Process. 4(3), 159–197 (2005)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gu C.H., Yang C.N.: A one-dimensional N Fermion problem with factorized S matrix. Commun. Math. Phys. 122(1), 105–116 (1989)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Bose, S., Korepin, V.: Quantum gates between flying qubits via spin-independent scattering. arXiv:1106.2329Google Scholar
  10. 10.
    Loss D., DiVincenzo D.P.: Quantum computation with quantum dots. Phys. Rev. A. 57, 120–126 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    DiVincenzo D.P. et al.: Universal quantum computation with the exchange interaction. Nature. 408, 339–342 (2000)ADSCrossRefGoogle Scholar
  12. 12.
    Terhal B.M., DiVincenzo D.P. et al.: Classical simulation of noninteracting-Fermion quantum circuits. Phys. Rev. A. 65, 032325/1–10 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Batchelor M. et al.: The Bethe ansatz after 75 years. Phys. Today. 60, 36–40 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    Zhang, Y.: Quantum error correction code in the Hamiltonian formulation. arXiv:0801.2561Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute of PhysicsChinese Academy of SciencesBeijingPeople’s Republic of China

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