Improved BDD Algorithms for the Simulation of Quantum Circuits

  • Vasilis Samoladas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)

Abstract

In this paper we develop novel algorithms for the simulation of quantum circuits on classical computers. The most efficient techniques previously studied, represent both quantum state vectors and quantum operator matrices as Multi-Terminal Binary Decision Diagrams (MTBDDS). This paper shows how to avoid representing quantum operators as matrices. Instead, we introduce a class of quantum operators that can be represented more compactly using a symbolic, BDD-based representation. We propose algorithms that apply operators on quantum states, using the symbolic representation. Our algorithms are shown to have superior performance over previous techniques, both asymptotically and experimentally.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdollahi, A., Pedram, M.: Analysis and synthesis of quantum circuits by using quantum decision diagrams. In: DATE 2006: Proc. of the Conf. on Design, Automation and Test in Europe, 3001 Leuven, Belgium, pp. 317–322. European Design and Automation Association (2006)Google Scholar
  2. 2.
    Beckman, D., Chari, A.N., Devabhaktuni, S., Preskill, J.: Efficient networks for quantum factoring. Phys. Rev. A 54(2), 1034–1063 (1996)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)MATHCrossRefGoogle Scholar
  4. 4.
    Fujita, M., McGeer, P.C., Yang, J.C.-Y.: Multi-terminal binary decision diagrams: An efficient data structure for matrix representation. Form. Methods Syst. Des. 10(2-3), 149–169 (1997)CrossRefGoogle Scholar
  5. 5.
    Minato, S.i.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: DAC 1993: Proceedings of the 30th international conference on Design automation, pp. 272–277. ACM Press, New York (1993)CrossRefGoogle Scholar
  6. 6.
    Koufogiannakis, C.: Techniques for simulating quantum computers. Master’s thesis, Technical U. of Crete (2004)Google Scholar
  7. 7.
    Miller, D.M., Thornton, M.A., Goodman, D.: Qmdd: A decision diagram structure for reversible and quantum circuits. In: IEEE Int’l Symp. on Multiple-Valued Logic (ISMVL), pp. 30–30 (2006)Google Scholar
  8. 8.
    Misra, J.: Powerlist: a structure for parallel recursion. ACM Trans. Program. Lang. Syst. 16(6), 1737–1767 (1994)CrossRefGoogle Scholar
  9. 9.
    Niwa, J., Matsumoto, K., Imai, H.: General-purpose parallel simulator for quantum computing. Phys. Rev. A 66(6), 062317 (2002)CrossRefGoogle Scholar
  10. 10.
    Viamontes, G., Markov, I., Hayes, J.: Improving gate-level simulation of quantum circuits. Quantum Information Processing 2(5), 347–380 (2003)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Viamontes, G.F., Markov, I.L., Hayes, J.P.: Graph-based simulation of quantum computation in the density matrix representation. Quantum Information Processing 5(2), 113–130 (2005)MathSciNetGoogle Scholar
  12. 12.
    Viamontes, G.F.: Gate-level simulation of quantum circuits. In: Proc. of the 6th Intl. Conference on Quantum Communication, Measurement, and Computing, pp. 311–314 (2002)Google Scholar
  13. 13.
    Viamontes, G.F.: Efficient Quantum Circuit Simulation. PhD thesis, University of Michigan (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vasilis Samoladas
    • 1
  1. 1.Technical University of CreteChaniaGreece

Personalised recommendations