The Circuit Model of Quantum Computation and Its Simulation with Mathematica

  • Vladimir P. Gerdt
  • Alexander N. Prokopenya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


We consider an application of the Mathematica package QuantumCircuit to simulation of quantum circuits implementing two of the best known quantum algorithms, namely, the Grover search algorithm and the Shor algorithm for order finding. The algorithms are discussed in detail and concrete examples of their application are demonstrated. The main features of the package QuantumCircuit which can be used for the simulation of an arbitrary quantum algorithm are briefly described.


Quantum computation quantum circuit algorithm simulation Mathematica 


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  1. 1.
    Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press (1930)Google Scholar
  2. 2.
    Galindo, A., Martin-Delgado, M.A.: Information and Computation: Classical and Quantum Aspects. Rev. Mod. Phys. 74, 347–423 (2002) arXiv:quant-ph/0112105MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Gerdt, V.P., Kragler, R., Prokopenya, A.N.: A Mathematica Package for Simulation of Quantum Computation. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2009. LNCS, vol. 5743, pp. 106–117. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Gerdt, V.P., Kragler, R., Prokopenya, A.N.: A Mathematica program for constructing quantum circuits and computing their unitary matrices. Physics of Particles and Nuclei, Letters 6(7), 526–529 (2009)CrossRefGoogle Scholar
  5. 5.
    Gerdt, V.P., Prokopenya, A.N.: Some algorithms for calculating unitary matrices for Quantum Circuits. Programming and Computer Software 36, 111–116 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum Cryptography. Rev. Mod. Phys. 74, 145–195 (2002)CrossRefGoogle Scholar
  7. 7.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)CrossRefGoogle Scholar
  8. 8.
    Kollmitzer, C., Pivk, M. (eds.): Applied Quantum Cryptography. Lect. Notes Phys., vol. 797. Springer, Berlin (2010)zbMATHGoogle Scholar
  9. 9.
    Mermin, N.D.: Quantum Computer Science. An Introduction. Cambridge University Press (2007)Google Scholar
  10. 10.
    Miller, G.L.: Riemann’s hypothesis and tests for primality. J. Comput. System Sci. 13, 300–317 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
  12. 12.
    Rivest, R.L., Shamir, A., Adleman, L.: A method of obtaining digital signatures and public-key cryptosystems. Comm. Assoc. Comput. Mach. 21, 120–126 (1978)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comp. 26(5), 1484–1509 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media/Cambridge University Press (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vladimir P. Gerdt
    • 1
  • Alexander N. Prokopenya
    • 2
    • 3
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Collegium Mazovia in SiedlceSiedlcePoland
  3. 3.Brest State Technical UniversityBrestBelarus

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