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The Circuit Model of Quantum Computation and Its Simulation with Mathematica

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Mathematical Modeling and Computational Science (MMCP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7125))

Abstract

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.

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References

  1. Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press (1930)

    Google Scholar 

  2. Galindo, A., Martin-Delgado, M.A.: Information and Computation: Classical and Quantum Aspects. Rev. Mod. Phys. 74, 347–423 (2002) arXiv:quant-ph/0112105

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  5. Gerdt, V.P., Prokopenya, A.N.: Some algorithms for calculating unitary matrices for Quantum Circuits. Programming and Computer Software 36, 111–116 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum Cryptography. Rev. Mod. Phys. 74, 145–195 (2002)

    Article  Google Scholar 

  7. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)

    Article  Google Scholar 

  8. Kollmitzer, C., Pivk, M. (eds.): Applied Quantum Cryptography. Lect. Notes Phys., vol. 797. Springer, Berlin (2010)

    MATH  Google Scholar 

  9. Mermin, N.D.: Quantum Computer Science. An Introduction. Cambridge University Press (2007)

    Google Scholar 

  10. Miller, G.L.: Riemann’s hypothesis and tests for primality. J. Comput. System Sci. 13, 300–317 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press (2000)

    Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media/Cambridge University Press (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia

    Vladimir P. Gerdt

  2. Collegium Mazovia in Siedlce, ul. Sokolowska 161, 08-110, Siedlce, Poland

    Alexander N. Prokopenya

  3. Brest State Technical University, Moskovskaya str. 267, 224017, Brest, Belarus

    Alexander N. Prokopenya

Authors
  1. Vladimir P. Gerdt
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  2. Alexander N. Prokopenya
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot Curie St., 141980, Dubna, Russia

    Gheorghe Adam

  2. Technical University of Košice, Němcovej 32, 042 00, Košice, Slovakia

    Ján Buša

  3. Pavol Jozef Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Michal Hnatič

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© 2012 Springer-Verlag Berlin Heidelberg

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Gerdt, V.P., Prokopenya, A.N. (2012). The Circuit Model of Quantum Computation and Its Simulation with Mathematica. In: Adam, G., Buša, J., Hnatič, M. (eds) Mathematical Modeling and Computational Science. MMCP 2011. Lecture Notes in Computer Science, vol 7125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28212-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-28212-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28211-9

  • Online ISBN: 978-3-642-28212-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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