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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press (1930)
Galindo, A., Martin-Delgado, M.A.: Information and Computation: Classical and Quantum Aspects. Rev. Mod. Phys. 74, 347–423 (2002) arXiv:quant-ph/0112105
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)
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)
Gerdt, V.P., Prokopenya, A.N.: Some algorithms for calculating unitary matrices for Quantum Circuits. Programming and Computer Software 36, 111–116 (2010)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum Cryptography. Rev. Mod. Phys. 74, 145–195 (2002)
Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)
Kollmitzer, C., Pivk, M. (eds.): Applied Quantum Cryptography. Lect. Notes Phys., vol. 797. Springer, Berlin (2010)
Mermin, N.D.: Quantum Computer Science. An Introduction. Cambridge University Press (2007)
Miller, G.L.: Riemann’s hypothesis and tests for primality. J. Comput. System Sci. 13, 300–317 (1976)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press (2000)
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)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comp. 26(5), 1484–1509 (1997)
Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media/Cambridge University Press (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)