Abstract
This paper is the second part of a series of two articles on quantum computation. If the first part was mostly concerned with the mathematical formalism, here we turn to the programmer’s perspective. We analyze the various existing models of quantum computation and the problem of the stability of quantum information. We discuss the needs and challenges for the design of a scalable quantum programming language. We then present two interesting approaches and examine their strengths and weaknesses. Finally, we take a step back, and review the state of the research on the semantics of quantum computation, and how this can help in achieving some of the goals.
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Abramsky, S. and Coecke, B., "A categorical semantics of quantum protocols," in Proc. of LICS’04, pp. 415–425, 2004.
Altenkirch, T. and Grattage, J., "A functional quantum programming language," in Proc. of LICS’05, pp. 249–258, 2005.
Barendregt, H. P., The Lambda-Calculus, its Syntax and Semantics, North Holland, 1984.
Bettelli S., Calarco T., Serafini L.: "Toward an architecture for quantum programming". The European Physical Journal D. 25(2), 181–200 (2003)
Blute R.F., Cockett J. R.B., Seely R. A. G.: "Differential categories". Math. Struct. in Comp. Sc. 16(6), 1049–1083 (2006)
Broadbent A., Kashefi E.: "Parallelizing quantum circuits," . Th. Comp. Sc. 410(26), 2489–2510 (2009)
Danos, V., Kashefi, E., Panangaden, P. and Perdrix, S., "Extended measurement calculus," Ch. 713), pp. 235–310.
Dixon L., Duncan R.: "Graphical reasoning in compact closed categories for quantum computation". Annals of Math. and Art. Int. 56, 23–42 (2009)
Duncan, R. and Perdrix, S., "Rewriting measurement-based quantum computations with generalised flow," in Proc. of ICALP’10, pp. 285–296, 2010.
Ehrhard T.: "On Kö the sequence spaces and linear logic". Math. Struct. in Comp. Sc. 12(5), 579–623 (2002)
Ehrhard T.: "Finiteness spaces". Math. Struct. in Comp. Sc. 15(4), 615–646 (2005)
Ehrhard, T. and Regnier, L., "The differential lambda-calculus," Th. Comp. Sc., 309, 1–2, pp. 1–41, 2003.
Gay, S. J., Mackie, I., editors, Semantic Techniques in Quantum Computation, Cambridge University Press, 2009.
Gay S. J: "Quantum programming languages Survey and bibliography". Math. Struct. in Comp. Sc. 16(4), 581–600 (2006)
Girard J.Y.: "Linear logic". Th Comp Sc. 50(1), 1–101 (1987)
Girard, J. Y., "Between logic and quantic: A tract," in Linear logic in computer science, Cambridge University Press, 2004.
Green, A. and Altenkirch, T., "The quantum IO monad," Ch. 513), pp. 173–205.
Hasuo, I. and Hoshino, N., "Semantics of higher-order quantum computation via geometry of interaction," in Proc. of LICS’11, pp. 237–246, 2011.
Howard, W., "The formulae–as–types notion of construction," in To H.B. Curry: essays on combinatory logic, lambda calculus, and formalism, Academic Press, pp. 479–490, 1980.
Kaye, P., Laflamme, R, and Mosca M., An Introduction to Quantum Computing, Oxford University Press, 2007.
Knill, E. H., "Conventions for quantum pseudocode," Tech. Rep. LAUR-96- 2724, Los Alamos National Laboratory, 1996.
Nielsen M. A. and Chuang I. L., Quantum Computation and Quantum Information, Cambridge University Press, 2002.
Ömer B., "Quantum programming in QCL", Master’s thesis, Institute of Information Systems, Technical University of Vienna, 2000.
Raussendorf R., Briegel H. J.: "A one-way quantum computer". Phys Rev Lett. 86(22), 5188–5191 (2001)
Sanders, J. W. and Zuliani, P., "Quantum programming," in Proc. of MPC’00, pp. 80–99, 2000.
Selinger P.: "Towards a quantum programming language". Math. Struct. in Comp. Sc. 14(4), 527–586 (2004)
Selinger, P. and Valiron, B., "On a fully abstract model for a quantum linear functional language," in Proc. of QPL’06, ENTCS 210, pp. 123–137, 2008.
Selinger P., Valiron B.: "A lambda calculus for quantum computation with classical control". Math. Struct. in Comp. Sc. 16(3), 527–552 (2006)
Selinger P. and Valiron, B., "Quantum lambda-calculus," Ch413), pp. 135–172.
Valiron, B., "Quantum computation: a tutorial," New Generation Computing, 2012. To appear.
van Tonder A.: "A lambda calculus for quantum computation". SIAM Journal of Computing. 33(5), 1109–1135 (2004)
Winskel, G., The Formal Semantics of Programming Languages, MIT Press, 1993.
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Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center contract number D11PC20168. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC, or the U.S. Government.
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Valiron, B. Quantum Computation: From a Programmer’s Perspective. New Gener. Comput. 31, 1–26 (2013). https://doi.org/10.1007/s00354-012-0120-0
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DOI: https://doi.org/10.1007/s00354-012-0120-0