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Quantum Software Models: Density Matrix for Universal Software Design

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Quantum Software Engineering

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Abstract

The concept of this chapter is universal software design for all software system types—quantum, classical, or hybrid. It is based on the quantum density matrix for correct-by-design software modularization. It is complemented by higher-order functions in the hybrid transition cases.

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References

  1. Exman I, Shmilovich AT (2021) Quantum software models: the density matrix for classical and quantum software systems design. http://arxiv.org/abs/2103.13755

  2. Exman I (2012) Linear software models. In: Jacobson I, Goedicke M, Johnson P (eds) GTSE 2012, SEMAT Workshop on General Theory of Software Engineering, KTH, Stockholm, Sweden, pp 23–24. Video: http://www.youtube.com/watch?v=EJfzArH8-ls

  3. Exman I (2014) Linear software models: standard modularity highlights residual coupling. Int J Softw Eng Knowl Eng 24:183–210. https://doi.org/10.1142/S0218194014500089

    Article  Google Scholar 

  4. Exman I, Sakhnini R (2018) Linear software models: bipartite isomorphism between laplacian eigenvectors and modularity matrix eigenvectors. Int J Softw Eng Knowl Eng 28(7):897–935. https://doi.org/10.1142/S0218194018400107

    Article  Google Scholar 

  5. Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  6. Merris R (1994) Laplacian matrices of graphs: a survey. Linear Algebr Appl 197–198:143–176

    Article  MathSciNet  Google Scholar 

  7. Weisstein EW (2021) Positive definite matrix. https://mathworld.wolfram.com/PositiveDefiniteMatrix.html

  8. von Neumann J (1927) Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechnik. Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen, Mathematisch-Physikalische Klasse:245–272. https://eudml.org/doc/59230

  9. Braunstein SL, Ghosh S, Severini S (2006) The Laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states. arXiv:quant-ph/0406165v2

    Google Scholar 

  10. Paul AM (1974) Dirac, the principles of quantum mechanics, 4th edn. Oxford University Press, Oxford

    Google Scholar 

  11. Selinger P, Valiron B (2009) Quantum lambda calculus. In: Gay S, Mackie I (eds) Semantic techniques in quantum computation. Cambridge University Press, Cambridge, pp 135–172

    Chapter  Google Scholar 

  12. Green AS, Lumsdaine PL, Ross NJ, Selinger P, Valiron B (2013) Quipper: a scalable quantum programming language. arXiv:1304.3390

    Google Scholar 

  13. Deutsch D (1985) Quantum theory, the Church-Turing Principle and the universal quantum computer. Proc R Soc Lond A 400:97

    Article  MathSciNet  Google Scholar 

  14. Grover LK (1997) Quantum Computers can search arbitrarily large databases by a single query. Phys Rev Lett 79(23):4709–4712

    Article  Google Scholar 

  15. Arikan E (2002) An information-theoretic analysis of Grover’s algorithm. arXiv:quant-ph/0210068v2

    Google Scholar 

  16. Figgatt C, Maslov D, Landsman KA, Linke NM, Debnath S, Monroe C (2018) Complete 3-Qubit Grover Search on a programmable quantum computer. Nat Commun 8:1918. https://doi.org/10.1038/s41467-017-01904-7

    Article  Google Scholar 

  17. Gamma E, Helm R, Johnson R, Vlissides J (1995) Design patterns: elements of reusable object-oriented software. Addison-Wesley, Boston, MA. {the GoF book}

    MATH  Google Scholar 

  18. GitHub, Firefox iOS mobile browser (2021) https://github.com/mozilla-mobile/firefox-ios

  19. Fu X et al. eQASM: an executable quantum instruction set architecture. In: Proceedings of the 25th International Symposium on High-Performance Computer Architecture (HPCA’19). arXiv:1808.02449

    Google Scholar 

  20. Fu X et al (2017) An experimental microarchitecture for a superconducting quantum processor. http://arxiv.org/abs/1708.07677 [quant-ph]

  21. Fu X, Rol MA, Bultink CC, van Someren J, Khammassi N, Ashraf I, Vermeulen RFL, de Sterke JC, Vlothuizen WJ, Schouten RN, Almudéver CG, DiCarlo L, Bertels K (2018) A microarchitecture for a superconducting quantum processor. IEEE Micro:40–47

    Google Scholar 

  22. Exman I, Wallach H (2020) Linear software models: an Occam’s razor set of algebraic connectors integrates modules into a whole software system. Int J Softw Eng Knowl Eng 30(10):1375–1413. https://doi.org/10.1142/S0218194020400185

    Article  Google Scholar 

  23. Shi Y, Leung N, Gokhale P, Rossi Z, Schuster DI, Hoffmann H, Chong FT (2019) Optimized compilation of aggregated instructions for realistic quantum computers. In: Proceedings of the Asplos’19. pp 1031–1044

    Google Scholar 

  24. Wu CW (2009) Multipartite separability of Laplacian matrices of graphs. Electr J Combinat 16:#R61

    Article  MathSciNet  Google Scholar 

  25. Baldwin CY, Clark KB (2000) Design rules, vol I. The power of modularity. MIT Press, MA

    Book  Google Scholar 

  26. Cai Y, Sullivan KJ (2006) Modularity analysis of logical design models. In: Proc. 21st IEEE/ACM Int. Conf. Automated Software Eng. ASE’06, Tokyo, Japan, pp 91–102

    Google Scholar 

  27. McCaskey J, Dumitrescu EF, Liakh D, Chen M, Feng W, Humble TS (2018) A language and hardware independent approach to quantum–classical computing. SoftwareX 7:245–254. https://doi.org/10.1016/j.softx.2018.07.007

    Article  Google Scholar 

  28. Hornibrook JM et al (2014) Cryogenic control architecture for large-scale quantum computing. arXiv:1409.2202

    Google Scholar 

  29. Deutsch D, Barenco A, Ekert A (1995) Universality in quantum computation. Proc R Soc Lond A. Also: arXiv:quant-ph/9505018 – May 1995

    Google Scholar 

  30. Perez-Castillo R, Jimenez-Navajas L, Piattini M. Modelling quantum circuits with UML. In: Proceedings of the QSE’2021 Quantum Software Engineering Workshop. arXiv:2103.16169

    Google Scholar 

  31. Feynman RP (1982) Simulating physics with computers. Int J Theor Phys 21:467

    Article  MathSciNet  Google Scholar 

  32. Lloyd S (1995) Almost any quantum logic gate is universal. Phys Rev Let 75(2):346–349

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Software Engineering Department, The Jerusalem College of Engineering – Azrieli, Jerusalem, Israel

    Iaakov Exman & Alon Tsalik Shmilovich

Authors
  1. Iaakov Exman
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  2. Alon Tsalik Shmilovich
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Corresponding author

Correspondence to Iaakov Exman .

Editor information

Editors and Affiliations

  1. aQuantum, University of Castilla-La Mancha (UCLM), Ciudad Real, Spain

    Manuel A. Serrano

  2. aQuantum, University of Castilla-La Mancha (UCLM), Talavera de la Reina, Spain

    Ricardo Pérez-Castillo

  3. aQuantum, University of Castilla-La Mancha (UCLM), Ciudad Real, Spain

    Mario Piattini

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Exman, I., Shmilovich, A.T. (2022). Quantum Software Models: Density Matrix for Universal Software Design. In: Serrano, M.A., Pérez-Castillo, R., Piattini, M. (eds) Quantum Software Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-05324-5_7

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  • DOI: https://doi.org/10.1007/978-3-031-05324-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-05323-8

  • Online ISBN: 978-3-031-05324-5

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