Quantum computing beyond applied linear algebra
DOI:
https://doi.org/10.55630/mem.2023.52.50-68Keywords:
quantum logic, quantum computations, quantum algorithmsAbstract
Quantum Informatics is a field studying the new possibilities that quantum theory offers for the purposes of information processing and transfer. This involves Quantum Computing. In this lecture we first give a brief introduction to quantum theory. The content follows a more abstract and higher mathematical level in line with the ideas coming from Birkhoff and von Neumann in their outstanding work on the “logic of quantum mechanics” (Annals of Mathematics, Second Series, 37, No. 4 (1936), 823–843). This is followed by a brief introduction to the problems of Quantum Computing from the perspective of Computer Science and Mathematics.
References
G. Birkhoff. Lattice Theory. American Mathematical Society, Providence, Rhode Island, 1st edition 1940, 3d edition 1973.
A. De Vos. Reversible Computing: Fundamentals, Quantum Computing, and Applications. Wiley, 2010
G. Birkhoff, J. Von Neumann. The Logic of Quantum Mechanics. Annals of Mathematics, Second Series, 37, No. 4 (1936), 823–843.
D. Deutsch. Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer. 1985
P. A. M. Dirac. The Principles of Quantum Mechanics. Oxford University Press, 1st edition 1930, 4th edition 1967.
M. Dubois-Violette. Exceptional quantum geometry and particle physics. Nucl. Phys. B 912 (2016), 426–444; arXiv:1604.01247
R. P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21, Nos. 6/7 (1982), 467-488.
R. Goldblatt. Topoi: The Categorial Analysis of Logic. Revised Edition, Elsevier, New York, 1984.
G. Gratzer. ¨ Lattice Theory: Foundation. Basel, Birkhauser, 2011.
P. Jordan, J. Von Neumann, E. Wigner. On an Algebraic Generalization of the Quantum Mechanical Formalism. Annals of Mathematics, Second Series, 35, No. 1 (1934), 29–64.
M. A. Nielsen, I. L. Chuang. Quantum Computation and Quantum Information. 10th Anniversary Edition, Cambridge University Press, 2010.
C. Piron. Foundations of Quantum Physics. London, W.A. Benjamin, Inc., 1976.
V. S. Varadarajan. Geometry of Quantum Theory, Volume 1. New York, Springer, 1968.
V. S. Varadarajan. Geometry of Quantum Theory, Second Edition. New York, Springer, 1968.
J. von Neumann. Mathematical Foundations of Quantum Mechanics, Springer, 1st edition 1932; english translation by Princeton University Press 1955, 2018
M. Ying. Foundations of Quantum Programming. Elsevier, 2016.
Н. М. Николов. Квантова информатика, учебно пособие, 2022. [N. M. Nikolov. Kvantova informatika, uchebno posobie, 2022] (in Bulgarian).
