Special Issue — Dedicated to 60th Birthday of Jozef Przytycki; Guest Editors: M. K. Dabkowski, V. Harizanov, J. H. Przytycki, R. Sazdanovic and A. SikoraNo Access

Quantum mechanics for quantum computing

Robert Owczarek

Robert Owczarek

Department of Mathematics, University of New Mexico, Los Alamos, USA

Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA

E-mail Address: rowczare@unm.edu

These are expanded notes (limited time allowed for presenting only a subset of the material) for lectures that I gave on 18th and 20th of November 2014 at the Department of mathematics of George Washington University at Washington, DC, on an invitation of Profs. Valentina Harizanov, and Józef Przytycki. The lectures were a part of activities of the Center for Quantum Computing, Information, Logic, and Topology. They were also honoring 60th birthday of Professor Przytycki.

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https://doi.org/10.1142/S0218216516400095Cited by:1 (Source: Crossref)

Abstract

Quantum computing is a field of great interest, attracting, among others, the attention of many mathematicians. Although not all quantum mechanics is needed to successfully engage in research on quantum computing, the somewhat superficial approach usually applied by non-physicists is, in the opinion of the author of the lectures, not feasible. The following notes from lectures given at the mathematics department of George Washington University are meant to be a partial remedy to the situation, offering a very brief and slightly unorthodox introduction to one-particle quantum mechanics, and even shorter discussion of passage to multi-particle quantum mechanics, as needed for quantum computing.

Keywords:

AMSC: 81P68, 81S10, 81Q05

References

1. V. I. Arnol’d, K. Vogtmann and A. Weinstein, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, Vol. 60, 2nd edn. (Springer, 1997). Google Scholar
2. V. I. Arnol’d and B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, Vol. 125 (Springer, 1999). Google Scholar
3. B. A. Khesin and R. Wendt, The Geometry of Infinite-Dimensional Groups (Springer, 2009). Crossref, Google Scholar
4. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Springer-Verlag, New York, 2009). Google Scholar
5. R. Abraham, J. E. Marsden, Foundations of Mechanics, 2nd edn. (Addison-Wesley Publishing Company, 1980). Google Scholar
6. J. J. Sławianowski, Geometry of Phase Spaces, 1st edn. (Wiley, 1992). Google Scholar
7. L. D. Landau and L. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd edn. (Butterworth-Heinemann, 1981). Google Scholar
8. A. Messiah, Quantum Mechanics, Dover Books on Physics (Dover Publications, 2014). Google Scholar
9. L. I. Schiff, Quantum Mechanics, International series in pure and applied physics, 2nd edn. (McGraw-Hill Book Co., 1955). Google Scholar
10. E. Elbaz, Quantum: The Quantum Theory of Particles, Fields and Cosmology, Theoretical and Mathematical Physics (Springer, 2011). Google Scholar
11. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, Dover Books on Physics, Emended Edition edition (Dover Publications, 2010). Google Scholar
12. J. S. Briggs, The equivalent emergence of time dependence in classical and quantum mechanics, preprint (2015), arXiv:1503.02146 v1 [quant-ph]. Google Scholar
13. A. Bohm, M. Gadella and J. D. Dollard, Dirac Kets, Gamow Vectors and Gel’fand Triplets: The Rigged Hilbert Space Formulation of Quantum Mechanics. Lectures in Mathematical Physics at the University of Texas at Austin, Lecture Notes in Physics, Vol. 348, 1st edn. (Springer, 2013). Google Scholar
14. E. Celeghini, A constructive presentation of rigged Hilbert spaces, preprint (2015), arXiv:1502.04891 v1 [math-ph]. Google Scholar
15. http://www.lorentz.leidenuniv.nl/history/spin/goudsmit.html. Google Scholar