Abstract
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs can be found in standard references such as Kitaev et al. (Classical and quantum computation, vol. 47. American Mathematical Society, Providence, 2002) and Nielson and Chuang (Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000) as well as Landsberg (Quantum computation and information: Notes for fall 2017 TAMU class, 2017).
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Physicists use the word “super” in the same way American teenagers use the word “like”.
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Acknowledgements
I thank the organizers of the International workshop on Quantum Physics and Geometry, especially Alessandra Bernardi, who also co-organized an intensive summer class on Quantum computing and quantum information theory that I gave June–July 2017. I also thank L. Chiantini, F. Gesmundo, F. Holweck, and G. Ottaviani for useful comments on a draft of this article. I am especially grateful to the anonymous referee for a very careful reading of the draft and numerous useful suggestions.
The author Landsberg supported by NSF grant DMS-1405348.
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Landsberg, J.M. (2019). A Very Brief Introduction to Quantum Computing and Quantum Information Theory for Mathematicians. In: Ballico, E., Bernardi, A., Carusotto, I., Mazzucchi, S., Moretti, V. (eds) Quantum Physics and Geometry. Lecture Notes of the Unione Matematica Italiana, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-06122-7_2
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