Abstract
The concepts of bit and qubit, the fundamental units of information in classical and quantum computing respectively, are introduced. We discuss features of the binary number system, linear vector, and Hilbert spaces. We learn how to manipulate qubits and introduce Dirac’s bra-ket formalism to facilitate operations in Hilbert space. Scalar, direct and outer products of bra-kets in multi-qubit systems are introduced. We define Hermitian and unitary operators in a 2n-dimensional Hilbert space and use the bra-ket formalism to construct them. I summarize the foundational postulates of quantum mechanics, as espoused by the Copenhagen interpretation, for a finite set of qubits.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
David Wineland [7], shows that such a notion is not as fanciful as might first appear.
- 2.
In older textbooks the definition for the inner product is given by the alternative notation (|Φ〉, |Ψ〉) and does not rely on the use of dual space.
- 3.
Thought experiment.
- 4.
References
David Deutsch, The Fabric of Reality, (Allen Lane, London 1997)
Claude Cohen-Tannoudji, Bernard Dieu, Frank Laloe, Quantum Mechanics Vol 1, (Wiley 1991)
R. B. Griffiths, in Stanford Encyclopedia of Philosophy (2014), http://plato.stanford.edu/entries/qm-consistent-histories
Thomas F. Jordan, Linear Operators for Quantum Mechanics, (Dover Publications Inc., Mineola New York 1997)
David Mermin, Physics Today 39; https://doi.org/10.1063/1.2815188
Jan-Markus Schwindt, Conceptual Basis of Quantum Mechanics, (Springer, 2017)
David Wineland, http://www.youtube.com/watch?v=RFkyvkBV5dM#t=32m50s
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zygelman, B. (2018). A Quantum Mechanic’s Toolbox. In: A First Introduction to Quantum Computing and Information. Springer, Cham. https://doi.org/10.1007/978-3-319-91629-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-91629-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91628-6
Online ISBN: 978-3-319-91629-3
eBook Packages: Computer ScienceComputer Science (R0)