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A Lambda Calculus for Density Matrices with Classical and Probabilistic Controls

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Programming Languages and Systems (APLAS 2017)

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Abstract

In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, \(\lambda _\rho \), follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide an interpretation for programs as density matrices and functions upon them. The second one, \(\lambda _\rho ^\circ \), takes advantage of the density matrices presentation in order to follow the mixed trace of programs in a kind of generalised density matrix. Such a control can be seen as a weaker form of the quantum control and data approach.

A. Díaz-Caro—Supported by projects STIC-AmSud 16STIC05 FoQCoSS, PICT 2015-1208 and the Laboratoire International Associé “INFINIS”.

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Notes

  1. 1.

    A generalisation to any arbitrary measurement can be considered in a future, however, for the sake of simplicity in the classical control, we consider only measurements in the computational basis, which is a common practice in quantum lambda calculi [11, 17, 19, 21, 22, 31].

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Acknowledgements

We want to thank the anonymous reviewer for some important references and suggestions on future lines of work.

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Authors and Affiliations

  1. Universidad Nacional de Quilmes & CONICET, Roque Sáenz Peña 352, B1876BXD Bernal, Buenos Aires, Argentina

    Alejandro Díaz-Caro

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  1. Alejandro Díaz-Caro
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Correspondence to Alejandro Díaz-Caro .

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  1. University of Colorado, Boulder, Colorado, USA

    Bor-Yuh Evan Chang

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Díaz-Caro, A. (2017). A Lambda Calculus for Density Matrices with Classical and Probabilistic Controls. In: Chang, BY. (eds) Programming Languages and Systems. APLAS 2017. Lecture Notes in Computer Science(), vol 10695. Springer, Cham. https://doi.org/10.1007/978-3-319-71237-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-71237-6_22

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