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Quantum Expectation Transformers for Cost Analysis

Martin Avanzini 1 Georg Moser 2 Romain Péchoux 3 Simon Perdrix 3 Vladimir Zamdzhiev 3
1 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
3 MOCQUA - Designing the Future of Computational Models
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We introduce a new kind of expectation transformer for a mixed classical-quantum programming language. Our semantic approach relies on a new notion of a cost structure, which we introduce and which can be seen as a specialisation of the Kegelspitzen of Keimel and Plotkin. We show that our weakest precondition analysis is both sound and adequate with respect to the operational semantics of the language. Using the induced expectation transformer, we provide formal analysis methods for the expected cost analysis and expected value analysis of classical-quantum programs. We illustrate the usefulness of our techniques by computing the expected cost of several well-known quantum algorithms and protocols, such as coin tossing, repeat until success, entangled state preparation, and quantum walks.
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https://hal.inria.fr/hal-03540366
Contributor : Vladimir Zamdzhiev Connect in order to contact the contributor
Submitted on : Sunday, January 23, 2022 - 9:52:32 PM
Last modification on : Monday, February 14, 2022 - 11:05:05 AM
Long-term archiving on: : Sunday, April 24, 2022 - 6:09:47 PM

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  • HAL Id : hal-03540366, version 1

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Martin Avanzini, Georg Moser, Romain Péchoux, Simon Perdrix, Vladimir Zamdzhiev. Quantum Expectation Transformers for Cost Analysis. 2022. ⟨hal-03540366⟩

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