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Quantum Expectation Transformers for Cost Analysis

Authors: Avanzini, Martin; Moser, Georg; Péchoux, Romain; Perdrix, Simon; Zamdzhiev, Vladimir;

Quantum Expectation Transformers for Cost Analysis

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.

Countries
France, Austria
Keywords

FOS: Computer and information sciences, formal semantics, Quantum Physics, Computer Science - Logic in Computer Science, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Computer Science - Programming Languages, FOS: Physical sciences, complexity analysis, [INFO.INFO-PL] Computer Science [cs]/Programming Languages [cs.PL], Logic in Computer Science (cs.LO), quantum programming, expectation transformer, Quantum Physics (quant-ph), [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Programming Languages (cs.PL)

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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