Phd thesis on reversible logic

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(PDF) Reversible arithmetic logic unit for quantum arithmetic | Holger Axelsen -

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Reversible computing is the study of models of computation that exhibit both forward and backward determinism. To set reversible computing on a foundation as solid as the one for conventional computing requires both a significant adaptation of existing techniques and the development of new ones. In this thesis, we investigate reversible computing from a perspective of logic, broadly construed. To complement the operational point of view from which reversible computing is often studied, we offer a denotational account of reversibility in computation based on recent work in category theory. We propose two new techniques, founded in formal logic, for reasoning about reversible logic circuits.
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Grattage, Jonathan James A functional quantum programming language. PhD thesis, University of Nottingham. This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits.

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