Quantum Computing
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Work description
Topic: Harnessing paraconsistent logic and non-additive probability in the formulation of quantum theory Background and objectives: Standard classical logic obeys the principle of explosion: from a contradiction, every statement follows. Any theory containing a single contradiction is thereby trivialized — it proves everything and becomes useless. This is a structural obstacle wherever contradictory assertions arise without genuine pathology: inconsistent databases, conflicting legal norms, and — most relevant here — the no-go theorems arising in quantum theory (Bell, Kochen–Specker,...). Such theorems establish a contradiction between the predictions of quantum theory and the assumptions of certain hidden-variable models, whose underlying structure is classical (a Boolean algebra of properties with classical probability). Paraconsistent logics reject the principle of explosion: a contradiction is tolerated locally without trivializing the surrounding theory. The natural algebraic setting is the class of co-Heyting algebras — the order-duals of Heyting algebras — in which the law of non-contradiction p ? ¬p = ? may fail. Co-Heyting algebras arise canonically in point-free topology: the lattice of sublocales of a locale is a coframe, hence a co-Heyting algebra, providing a large and well-understood class of paraconsistent models. This project develops models based on paraconsistent logic and non-additive probability theory to replace the hidden-variable models. The project has two objectives: (i) a paraconsistent reformulation of the no-go theorems of quantum theory (starting from Bell's theorem), and (ii) the corresponding development of the theory of non-additive probability on co-Heyting algebras. Activities: - prepare a report on paraconsistent models in quantum theory; - prepare a report on the development of non-additive probability theory in co-Heyting algebras; - analyse the possible implications for quantum computing, particularly in the development of algorithms that exploit contextuality; - submit two articles on the research results obtained; - collaborate with the quantum computing group at INESC TEC, exploring synergies between this topic and the group’s current research; - deliver a module on transferable skills.
Academic Qualifications
- Master’s degree in Computer Science, Physics or a related field.
Minimum profile required
- Knowledge and previous research experience in paraconsistent logic, quantum theory and quantum computing;- 2 articles published in a conference proceedings or peer-reviewed journal in the field of quantum theory or quantum computing.
Preference factors
- Publications in paraconsistent logics, quantum theory, and quantum computing.
Application Period
Since 15 Jun 2026 to 26 Jun 2026
[Open soon]
Centre
High-Assurance Software