Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.779330
Title: Logical aspects of probability and quantum computation
Author: Zapata Fonseca, Octavio Baltasar
ISNI:       0000 0004 7965 0267
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2019
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Abstract:
Most of the work presented in this document can be read as a sequel to previous work of the author and collaborators, which has been published and appears in [DSZ16, DSZ17, ABdSZ17]. In [ABdSZ17], the mathematical description of quantum homomorphisms of graphs and more generally of relational structures, using the language of category theory is given. In particular, we introduced the concept of 'quantum' monad. In this thesis we show that the quantum monad fits nicely into the categorical framework of effectus theory, developed by Jacobs et al. [Jac15, CJWW15]. Effectus theory is an emergent field in categorical logic aiming to describe logic and probability, from the point of view of classical and quantum computation. The main contribution in the first part of this document prove that the Kleisli category of the quantum monad on relational structures is an effectus. The second part is rather different. There, distinct facets of the equivalence relation on graphs called cospectrality are described: algebraic, combinatorial and logical relations are presented as sufficient conditions on graphs for having the same spectrum (i.e. being 'cospectral'). Other equivalence of graphs (called fractional isomorphism) is also related using some 'game' comonads from Abramsky et al. [ADW17, Sha17, AS18]. We also describe a sufficient condition for a pair of graphs to be cospectral using the quantum monad: two Kleisli morphisms (going in opposite directions) between them satisfying certain compatibility requirement.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.779330  DOI: Not available
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