Enhorabona al nou graduat de doctorat de l'ICFO
El Dr Luke Mortimer s’ha doctorat amb una tesi titulada “A Variety of Optimization Techniques Applied In the Context of Quantum Information Theory"
Felicitem el Dr. Luke Mortimer que ha defensat la seva tesi aquest matí a l’Auditori de l'ICFO.
El Dr. Mortimer va obtenir el seu Màster en Física Teòrica a la University of York, abans d'incorporar-se al grup de recerca de Quantum Information Theory dirigit pel professor ICREA a l’ICFO Dr. Antonio Acín. La seva tesi titulada " A Variety of Optimization Techniques Applied In the Context of Quantum Information Theory" ha estat dirigida pel prof. Dr. Antonio Acín.
RESUMEN:
The thesis considers a number of optimisation techniques applied in the context of quantum information theory. After a pedagogical introduction of both quantum information theory and optimisation, it considers three main avenues of research. The first is the well-known foundational open problem of mutually unbiased bases, which consists of finding sets of orthonormal bases that are each unbiased with one another. More specifically, it remains unknown whether one can find a set of 4 mutually unbiased bases in dimension 6. A variety of optimisation techniques are applied, including non-linear semidefinite programming, see-saw optimisation, semidefinite programming relaxations, branch-and-cut, gradient descent methods and the method of Lagrange multipliers, each providing further insights into the problem. The second avenue is that of Bell nonlocality, more specifically attempting to simplify the hierarchy of semidefinite programs known as the NPA (Navascués-Pironio-Acín) hierarchy used to find bounds on the maximum quantum violation of Bell inequalities. For the case in which one has a large number of inputs per party, advantage in both memory and time versus state-of-the-art solvers is demonstrated using a combination several optimisation techniques. The third avenue is that of many-body quantum physics, which encompasses a wide range of topics. The thesis considers the problems of bounding expectation values of observables over the steady-states of open quantum systems, finding improved Fermion-to-qubit mappings and solving the graph colouring problem with a novel qudit-inspired optimisation algorithm. In each case, advantage versus comparable methods is demonstrated.
Tribunal de Tesi:
Prof. Dr. Miguel Navascues Cobo, Austrian Academy of Sciences
Prof. Dr. Darrick Edward Chang, ICFO
Prof. Dr. Victoria Jane Wright, Quantinuum