In this thesis proposal I first give an overview of a number of active research topics: mutually unbiased bases, semidefinite optimisation, computational complexity and Bell non-locality. This is then followed by a description of several projects in which the proposed thesis will consist. The first of these involves using a hierarchy of semidefinite programs to bound the minimum circuit depth required to recreate a quantum circuit unitary with a given gate set. The second involves using a variational quantum circuit to optimise a Bell scenario, which can then be applied to a wide range of problems. The third involves finalizing the work on a new state-initialisation method. Throughout all of these we hope to find novel ways to improve the computational performance of the applied optimisation techniques. Several other side projects are also listed, in which I will continue to provide assistance/ideas but will not be the main researcher. All of the listed problems have useful applications in the fields of quantum circuit design and quantum information theory.

Monday October 06, 11:00 h. ICFO Auditorium

Thesis Director: Prof. Dr. Antonio Acín