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UID:69d4b3e13aa48
DTSTART:20251006T090000Z
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TRANSP:OPAQUE
LOCATION:ICFO Auditorium
SUMMARY:ICFO | LUKE MORTIMER
CLASS:PUBLIC
DESCRIPTION:The thesis considers a number of optimisation techniques applie
 d in the context of quantum information theory. After a pedagogical introd
 uction of both quantum information theory and optimisation\, it considers 
 three main avenues of research. The first is the well-known foundational o
 pen problem of mutually unbiased bases\, which consists of finding sets of
  orthonormal bases that are each unbiased with one another. More specifica
 lly\, 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\, sem
 idefinite programming relaxations\, branch-and-cut\, gradient descent meth
 ods and the method of Lagrange multipliers\, each providing further insigh
 ts 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 (Navascu&eacute\;s-Pironio-Ac&iacute\;n) 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 i
 n both memory and time versus state-of-the-art solvers is demonstrated usi
 ng 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 observ
 ables over the steady-states of open quantum systems\, finding improved Fe
 rmion-to-qubit mappings and solving the graph colouring problem with a nov
 el qudit-inspired optimisation algorithm. In each case\, advantage versus 
 comparable methods is demonstrated.\n&nbsp\;\nMonday October 06\, 11:00 h.
  ICFO Auditorium \nThesis Director: Prof. Dr. Antonio Ac&iacute\;n
DTSTAMP:20260407T073601Z
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