DC 1 – An Algorithm for solving SDPs arising in Quantum Computing

Project Title: An Algorithm for solving SDPs arising in Quantum Computing
Doctoral Candidate: N.N.
Host Institution: University of Klagenfurt
Supervisor: Angelika Wiegele, Etienne de Klerk

Objectives: We investigate semidefinite programs arising in the context of the causal compatibility question. In the so-called inflation technique, any causal structure is associated to a hierarchy of increasingly strict compatibility test, and each test can be formulated as a convex optimisation problem. These optimisation problems lead to large SDPs with a certain structure. Our aim is to develop an algorithm specialised for solving these SDPs. That means that one must exploit the low-rank structure of the optimal solution. Moreover, the problem will face a lot of symmetry. Symmetry reduction must be investigated in order that the algorithm is computationally tractable.

Expected Results: An efficient implementation of a solver for SDPs arising in Quantum Computing; this algorithm will be also applicable to SDP arising in energy applications such as the unit commitment problems.

Planned secondment: 3 months at Optit (A. Bettinelli) at the end of the 1st year to learn about the application of SDP arising in the optimisation of industrial energy production; 3 months at TiU (E. de Klerk) to gain insight into symmetry reduction in the 2nd year.

Degree awarding institution: University of Klagenfurt