Trace polynomial optimization with applications in quantum information

Igor Klep, Victor Magron, Jurij Volčič

Felix Huber, Victor Magron, Jurij Volčič

Felix Huber, Victor Magron, Jurij Volčič

Moisés Bermejo Morán, Abhishek Mishra

Here we present PCPOP, a Julia package for polynomial optimization that supports non-commutative optimization, tracial polynomial optimization, trace polynomial optimization and state polynomial optimization. PCPOP fully supports exact arithmetic computations and incorporates convenient functionalities such as algebraic reductions based on Gröbner basis methods, automatized symmetrization via Wedderburn decompositions, and Jordan algebra reductions. As a distinguished feature, PCPOP implements a specialized framework for polynomial computations in partially commutative variables that provides significant computational advantages for problems appearing in quantum information.

Xin Wang

Euimin Lee, Shiho Kim