PCPOP.jl: A Julia package for partially commutative polynomial optimization
arXiv:2607.09339
PCPOP.jl is a Julia package for polynomial optimization that supports non‑commutative, tracial, trace, and state polynomial problems, offering exact arithmetic, Gröbner basis reductions, symmetrization via Wedderburn decompositions, and specialized handling of partially commutative variables for quantum information applications.
Abstract
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.
Implementation of the Partially-commutative polynomial optimization. Package available at https://github.com/abh1mishra/PCPOP.jl. Updated cross-referencing