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arXiv:2607.09339

PCPOP.jl: A Julia package for partially commutative polynomial optimization

Moisés Bermejo Morán, Abhishek Mishra

quant-phmath.OCSubmitted Jul 10, 2026• Announced Jul 13, 2026• 0 citations• Revised Jul 13, 2026 (v2)
v1 · Jul 10, 2026v2 · Jul 13, 2026
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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.

Comments
Implementation of the Partially-commutative polynomial optimization. Package available at https://github.com/abh1mishra/PCPOP.jl. Updated cross-referencing

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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.
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