Quantum Physics, Mathematics

Julia Package Cuts Polynomial Optimization Time

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July 13, 2026 by Ivy Delaney

Researchers Moisés Bermejo Morán and Abhishek Mishra have developed PCPOP.jl, a new package for the Julia programming language designed for a specialized area of mathematical optimization. The package supports non-commutative, tracial, trace, and state polynomial optimization, addressing more complex mathematical structures than standard methods. PCPOP.jl incorporates automatized symmetrization via Wedderburn decompositions and Jordan algebra reductions to streamline calculations and features a framework for polynomial computations in partially commutative variables. The authors state that this approach provides computational advantages for problems in quantum information, potentially accelerating solutions in this demanding field. The team’s implementation of partially-commutative polynomial optimization is now publicly available as a Julia package.

The PCPOP.jl package extends the capabilities of the Julia programming language to partially commutative polynomial optimization, a specialized area beyond standard polynomial methods. It is now available for use, offering a tool for tackling complex optimization challenges. The development of PCPOP.jl also fully supports exact arithmetic computations, a feature crucial for maintaining precision in demanding mathematical operations. The implementation of Gröbner basis methods within the package allows for algebraic reductions, further enhancing its computational efficiency.

This combination of techniques positions PCPOP.jl as a valuable tool for tackling optimization challenges in quantum information science and related fields. The package is now available for researchers seeking to explore these advanced polynomial computations, offering a dedicated environment for manipulating partially commutative variables and implementing sophisticated optimization strategies.

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Ivy Delaney

Ivy Delaney has been working with neural networks and machine learning since the mid-nineties, back when a couple of hidden layers and a long afternoon of training counted as ambitious. She has watched the field go from academic curiosity to the thing quietly running underneath everything, and she brings that long view to quantum computing. For Quantum Zeitgeist she covers the ground where the two fields meet. That means quantum machine learning and the variational algorithms it leans on, and it also means the less glamorous but more interesting story of classical machine learning already doing real work inside quantum machines, decoding error-correcting codes, calibrating noisy hardware and learning the error models that simulators depend on. She writes about the hardware those algorithms have to run on too, and about the post-quantum cryptography scramble that the same hardware has set off. Her stories typically start with the paper, whether that is peer-reviewed work, conference proceedings or an arXiv preprint, with the source linked so you can hold a claim up against the research it came from. She is unimpressed by benchmarks that will not say what they beat, and by demonstrations that only work in the press release.

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