Optimization Techniques in Quantum Information

Quantum Physics arXiv:2512.15831 (quant-ph) [Submitted on 17 Dec 2025] Title:Optimization Techniques in Quantum Information Authors:Benjamin Desef View a PDF of the paper titled Optimization Techniques in Quantum Information, by Benjamin Desef View PDF Abstract:This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make difficult problems more accessible. A demonstration of how to efficiently implement such an algorithm, avoiding interfacial bottlenecks, is provided, finding optimal protocols to establish entanglement through a lossy channel. The central software package developed addresses polynomial optimization problems. Many problems naturally involve only a polynomial objective and constraint polynomials. Such problems can automatically be cast into semidefinite programs that provide a hierarchy of outer approximations. The resulting problems are often so large and scale so unfavorably with respect to the variable number and degree involved that the boundary of the doable is reached quickly. However, technical progress both in hardware and algorithms has pushed this boundary - but software frameworks for polynomial optimization have not followed in the same manner, often now making them the bottleneck that before was the solver. The package this http URL developed during this thesis aims to fill the gap and provide a very resource-efficient intermediate layer together with a wide number of algorithms to reduce the problem size, and naturally supporting complex numbers and semidefinite constraints ubiquitous in quantum information problems. Its application on an entanglement distribution problem is demonstrated, showing that even relaxations with semidefinite matrices of three- and four-digit size can be solved conveniently. Finally, a new way to calculate interior-point barriers for the cone of sums-of-squares matrices in a nearly time-optimal way is developed, whose efficient implementation has the potential of further reducing resource consumption. Comments: Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) MSC classes: 65-01, 65-04, 65K05, 65Z05, 68Q17, 81-01, 81-04, 81-10, 81P45, 94A40 ACM classes: G.1.6; G.4; J.2 Cite as: arXiv:2512.15831 [quant-ph] (or arXiv:2512.15831v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.15831 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Related DOI: https://doi.org/10.18725/OPARU-58732 Focus to learn more DOI(s) linking to related resources Submission history From: Benjamin Desef [view email] [v1] Wed, 17 Dec 2025 17:51:10 UTC (1,691 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimization Techniques in Quantum Information, by Benjamin DesefView PDF view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: math math.OC References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)