Quantum thermodynamics and semidefinite optimization: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks

Abstract:Here we argue how quantum thermodynamics offers a unifying interpretation for a wide class of semidefinite programs (SDPs) that arise in quantum information. Three SDP variable constraints, namely trace-one density operators, operator-bounded measurements, and the unbounded positive semidefinite cone, admit thermodynamic regularizations associated with Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, respectively. In each case the entropy-regularized dual is unconstrained and concave in a chemical-potential vector, and the primal optimum is a thermal operator of the matched statistics. The dual gradient and Hessian are thermal expectation values, enabling hybrid quantum-classical algorithms for solving a wide variety of SDPs.

5 pages. To be presented as a talk at the 2026 Asian Quantum Information Science Conference, August 24-28, 2026, Daejeon, Korea

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2608.21123 [quant-ph]

(or arXiv:2608.21123v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.21123 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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.