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

• URL: http://arxiv.org/abs/2608.21123v1
• Date: Fri, 21 Aug 2026 14:01:26 GMT
• Title: Quantum thermodynamics and semidefinite optimization: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks
• Abstract summary: We argue how quantum thermodynamics offers a unifying interpretation for a wide class of semidefinite programs (SDPs)<n>The dual gradient and Hessian are thermal expectation values, enabling hybrid quantum-classical algorithms for solving a wide variety of SDPs.
• Score: 9.811303336285961
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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