Speaker
Description
We show 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. Building on the Boltzmann framework presented at QTML 2025 (arXiv:2505.04514), this extended abstract presents a unified picture of quantum thermodynamics and SDPs that incorporates the more recent Fermi-Dirac (arXiv:2603.04061) and Bose-Einstein (arXiv:2605.27228) works, which natively address measurement-bounded SDPs (and in particular quantum hypothesis testing) and standard-form SDPs over the unbounded positive semidefinite cone, respectively.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
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| Additional Topic | Quantum algorithms for machine learning applications |