Fermi-Dirac thermal measurements: A framework for quantum hypothesis testing and semidefinite optimization

The paper introduces Fermi-Dirac thermal measurements as a new framework for quantum hypothesis testing and semidefinite optimization. By treating measurement eigenmodes as independent fermionic modes, the authors show that minimizing fermionic free energy yields optimal measurements whose eigenvalues follow Fermi‑Dirac distributions. These measurements can be learned with classical or hybrid quantum‑classical algorithms, leading to a new quantum machine‑learning model—Fermi‑Dirac machines—and a novel approach to semidefinite optimization on quantum computers.

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