Quantum-Classical Neural Networks for Solving Lindblad Master Equations

The paper introduces a variational framework that combines a classical neural network with a parameterized quantum circuit to solve Lindblad master equations. It represents the density matrix via purification, guaranteeing physical properties, and evaluates gradients exactly using the parameter‑shift rule. The authors also derive an upper bound on the covering number of this compositional model, compare it to purely quantum neural networks, and provide numerical evidence supporting both accuracy and theoretical predictions about gradient concentration.

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