AI and the World's Hard Problems · Quantum physics & quantum computing · arXiv · 2026-10-19
Quantum-Classical Neural Networks for Solving Lindblad Master Equations
The authors propose a variational method for solving Lindblad master equations, which describe open quantum systems, using a classical neural network combined with a parameterized quantum circuit. The density matrix is built by purification so that positivity, Hermiticity, and unit trace hold by construction, and gradients are computed exactly with the parameter-shift rule. They also bound the covering number of the model and show numerically that the method is accurate on representative equations and that gradient concentration matches their theoretical predictions.