Adaptive Minimum-Variance Phase Gradient Estimator Overcomes Trainability Barriers in Neural-Network-Based Variational Quantum Optimization

Neural networks offer expressive representations for scientific computing in quantum physics and chemistry. This paper addresses training failures in weak-gradient regimes that limit practical applications of neural-network-based variational methods in quantum many-body physics and ab initio quantum chemistry. The authors derive an unbiased direct gradient estimator and introduce the adaptive minimum-variance phase (AMVP) estimator, which improves training stability for neural-network variational optimization in quantum systems.