Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms

Abstract: The Quantum Fisher Information matrix (QFIM) plays a crucial role in quantum optimization algorithms, such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a quadratic computational cost of O(d^2) with respect to the number of parameters d, limiting its scalability for high-dimensional quantum systems. To address this bottleneck, we introduce a novel estimation framework based on Stein's identity that reduces the computational complexity to a constant. Numerical simulations on the Ising and Schwinger models demonstrate the efficiency and scalability of our approach, enabling effective optimization in Variational Quantum Algorithms.