QuanVI: Score-based Variational Inference via Quantum Maximally Mixed States
This study addresses the exponential parameter explosion in eigenvalue-based methods and the non-uniqueness of eigenvectors within degenerate subspaces during high-dimensional variational inference. To overcome these challenges, we propose QuanVI, a variational framework built upon Fisher divergence that incorporates density operators and quantum tensor network representations. Specifically, QuanVI employs maximally mixed states to characterize degenerate subspaces, thereby eliminating solution non-uniqueness, and leverages matrix product operator (MPO) structures to compress density operators, circumventing traditional dimensional bottlenecks. Experimental results demonstrate that QuanVI achieves exact agreement with analytical solutions in low-dimensional settings while successfully scaling to high-dimensional synthetic data and Bayesian posterior benchmarks. By effectively approximating complex non-Gaussian target distributions, this work establishes QuanVI as an efficient and scalable approach for high-dimensional variational inference.