Quantum-Inspired Score-Based Variational Inference

원문 초록

Score-based variational inference (SBVI) provides an alternative to classical Kullback--Leibler (KL)-based variational inference by learning a distribution using only score queries of the target. EigenVI~\cite{cai2024eigenvi} formulates SBVI as an eigenvalue problem, but faces two limitations: the number of variational parameters grows exponentially with the data dimension, and the single-eigenvector formulation cannot represent the full minimum-eigenvalue eigenspace. We propose QuanVI, a quantum-inspired SBVI algorithm that addresses both limitations. Rather than selecting a single eigenvector, QuanVI captures a learned subspace through a density-operator formulation. To enable scalable computation, \model{} employs a matrix-product-operator (MPO) structure parameterized by a quantum tensor network (QTN) with unitary-constrained local tensors and auxiliary ancilla wires. Numerical experiments demonstrate the scalability of QuanVI beyond EigenVI and competitive performance on synthetic distributions and Bayesian posterior-approximation benchmarks, including challenging non-Gaussian targets. The code is available at https://github.com/ChaoLiAtRIKEN/quanvi.