Score-based Variational Inference via Quantum Maximally Mixed States

Keywords: variational inference, tensor networks

Abstract:

Score-based variational inference (VI) provides an alternative to Kullback--Leibler
(KL)-based VI by minimizing the Fisher divergence between the variational
distribution and the target. Existing eigenvalue-based score-VI methods face two
high-dimensional obstacles: exponential parameter growth and instability under
degenerate or nearly degenerate low-energy eigenspaces. We propose QuanVI, a
scalable quantum-inspired algorithm that combines a mixed-state density-operator
formulation with an MPO-motivated quantum tensor network (QTN) parameterization.
The former represents degenerate low-energy eigenspaces by their maximally mixed
state, avoiding arbitrary eigenvector selection; the latter realizes a compact
density operator without explicitly constructing exponentially large matrices.
Experiments and ablations show that QuanVI preserves low-dimensional accuracy
while scaling to high-dimensional synthetic and Bayesian posterior-approximation
benchmarks, including challenging non-Gaussian targets.

Submission Number: 108