[4O5-IS-2c] Machine learning

4:30 PM - 4:45 PM JST(7:30 AM - 7:45 AM UTC)

[4O5-IS-2c-05] Score-based Variational Inference via Quantum Maximally Mixed States

〇Yuchen CONG¹, Zhe SUN^2,3, Chao LI² (1. Graduate School of Health Data Science, Juntendo University, 2. Faculty of Health Data Science, Juntendo University, 3. Graduate School of Medicine, Juntendo University)

work-in-progress

Keywords:

tensor networks,variational inference,quantum-inspired optimization

Score-based variational inference (VI), which minimizes the Fisher divergence, offers a promising alternative to Kullback–Leibler (KL) divergence but suffers from scalability issues and spectral ill-conditioning in high-dimensional settings. The objective of this work is to reformulate score-based VI from a quantum many-body perspective to address these challenges. We show that the problem is equivalent to finding the ground maximally mixed state (GMMS), which admits low-rank matrix product operator (MPO) approximations. Based on this equivalence, we introduce QuanVI, a quantum-inspired algorithm that encodes MPOs as tensorized circuits and optimizes them via alternating eigenvalue decomposition. Preliminary experiments demonstrate the efficacy of QuanVI on challenging targets (e.g., funnel) in low dimensions, together with a D=15 Gaussian sanity check. Ongoing work will extend the method to higher-dimensional regimes.