QuanVI：基于量子最大混合态的得分变分推断
QuanVI: Score-based Variational Inference via Quantum Maximally Mixed States
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中文总结 AI 辅助
QuanVI提出一种结合混合态密度算子与量子张量网络参数化的得分变分推断算法，解决高维特征值问题中的参数爆炸和简并本征向量非唯一性，实现可扩展的高维后验逼近。
中文摘要 AI 辅助
得分变分推断（score-based variational inference, VI）通过最小化变分分布与目标之间的Fisher散度，为基于Kullback-Leibler（KL）散度的变分推断提供了一种替代方案。先前的得分VI方法将此优化问题表述为特征值问题，其中变分分布由低能本征态构建。然而，这种基于特征值的公式面临两个高维障碍：由于指数级扩展导致的参数数量难以处理，以及在简并或近简并低能子空间中单个本征向量的非唯一性。我们提出了QuanVI，一种可扩展的量子启发算法，它将混合态密度算子公式与使用矩阵乘积算子（MPO）结构的量子张量网络（QTN）参数化相结合。在简并低能子空间中，密度算子公式通过其最大混合态来表示该子空间，而不是依赖于非唯一的单个本征向量，而QTN参数化则压缩密度算子以避免指数级参数增长。实验和消融研究表明，QuanVI在低维情况下与精确解一致，并可扩展到高维合成和贝叶斯后验逼近基准，包括具有挑战性的非高斯目标。
英文摘要
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. A prior score-VI approach formulates this optimization as an eigenvalue problem, with the variational distribution constructed from low-energy eigenstates. However, this eigenvalue-based formulation faces two high-dimensional obstacles: an intractably large parameter count due to exponential scaling and non-uniqueness of individual eigenvectors in degenerate or nearly degenerate low-energy subspaces. We propose QuanVI, a scalable quantum-inspired algorithm that combines a mixed-state density-operator formulation with a quantum tensor network (QTN) parameterization using the matrix product operator (MPO) structure. In degenerate low-energy subspaces, the density-operator formulation represents the subspace by its maximally mixed state rather than relying on a non-unique individual eigenvector, while the QTN parameterization compresses the density operator to avoid exponential parameter growth. Experiments and ablations show that QuanVI agrees with exact solutions in low dimensions and scales to high-dimensional synthetic and Bayesian posterior-approximation benchmarks, including challenging non-Gaussian targets.
发表机构
- Juntendo University（顺天堂大学）
- RIKEN-AIP（理化学研究所革新智能统合研究中心）
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