Author

Longxiu Huang

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Preprint Sep 2026

A Geometric View of Adaptive Cross Approximation via Exterior Algebra

Adaptive cross approximation (ACA) constructs low-rank CUR approximations from selected rows and columns of a matrix, making it attractive when individual entries are inexpensive to query but forming or repeatedly multiplying by the full matrix is not. Its practical performance, however, is not well explained by existi...

Trevor Loe, Long-Xiu Huang, Deanna Needell · 0 citations

Preprint Aug 2026

Quantized Low-Rank Quantum State Tomography: Hyperbolic Quantization and Riemannian Least-Squares Recovery

We study low-rank quantum state tomography from finite-bit Pauli batch responses. To avoid bias introduced by generic quantization, we propose HyperQuant, a mean-preserving hyperbolic quantizer adapted to the second-moment scale of Pauli responses. We establish minimax distortion guarantees and show that exact mean pre...

Hanqin Cai, Longxiu Huang, Juntao You · 0 citations

Preprint Aug 2026

Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling

Robust Iterative t-CUR (R-ItCUR), a tensor-native algorithm that partitions the sampled tensor cross into two exterior blocks and an intersection block, applies adaptive blockwise Welsch correction for outlier suppression, and updates the low-rank component through projected blockwise gradient descent is proposed.

Hanqin Cai, Long-Xiu Huang, Jing Qin et al. · 0 citations