[论文解读] Adaptive Patching for Tensor Train Computations

Gianluca Grosso, Marc K. Ritter+6 more|arXiv (Cornell University)|Feb 25, 2026

Quantum Computing Algorithms and Architecture被引用 0

一句话总结

The paper introduces an adaptive patching scheme for Quantics Tensor Trains (QTT) that partitions tensors with localized features into smaller patches to reduce bond dimensions and computation, enabling efficient large-scale QTT-based calculations such as bubble diagrams and Bethe-Salpeter equations.

ABSTRACT

Quantics Tensor Train (QTT) operations such as matrix product operator contractions are prohibitively expensive for large bond dimensions. We propose an adaptive patching scheme that exploits block-sparse QTT structures to reduce costs through divide-and-conquer, adaptively partitioning tensors into smaller patches with reduced bond dimensions. We demonstrate substantial improvements for sharply localized functions and show efficient computation of bubble diagrams and Bethe-Salpeter equations, opening the door to practical large-scale QTT-based computations previously beyond reach.

研究动机与目标

• Motivate and address the high cost of QTT operations for large bond dimensions in quantum many-body problems.
• Develop an adaptive, divide-and-conquer patching strategy that exploits block-sparse QTT structures.
• Demonstrate efficiency gains in TT/patched TT operations and practical applications to Green’s functions and Bethe-Salpeter equations.
• Provide a framework for patch ordering, complexity analysis, and mitigation of overpatching.

提出的方法

• Introduce adaptive patching for QTT by partitioning tensors into patches with individual, smaller bond dimensions.
• Represent patches with TT decompositions and sum over patches to recover the full tensor.
• Couple patching with Tensor Cross Interpolation (TCI) to build TT representations efficiently.
• Analyze computational complexity: memory, function evaluations, and arithmetic costs with patch-based TT ranks.
• Apply patched QTCI to realistic 2D Green’s functions and to Bethe-Salpeter-type calculations.
• Discuss patch ordering, overpatching, and patching patterns to optimize performance.

实验结果

研究问题

• RQ1 Can adaptive patching reduce the effective bond dimension and memory requirements for QTT representations with localized features?
• RQ2 How does patching affect the computational cost of TT/MPO contractions and related tensor operations?
• RQ3 What are the practical gains of patched QTT in computing Green’s functions and Bethe-Salpeter equations?
• RQ4 How should patches be ordered and sized to avoid overpatching and maximize speedups?

主要发现

• Adaptive patching exploits block-sparse tensor cores to achieve reduced bond dimensions per patch and overall memory savings.
• Patched TT representations can match standard QTT accuracy while using fewer parameters and reduced runtime in many cases.
• Two classes of patches emerge: large, low-rank patches for smooth regions and small, higher-rank patches for sharp features, enabling targeted resource allocation.
• Patched MPO–MPO contractions can be performed efficiently via a divide-and-conquer approach, improving feasibility of large-scale QTT-based computations.
• Patch quality and ordering significantly influence performance; there is an optimal bond-cap per patch that minimizes total cost, and overpatching can negate benefits.
• Applications demonstrated include realistic 2D Green’s functions and exploration of bubble diagrams and Bethe-Salpeter equations.