Adaptive Patching for Tensor Train Computations

TL;DR

This paper introduces an adaptive patching scheme for tensor train computations that leverages block-sparse structures to significantly reduce computational costs, enabling large-scale applications.

Contribution

It proposes a novel divide-and-conquer method that adaptively partitions tensors into smaller patches, improving efficiency for large bond dimensions in QTT operations.

Findings

Substantial cost reductions for localized functions.

Efficient computation of bubble diagrams and Bethe-Salpeter equations.

Enables practical large-scale QTT-based computations.

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.