Advantages of density in tensor network geometries for gradient based training

TL;DR

This paper demonstrates that densely connected tensor network geometries outperform sparse ones in gradient-based training for quantum state encoding, highlighting the importance of density for performance and resource efficiency.

Contribution

It provides empirical evidence that dense tensor network structures improve training success and efficiency, and offers insights on memory optimization and GPU acceleration.

Findings

Densely connected tensor networks achieve lower infidelity.

Higher success rates with dense structures in training.

GPU acceleration enhances performance on supercomputers.

Abstract

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their flexibility and performance exploiting hardware acceleration. As ans\"atze, tensor networks can be used with flexible geometries, and it is known that for highly regular ones their dimensionality has a large impact in performance and representation power. For heterogeneous structures, however, these effects are not completely characterized. In this article, we train tensor networks with different geometries to encode a random quantum state, and see that densely connected structures achieve better infidelities than more sparse structures, with higher success rates and less time. Additionally, we give some general insight on how to improve memory requirements on these sparse structures and its impact on the trainings. Finally, as we use HPC resources for the calculations, we discuss the requirements for this approach and showcase performance improvements with GPU acceleration on a last-generation supercomputer.