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Quantum-inspired Techniques in Tensor Networks for Industrial Contexts

Alejandro Mata Ali, Iñigo Perez Delgado, Aitor Moreno Fdez. de Leceta

TL;DR

The paper addresses the challenge of assessing the applicability and scalability of quantum-inspired tensor-network techniques in industrial settings. It surveys the literature, categorizes TN methods by use case, and analyzes practical limitations to guide deployment. The findings highlight that TNs enable efficient representation, compression, and high-dimensional processing across finance, medicine, materials, and optimization, while NP-hard problems and problem-specific constraints pose scalability challenges. The work provides an actionable map for industry practitioners and researchers to leverage TNs for large-scale, high-dimensional problems with realistic resource constraints.

Abstract

In this paper we present a study of the applicability and feasibility of quantum-inspired algorithms and techniques in tensor networks for industrial environments and contexts, with a compilation of the available literature and an analysis of the use cases that may be affected by such methods. In addition, we explore the limitations of such techniques in order to determine their potential scalability.

Quantum-inspired Techniques in Tensor Networks for Industrial Contexts

TL;DR

The paper addresses the challenge of assessing the applicability and scalability of quantum-inspired tensor-network techniques in industrial settings. It surveys the literature, categorizes TN methods by use case, and analyzes practical limitations to guide deployment. The findings highlight that TNs enable efficient representation, compression, and high-dimensional processing across finance, medicine, materials, and optimization, while NP-hard problems and problem-specific constraints pose scalability challenges. The work provides an actionable map for industry practitioners and researchers to leverage TNs for large-scale, high-dimensional problems with realistic resource constraints.

Abstract

In this paper we present a study of the applicability and feasibility of quantum-inspired algorithms and techniques in tensor networks for industrial environments and contexts, with a compilation of the available literature and an analysis of the use cases that may be affected by such methods. In addition, we explore the limitations of such techniques in order to determine their potential scalability.
Paper Structure (28 sections, 5 equations, 5 figures)

This paper contains 28 sections, 5 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Introduction to tensor networks
  3. Basic tensor properties and more complex techniques
  4. Simulation of quantum systems
  5. Machine learning model compression
  6. Application of high dimensionality operations
  7. Data compression and denoising
  8. Combinatorial optimization
  9. Use case studies
  10. Finance
  11. Portfolio optimization
  12. Interpretable predictions
  13. Medicine
  14. Drug discovery
  15. Medical image analysis
  16. ...and 13 more sections

Figures (5)

  • Figure 1: Tensor network representing the 2-tensor $T_{ip}$ of Eq. \ref{['eq: TN General']}.
  • Figure 2: a) MPS form of a 5-tensor, b) MPO form of a 10-tensor.
  • Figure 3: Process of compression of a matrix to its MPO representation. 1) We apply a splitting. 2) We join the indexes of each node in pairs. 3) We apply a grouping of the index pairs. 4) We perform the iterative SVD. 5) We apply a splitting to each physical index.
  • Figure 4: Eq. \ref{['eq: product kernel']} and MPO layer for an input vector of $N=5$ components.
  • Figure 5: Contraction of the first three nodes of the MPO layer with the first three nodes of the kernel. 1) We contract a kernel node with its corresponding MPO layer node. 2) We contract the next kernel node with its layer node. 3) We contract the two new nodes obtained. 4) We repeat the contraction process for the next pair of nodes. 5) We contract the current nodes, maintaining the physical index.