Quantum Algorithms for tensor-SVD

TL;DR

This paper introduces two novel quantum tensor-SVD algorithms that improve upon existing methods, addressing previous limitations and utilizing hybrid variational techniques for enhanced tensor decomposition in linear algebra applications.

Contribution

The paper presents two new quantum t-SVD algorithms, one fixing drawbacks of prior work and another employing a hybrid variational approach, advancing quantum tensor decomposition methods.

Findings

First algorithm improves upon previous quantum t-SVD methods.

Second algorithm utilizes a hybrid variational approach for tensor SVD.

Both algorithms demonstrate potential for efficient quantum tensor computations.

Abstract

A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work that proposed a quantum t-SVD algorithm for context-aware recommendation systems. The new algorithm however seeks to address and fix certain drawbacks to the original, and is fundamentally different in its approach compared to the existing work. The second algorithm proposed uses a hybrid variational approach largely based on a known variational quantum SVD algorithm.