Boolean Hierarchical Tucker Networks on Quantum Annealers

TL;DR

This paper explores the use of D-Wave quantum annealers to compute Boolean Hierarchical Tucker Network decompositions, demonstrating that complex tensor problems can be efficiently approximated despite current technological limitations.

Contribution

It introduces a method to formulate Boolean tensor decompositions as optimization problems suitable for quantum annealing, advancing quantum computing applications in tensor analysis.

Findings

BHTN can be formulated as a sequence of optimization problems for quantum annealers.

Quantum annealers can efficiently approximate BHTN despite technological restrictions.

The approach demonstrates potential for solving complex tensor problems with quantum hardware.

Abstract

Quantum annealing is an emerging technology with the potential to solve some of the computational challenges that remain unresolved as we approach an era beyond Moore's Law. In this work, we investigate the capabilities of the quantum annealers of D-Wave Systems, Inc., for computing a certain type of Boolean tensor decomposition called Boolean Hierarchical Tucker Network (BHTN). Boolean tensor decomposition problems ask for finding a decomposition of a high-dimensional tensor with categorical, [true, false], values, as a product of smaller Boolean core tensors. As the BHTN decompositions are usually not exact, we aim to approximate an input high-dimensional tensor by a product of lower-dimensional tensors such that the difference between both is minimized in some norm. We show that BHTN can be calculated as a sequence of optimization problems suitable for the D-Wave 2000Q quantum annealer. Although current technology is still fairly restricted in the problems they can address, we show that a complex problem such as BHTN can be solved efficiently and accurately.