Quantum Annealing Algorithms for Boolean Tensor Networks

TL;DR

This paper investigates the use of D-Wave quantum annealers to efficiently compute Boolean tensor networks, introducing algorithms and a novel parallel quantum annealing method for high-dimensional tensor decomposition.

Contribution

It introduces three algorithms for Boolean tensor networks and a new parallel quantum annealing method to decompose large tensors efficiently on quantum hardware.

Findings

Demonstrated tensor decomposition for tensors with millions of elements

Reduced tensor network computation to quadratic unconstrained binary optimization

Showed effectiveness of quantum annealing for high-dimensional tensor modeling

Abstract

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., {0, 1}) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called \textit{parallel quantum annealing}, we demonstrate that tensor with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.