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Boolean tensor networks on quantum annealers
Presenting Author: Elijah Pelofske, Los Alamos National Laboratory
Contributing Author(s): Georg Hahn, Daniel O'Malley, Hristo Djidjev, Maksim Eren, Boian Alexandrov
In this research we show that Boolean tensor networks can be computed using quantum annealing (QA). Tensors offer a representation of complex high dimensional data, which is a natural type of data in modern computing and scientific application. A Boolean tensor network represents an input binary tensor (i.e. a tensor containing two categories of data such as True and False) as a product of low-dimensional binary tensors which contain latent features of the high dimensional tensor. We show that quantum annealers can be used to implement three types of Boolean tensor network algorithms; Tensor Train, Tucker, and Hierarchical Tucker. This is accomplished by reducing tensor factorization to a sequence of Boolean matrix factorization problems, which can be expressed as a quadratic unconstrained binary optimization problems that can be solved using a QA. Utilizing this technique allows factorization of arbitrarily large tensors, the only constraint is on the rank of the factorization. Additionally, we demonstrate a novel method called parallel quantum annealing, which allows solves multiple sub-problems at the same time on the QA hardware. Python Quantum Boolean Tensor Networks (pyQBTNs) is a user-friendly software package that makes these methods available for public use. We show that tensors containing up to millions of elements can be efficiently factored using D-Wave quantum annealers.
Read this article online: https://arxiv.org/abs/2107.13659, https://arxiv.org/abs/2103.07399
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