  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.
