  For e-commerce websites, deciding the manner in which items are listed on
webpages is an important issue because it can dramatically affect item sales.
One of the simplest strategies of listing items to improve the overall sales is
to do so in a descending order of sales or sales numbers. However, in lists
generated using this strategy, items with high similarity are often placed
consecutively. In other words, the generated item list might be biased toward a
specific preference. Therefore, this study employs penalties for items with
high similarity being placed next to each other in the list and transforms the
item listing problem to a quadratic assignment problem (QAP). The QAP is
well-known as an NP-hard problem that cannot be solved in polynomial time. To
solve the QAP, we employ quantum annealing (QA), which exploits the quantum
tunneling effect to efficiently solve an optimization problem. In addition, we
propose a problem decomposition method based on the structure of the item
listing problem because the quantum annealer we use (i.e., D-Wave 2000Q) has a
limited number of quantum bits. Our experimental results indicate that we can
create an item list that considers both sales and diversity. In addition, we
observe that using the problem decomposition method based on a problem
structure can lead to a better solution with the quantum annealer in comparison
with the existing problem decomposition method.
