  In this work, we demonstrate how to apply non-linear cardinality constraints,
important for real-world asset management, to quantum portfolio optimization.
This enables us to tackle non-convex portfolio optimization problems using
quantum annealing that would otherwise be challenging for classical algorithms.
Being able to use cardinality constraints for portfolio optimization opens the
doors to new applications for creating innovative portfolios and
exchange-traded-funds (ETFs). We apply the methodology to the practical problem
of enhanced index tracking and are able to construct smaller portfolios that
significantly outperform the risk profile of the target index whilst retaining
high degrees of tracking.
