  This paper investigates the experimental performance of a discrete portfolio
optimization problem relevant to the financial services industry on the
gate-model of quantum computing. We implement and evaluate a portfolio
rebalancing use case on an idealized simulator of a gate-model quantum
computer. The characteristics of this exemplar application include trading in
discrete lots, non-linear trading costs, and the investment constraint. We
design a novel problem encoding and hard constraint mixers for the Quantum
Alternating Operator Ansatz, and compare to its predecessor the Quantum
Approximate Optimization Algorithm. Experimental analysis demonstrates the
potential tractability of this application on Noisy Intermediate-Scale Quantum
(NISQ) hardware, identifying portfolios within 5% of the optimal adjusted
returns and with the optimal risk for a small eight-stock portfolio.
