Portfolio rebalancing experiments using the Quantum Alternating Operator Ansatz

Abstract: 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.