QAOA Applications in Finance

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum algorithm designed to meet the constraints of Noisy Intermediate Scale Quantum (NISQ) computers. QAOA has been used to approximate NP-hard optimization problems. In this work we apply QAOA to study portfolio optimization problems that minimize portfolio volatility and maximize return. We design and examine different types of QAOA algorithms, evaluate their performance using the IBM Qiskit simulator, and benchmark the performance against the corresponding classical approximation and exact algorithms. In numerical experiments, we find our approach in some cases outperforms existing methods. Specifically, we present a novel technique that uses both pre-processing and post-processing of the trial solutions obtained from QAOA. The objective functions we encode on the cost Hamiltonian are either partial objectives, or some replacements of the classically non-convex problems.