Benchmarking the performance of portfolio optimization with QAOA

TL;DR

This paper evaluates the application of QAOA to portfolio optimization, analyzing technical implementation issues, error impacts, and criteria for problem difficulty, to guide future quantum algorithm deployment.

Contribution

It provides a comprehensive analysis of implementing QAOA for portfolio optimization, including variational forms, classical parameter optimization, and error considerations.

Findings

QAOA can be applied to portfolio optimization with specific variational forms.

Sampling and hardware errors significantly affect QAOA performance.

A criterion for distinguishing easy and hard problem instances is proposed.

Abstract

We present a detailed study of portfolio optimization using different versions of the quantum approximate optimization algorithm (QAOA). For a given list of assets, the portfolio optimization problem is formulated as quadratic binary optimization constrained on the number of assets contained in the portfolio. QAOA has been suggested as a possible candidate for solving this problem (and similar combinatorial optimization problems) more efficiently than classical computers in the case of a sufficiently large number of assets. However, the practical implementation of this algorithm requires a careful consideration of several technical issues, not all of which are discussed in the present literature. The present article intends to fill this gap and thereby provide the reader with a useful guide for applying QAOA to the portfolio optimization problem (and similar problems). In particular, we will discuss several possible choices of the variational form and of different classical algorithms for finding the corresponding optimized parameters. Viewing at the application of QAOA on error-prone NISQ hardware, we also analyze the influence of statistical sampling errors (due to a finite number of shots) and gate and readout errors (due to imperfect quantum hardware). Finally, we define a criterion for distinguishing between "easy" and "hard" instances of the portfolio optimization problem