Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation

TL;DR

This paper develops a quantum algorithm for portfolio optimization, analyzing its performance and noise resilience, and demonstrates potential quantum advantage in reducing measurement shots needed for optimal solutions.

Contribution

It introduces an end-to-end quantum approximate optimization algorithm for the discrete global minimum variance portfolio model and evaluates its robustness on noisy quantum hardware.

Findings

Dual annealing with layerwise optimization is most robust.

Thermal relaxation noise limits quantum advantage.

Favorable scaling in measurement shots suggests potential quantum advantage.

Abstract

We present a quantum algorithm for portfolio optimisation. Specifically, We present an end-to-end quantum approximate optimisation algorithm (QAOA) to solve the discrete global minimum variance portfolio (DGMVP) model. This model finds a portfolio of risky assets with the lowest possible risk contingent on the number of traded assets being discrete. We provide a complete pipeline for this model and analyses its viability for noisy intermediate-scale quantum computers. We design initial states, a cost operator, and ans\"atze with hard mixing operators within a binary encoding. Further, we perform numerical simulations to analyse several optimisation routines, including layerwise optimisation, utilising COYBLA and dual annealing. Finally, we consider the impacts of thermal relaxation and stochastic measurement noise. We find dual annealing with a layerwise optimisation routine provides the most robust performance. We observe that realistic thermal relaxation noise levels preclude quantum advantage. However, stochastic measurement noise will dominate when hardware sufficiently improves. Within this regime, we numerically demonstrate a favourable scaling in the number of shots required to obtain the global minimum -- an indication of quantum advantage in portfolio optimisation.