Quantum Portfolio Optimization: An Extensive Benchmark

Recently, several researchers proposed portfolio optimization as a potential use case for quantum optimization. However, the literature is lacking an extensive benchmark quantifying the potential of quantum computers for portfolio optimization. In this work, we fill this gap. We provide a computational study, comparing quantum approaches against state-of-the-art classical methods on a meaningful, real-world instance set. In particular, we compare quantum annealing and the quantum approximate optimization algorithm against classical mixed-integer programming, simulated annealing, steepest descent local search, tabu search and a problem-tailored heuristics. We consider a variant of portfolio optimization which we show to be particular difficult for classical solvers in practice. Our benchmark comprises 250 instances with up to 1,000 assets from actual stock data. The results show that all instances can be solved to proven optimality by mixed-integer programming in the order of seconds. Moreover, the problem-tailored heuristic consistently outperforms quantum approaches in terms of solution quality for fixed runtime. Thus, we conclude that there is only very limited room for a potential quantum advantage in portfolio optimization.