In this paper we briefly review two recent use-cases of quantum optimization algorithms applied to hard problems in finance and economy. Specifically, we discuss the prediction of financial crashes as well as dynamic portfolio optimization. We commen
t on the different types of quantum strategies to carry on these optimizations, such as those based on quantum annealers, universal gate-based quantum processors, and quantum-inspired Tensor Networks.
A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial
crashes are inherently difficult to predict, even for a regulator which has complete information about the financial system. In this paper we show how this problem can be handled by quantum annealers. More specifically, we map the equilibrium condition of a toy-model financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with 2-body interactions, i.e., a quadratic unconstrained binary optimization (QUBO) problem. The equilibrium market values of institutions after a sudden shock to the network can then be calculated via adiabatic quantum computation and, more generically, by quantum annealers. Our procedure could be implemented on near-term quantum processors, thus providing a potentially more efficient way to assess financial equilibrium and predict financial crashes.
We discuss how quantum computation can be applied to financial problems, providing an overview of current approaches and potential prospects. We review quantum optimization algorithms, and expose how quantum annealers can be used to optimize portfoli
os, find arbitrage opportunities, and perform credit scoring. We also discuss deep-learning in finance, and suggestions to improve these methods through quantum machine learning. Finally, we consider quantum amplitude estimation, and how it can result in a quantum speed-up for Monte Carlo sampling. This has direct applications to many current financial methods, including pricing of derivatives and risk analysis. Perspectives are also discussed.
