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 portfolios, 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.

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. arXiv:1810.07690v2 [q-fin.GN]

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In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory in a dataset of 50 assets spanning a 1 year trading period using the D-Wave 2000Q processor. Our method is remarkably efficient, and produces results much closer to the efficient frontier than typical portfolios. Moreover, we also show how our approach can easily produce trajectories adapted to different risk profiles, as typically offered in financial products. Our results are a clear example of how the combination of quantum and classical techniques can offer novel valuable tools to deal with real-life problems, beyond simple toy models, in current NISQ quantum processors.

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 comment 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.