October 2018

# Forecasting financial crashes with quantum computing

## Roman Orus, Samuel Mugel, Enrique Lizaso

### arXiv:1810.07690

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 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 can be implemented on near-term quantum processors, providing a potentially more efficient way to predict financial crashes.