Finding Optimal Arbitrage Opportunities Using a Quantum Annealer

By Gili Rosenberg

We present two formulations for finding optimal arbitrage opportunities as a quadratic unconstrained binary optimization problem, which can be solved using a quantum annealer. The formulations are based on finding the most profitable cycle in a graph in which the nodes are the assets and the edge weights are the conversion rates. The edge-based formulation is simpler, whereas the node-based formulation allows for the identification of specific optimal arbitrage strategies, while possibly requiring fewer variables. In addition, an alternative form is presented which allows the arbitrage opportunities that best balance profit and risk to be found, based on the trader’s risk aversion. We discuss considerations for usage in practice. In particular, we suggest an application to illiquid assets and present an illustrative example.