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In this note, we describe an experiment on portfolio optimization using theQuadratic Unconstrained Binary Optimization (QUBO) formulation. The dataset weuse is taken from a real-world problem for which a classical solution iscurrently deployed and used in production. In this work, carried out in acollaboration between the Raiffeisen Bank International (RBI) and Reply, wederive a QUBO formulation, which we solve using various methods: two D-Wavehybrid solvers, that combine the employment of a quantum annealer together withclassical methods, and a purely classical algorithm. Particular focus is givento the implementation of the constraint that requires the resulting portfolio'svariance to be below a specified threshold, whose representation in an Isingmodel is not straightforward. We find satisfactory results, consistent with theglobal optimum obtained by the exact classical strategy. However, since thetuning of QUBO parameters is crucial for the optimization, we investigate ahybrid method that allows for automatic tuning.

A real world test of Portfolio Optimization with Quantum Annealing