Benchmarking Portfolio Selection with Adiabatic Quantum Optimization*

Portfolio selection is a constrained optimization problem to choose a set of financial assets that maximizes returns while staying under budget and minimizing risk. Markowitz portfolio theory strategically uses correlated behaviors between assets to mitigate financial risk, which we formulate as a quadratic unconstrained binary optimization problem with frustrated stoquastic form. We benchmark the probability of success with the D-Wave 2000Q quantum annealer using problems derived from cryptocurrency market data. We retrieve the lowest energy result from the quantum annealer and compare to the ground truth of a brute force solver. We observe a weakly sub-exponential decay in the probability of success for up to 20 assets, which we extrapolate to estimate the samples required for larger problems. We also find that the relative contributions of the positive diagonal and negative off-diagonal elements have minor influence on the performance as described by the risk. We further investigate performance improvements due to changes in annealing duration, spin-reversal transformations, and reverse annealing post-processing techniques.