Hybrid quantum–classical optimization with cardinality constraints and applications to finance

Tracking a financial index boils down to replicating its trajectory of returns for well-defined time span by investing in weighted subset the securities included benchmark. Picking optimal combination assets becomes challenging NP-hard problem even moderately large indices consisting dozens or hundreds assets, thereby requiring heuristic methods find approximate solutions. Hybrid quantum-classical optimization with variational gate-based quantum circuits arises as plausible method improve performance current schemes. In this work we introduce pruning algorithm combinations subject cardinality constraints. We further consider different strategies respect such constraints and compare relevant ans\"{a}tze classical optimizers through numerical simulations.