Portfolio optimization via FALQON variants: warm starting, XY mixing, and circuit depth reduction

Discrete portfolio selection with cardinality constraints can be formulated as a quadratic unconstrained binary optimization (QUBO) problem. We investigate FALQON, TR-FALQON, and SO-FALQON combined with transverse-field, XY, and warm start mixers. Statevector simulations were performed for $$n=6$$ n = 6 assets over 25 random seeds and for a representative $$n=10$$ n = 10 instance. For $$n=6$$ n = 6 , the XY mixer achieved success probabilities above $$97%$$ 97 % , whereas for $$n=10$$ n = 10 , the warm start mixer was the only approach to exceed the $$50%$$ 50 % threshold. These results show that mixer design plays a central role in convergence and solution visibility.