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

Abstract 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 $$n=6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> assets over 25 random seeds and for a representative $$n=10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> instance. For $$n=6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> , the XY mixer achieved success probabilities above $$97\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>97</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> , whereas for $$n=10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> , the warm start mixer was the only approach to exceed the $$50\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>50</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> threshold. These results show that mixer design plays a central role in convergence and solution visibility.