<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$n=6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>6</mn> </mrow> </math></EquationSource> </InlineEquation> assets over 25 random seeds and for a representative <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$n=10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> instance. For <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$n=6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>6</mn> </mrow> </math></EquationSource> </InlineEquation>, the XY mixer achieved success probabilities above <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$97\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>97</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, whereas for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$n=10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation>, the warm start mixer was the only approach to exceed the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$50\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>50</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> threshold. These results show that mixer design plays a central role in convergence and solution visibility.</p>

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

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2026年7月30日

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Pedro M. Prado,
Rafael Simões do Carmo,
Lucas A. M. Rattighieri,
Luiz Gustavo Esmenard Arruda,
Giovanni S. Franco,
Marcos César de Oliveira,
Felipe F. Fanchini

摘要

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.