@article {pub5927,
	title = {Inequality constraints in variational quantum circuits with qudits},
	author = {Alberto  Bottarelli AND Sebastian Schmitt AND Philipp Hauke},
	year = {2025},
	month = {August},
	abstract = {  Quantum optimization is emerging as a prominent candidate for exploiting the
capabilities of near-term quantum devices. Many application-relevant
optimization tasks require the inclusion of inequality constraints, usually
handled by enlarging the Hilbert space through the addition of slack variables.
This approach, however, requires significant additional resources especially
when considering multiple constraints. Here, we study an alternative direct
implementation of these constraints within the QAOA algorithm, achieved using
qudit-SUM gates, and compare it to the slack variable method generalized to
qudits. We benchmark these approaches on three paradigmatic optimization
problems. We find that the direct implementation of the inequality penalties
vastly outperforms the slack variables method, especially when studying
real-world inspired problems with many constraints. Within the direct penalty
implementation, a linear energy penalty for unfeasible states outperforms other
investigated functional forms, such as the canonical quadratic penalty. The
proposed approach may thus be an enabling step for approaching realistic
industry-scale and fundamental science problems with large numbers of
inequality constraints.
},
	publisher = {APS},
	journal = {Physical Review Research }
}