Inequality constraints in variational quantum circuits with qudits

Year: 2025

Authors: Bottarelli A., Schmitt S., Hauke P.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR, INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; INFN, TIFPA, Trento Inst Fundamental Phys & Applicat, Trento, Italy; Honda Res Inst Europe GmbH, Carl Legien Str 30, D-63073 Offenbach, Germany.

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 quantum approximate optimization 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.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 7 (3)      Pages from: 33202-1  to: 33202-14

More Information: We acknowledge fruitful discussions with Gopal Chan-dra Santra, Linus Ekstrom, and Mikel Garcia de Andoin. A.B. acknowledges funding from the Honda Research Institute Europe. S.S. and P.H. acknowledge funding by the European Union under Horizon Europe Programme, Grant Agreement 101080086-NeQST. This project has received funding from the Italian Ministry of University and Research (MUR) through the FARE grant for the project DAVNE (Grant No. R20PEX7Y3A) , and was supported by the Provin-cia Autonoma di Trento, and Q@TN, the joint laboratory between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR-National Research Council. This project was funded under the National Recovery and Resilience Plan (NRRP) , Mission 4 Component 2 Investment 1.4-Call for tender No. 1031 of 17/06/2022 of Italian Ministry for University and Research funded by the European Union-NextGenerationEU (Project No. CN_00000013) . This work received funds from Project DYNAMITE QUANTERA2_00056 funded by the Ministry of University and Research through the ERANET COFUND QuantERA II-2021 call and co-funded by the European Union (H2020, GA No. 101017733) . The views and opinions expressed are those of the author (s) only and do not necessarily reflect those of the European Commission, the European Union, or of the Ministry of University and Research. Neither the European Union nor the granting authority can be held responsible for them.
KeyWords: Algorithms
DOI: 10.1103/3l96-41xf