analiza aiqbench
This research introduces a deep-learning-enhanced quantum annealing framework that eliminates the need for slack variables when solving inequality-constrained combinatorial optimization problems. By integrating trainable step-sizes with an unbalanced penalization method, the approach reduces embedding overhead and simplifies parameter tuning on current hardware. The study demonstrates improved convergence rates compared to fixed-step baselines, offering a practical pathway for handling complex constraints in near-term quantum devices without expanding qubit counts excessively.
Slack-Free Deep-Unfolded Combinatorial Optimization Solver for Inequality Constraints
arXiv:2607.20042v1 Announce Type: new Abstract: Quantum annealing (QA) is used to solve combinatorial optimization problems (COPs). When COPs are implemented on quantum annealers, they are typically encoded as quadratic unconstrained binary optimization (QUBO) problems, but constraint encodings often increase the number of qubits and the embedding overhead. This issue is particularly important for COPs with inequality constraints, where standard slack-variable formulations introduce additional binary variables. Unbalanced penalization (UP) avoids slack variables, but the original UP formulation requires tuning two penalty coefficients and contains a squared residual term that can increase the number of quadratic couplings. In this paper, we propose the unbalanced penalization Ohzeki method (UPOM), which combines UP with the Ohzeki method for inequality-constrained COPs. UPOM replaces the two static penalty coefficients of original UP with an auxiliary-variable update and removes the squared residual term from the Hamiltonian used for sampling. We further propose the deep-unfolded unbalanced penalization Ohzeki method (DU-UPOM), which learns the step-size schedule of the UPOM update from training instances. Numerical experiments on random knapsack problems show that UPOM improves over original UP and that DU-UPOM reaches optimal solutions in fewer iterations than fixed-step UPOM and other baseline. These results demonstrate that the proposed framework reduces the tuning and embedding burdens of UP while making the Ohzeki method trainable for inequality constraints.
Abstract:Quantum annealing (QA) is used to solve combinatorial optimization problems (COPs). When COPs are implemented on quantum annealers, they are typically encoded as quadratic unconstrained binary optimization (QUBO) problems, but constraint encodings often increase the number of qubits and the embedding overhead. This issue is particularly important for COPs with inequality constraints, where standard slack-variable formulations introduce additional binary variables. Unbalanced penalization (UP) avoids slack variables, but the original UP formulation requires tuning two penalty coefficients and contains a squared residual term that can increase the number of quadratic couplings. In this paper, we propose the unbalanced penalization Ohzeki method (UPOM), which combines UP with the Ohzeki method for inequality-constrained COPs. UPOM replaces the two static penalty coefficients of original UP with an auxiliary-variable update and removes the squared residual term from the Hamiltonian used for sampling. We further propose the deep-unfolded unbalanced penalization Ohzeki method (DU-UPOM), which learns the step-size schedule of the UPOM update from training instances. Numerical experiments on random knapsack problems show that UPOM improves over original UP and that DU-UPOM reaches optimal solutions in fewer iterations than fixed-step UPOM and other baseline. These results demonstrate that the proposed framework reduces the tuning and embedding burdens of UP while making the Ohzeki method trainable for inequality constraints.
arXiv:2607.20042 [quant-ph]
(or arXiv:2607.20042v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.20042 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 302 cuvinte
Subiecte conexe
Tokyo Institute of Science Builds Quantum Trainable Inequality Constraint Solver
Quantum Zeitgeist · 23 iul. 2026
Scalable Deep Unfolding of Conic Optimizers
arXiv · 15 iun. 2026
CVaR-Assisted Custom Penalty Function for Constrained Optimization
arXiv · 21 iul. 2026
Custom Penalty QAOA via Walsh-Hadamard Transform
arXiv · 6 oct. 2026