Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem

• URL: http://arxiv.org/abs/2603.00260v1
• Date: Fri, 27 Feb 2026 19:16:28 GMT
• Title: Constrained Quantum Optimization at Utility Scale: Application to the Knapsack Problem
• Authors: Naeimeh Mohseni, Julien-Pierre Houle, Ibrahim Shehzad, Giorgio Cortiana, Corey O'Meara, Adam Bene Watts,
• Abstract summary: Constrained optimization problems are challenging for quantum computing.<n>Cop-QAOA is a hardware-efficient approach for constrained optimization to a single-period UC.<n>This work presents the largest successful demonstration of the knapsack problem on IBM Quantum hardware using up to 150 qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Constrained combinatorial optimization problems are challenging for quantum computing, particularly at utility-relevant scales and on near-term hardware. At the same time, these problems are of practical significance in industry; for example, the Unit Commitment (UC) problem in energy systems involves complex operational constraints. To address this challenge, we apply copula-QAOA (cop-QAOA), a hardware-efficient approach for constrained optimization to a single-period UC that can be reduced to a one-dimensional knapsack. Cop-QAOA biases the quantum state toward feasible solutions using constant-depth mixers and appropriately biased initial states. We implement our benchmark on problem instances that are confirmed to be hard for classical solvers such as Gurobi. Our results show that cop-QAOA often finds solutions better than a lazy greedy baseline and very close to, and in some instances surpasses, those obtained by Gurobi, with only a few QAOA rounds. This work presents the largest successful demonstration of the knapsack problem on IBM Quantum hardware using up to 150 qubits, and more generally, the largest demonstration of constrained combinatorial optimization where constraints are enforced via shallow mixers.

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