Review of 'Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer'

The article discusses the potential for near-term quantum computers to solve constrained-optimization problems and their application in extractive summarization. The article presents a demonstration of the Quantum Alternating Operator Ansatz algorithm with a Hamming-weight-preserving XY mixer (XY-QAOA) on a trapped-ion quantum computer. The article also compares XY-QAOA to the Layer Variational Quantum Eigensolver algorithm and the Quantum Approximate Optimization Algorithm. The introduction provides a clear rationale for the importance of evaluating promising quantum algorithms on state-of-the-art hardware to assess their potential to provide quantum advantage in optimization. The authors also present experimental and numerical results to demonstrate the challenges associated with solving constrained-optimization problems with near-term quantum computers.

As for revisions, the article is well-written and clearly structured. However, some technical terms and concepts might be difficult to understand for readers with limited knowledge of quantum computing. The authors could consider providing more explanations and illustrations to improve the article's accessibility. Additionally, the authors could further explain the practical applications of extractive summarization and the potential benefits of solving this problem on a quantum computer.

The article lacks a detailed discussion on the limitations and assumptions of the proposed approach. While the authors acknowledge the challenges associated with solving constrained-optimization problems with near-term quantum computers, they do not provide a comprehensive analysis of the limitations and assumptions of their approach.

The strength of the article is its demonstration of the largest-to-date execution of a quantum optimization algorithm that natively preserves constraints on quantum hardware, using up to 20 qubits and a two-qubit gate depth of up to 159. The authors provide a clear rationale for the importance of solving practical optimization problems using quantum computers and present experimental and numerical results to support their arguments. The weakness of the article is its limited discussion on the limitations and assumptions of the proposed approach.