Realizing the potential of nearterm quantum computers to solve industryrelevant constrainedoptimization problems is a promising path to quantum advantage. In this work, we consider the extractive summarization constrainedoptimization problem and demonstrate the largesttodate execution of a quantum optimization algorithm that natively preserves constraints on quantum hardware. We report results with the Quantum Alternating Operator Ansatz algorithm with a Hammingweightpreserving XY mixer (XYQAOA) on trappedion quantum computer. We successfully execute XYQAOA circuits that restrict the quantum evolution to the inconstraint subspace, using up to 20 qubits and a twoqubit gate depth of up to 159. We demonstrate the necessity of directly encoding the constraints into the quantum circuit by showing the tradeoff between the inconstraint probability and the quality of the solution that is implicit if unconstrained quantum optimization methods are used. We show that this tradeoff makes choosing good parameters difficult in general. We compare XYQAOA to the Layer Variational Quantum Eigensolver algorithm, which has a highly expressive constantdepth circuit, and the Quantum Approximate Optimization Algorithm. We discuss the respective tradeoffs of the algorithms and implications for their execution on nearterm quantum hardware.
 Award ID(s):
 1818914
 NSFPAR ID:
 10273623
 Date Published:
 Journal Name:
 Proceedings of the National Academy of Sciences
 Volume:
 117
 Issue:
 41
 ISSN:
 00278424
 Page Range / eLocation ID:
 25402 to 25406
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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