aiqbench analysis
This study demonstrates that the Grover-mixer variant of the QAOA algorithm outperforms the standard transverse-field mixer on higher-order binary optimization problems by exhibiting monotonic performance gains with circuit depth. By introducing an analytical framework for parameter approximation, the authors achieve resource-efficient execution that nearly matches layerwise optimization results, offering a practical pathway for near-term quantum hardware.
Applying Grover-mixer quantum alternating operator ansatz algorithm to higher-order unconstrained binary optimization problems
arXiv:2512.23026v3 Announce Type: replace Abstract: The quantum approximate optimization algorithm (QAOA) is among the leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant (GM-QAOA) offers a compelling alternative due to its global search capabilities. This work investigates the application of GM-QAOA to higher-order unconstrained binary optimization (HUBO) problems, also known as polynomial unconstrained binary optimization (PUBO), which form a general class of combinatorial optimization problems involving multivariable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic improvement in performance with circuit depth and achieves superior results for HUBO problems within a layerwise optimization framework. An important component of our approach is an analytical framework for modeling GM-QAOA dynamics, which enables a classical approximation of the optimal parameters and helps reduce the optimization overhead. Our resource-efficient parametrized version of GM-QAOA nearly matches the performance of the version optimized using the layerwise approach while being significantly less demanding, making it a highly effective approach for complex optimization tasks. These findings highlight the potential of GM-QAOA and provide a practical pathway for its implementation on current quantum hardware.
Abstract:The quantum approximate optimization algorithm (QAOA) is among the leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant (GM-QAOA) offers a compelling alternative due to its global search capabilities. This work investigates the application of GM-QAOA to higher-order unconstrained binary optimization (HUBO) problems, also known as polynomial unconstrained binary optimization (PUBO), which form a general class of combinatorial optimization problems involving multivariable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic improvement in performance with circuit depth and achieves superior results for HUBO problems within a layerwise optimization framework. An important component of our approach is an analytical framework for modeling GM-QAOA dynamics, which enables a classical approximation of the optimal parameters and helps reduce the optimization overhead. Our resource-efficient parametrized version of GM-QAOA nearly matches the performance of the version optimized using the layerwise approach while being significantly less demanding, making it a highly effective approach for complex optimization tasks. These findings highlight the potential of GM-QAOA and provide a practical pathway for its implementation on current quantum hardware.
arXiv:2512.23026 [quant-ph]
(or arXiv:2512.23026v3 [quant-ph] for this version)
Phys. Rev. A 113, 052451 (2026)
https://doi.org/10.1103/p2t5-x8l5 DOI(s) linking to related resources
From: Evgeniy Kiktenko O. [view email] [v1] Sun, 28 Dec 2025 18:01:20 UTC (211 KB) [v2] Tue, 30 Dec 2025 10:31:14 UTC (211 KB) [v3] Wed, 3 Jun 2026 10:51:34 UTC (215 KB)
Full text under the publisher's open licence · 239 words
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