Applying Grover-mixer Quantum Alternating Operator Ansatz Algorithm to High-order Unconstrained Binary Optimization Problems
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915700659978240 |
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| author | Kiktenko, Evgeniy O. Krendeleva, Elizaveta V. Fedorov, Aleksey K. |
| author_facet | Kiktenko, Evgeniy O. Krendeleva, Elizaveta V. Fedorov, Aleksey K. |
| contents | The Quantum Approximate Optimization Algorithm (QAOA) is among 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 constitute a generalized class of combinatorial optimization tasks characterized by intrinsically multi-variable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic performance improvement with circuit depth and achieves superior results for HUBO problems. 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 parameterized GM-QAOA nearly matches the performance of the fully optimized algorithm while being far less demanding, establishing it as a highly effective approach for complex optimization tasks. These findings highlight GM-QAOA's potential and provide a practical pathway for its implementation on current quantum hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Applying Grover-mixer Quantum Alternating Operator Ansatz Algorithm to High-order Unconstrained Binary Optimization Problems Kiktenko, Evgeniy O. Krendeleva, Elizaveta V. Fedorov, Aleksey K. Quantum Physics The Quantum Approximate Optimization Algorithm (QAOA) is among 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 constitute a generalized class of combinatorial optimization tasks characterized by intrinsically multi-variable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic performance improvement with circuit depth and achieves superior results for HUBO problems. 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 parameterized GM-QAOA nearly matches the performance of the fully optimized algorithm while being far less demanding, establishing it as a highly effective approach for complex optimization tasks. These findings highlight GM-QAOA's potential and provide a practical pathway for its implementation on current quantum hardware. |
| title | Applying Grover-mixer Quantum Alternating Operator Ansatz Algorithm to High-order Unconstrained Binary Optimization Problems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.23026 |