Combinatorial optimization plays a crucial role in many industrial applications. While classical computing often struggles with complex instances, quantum optimization emerges as a promising alternative. Here, we present an enhanced bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm to address higher-order unconstrained binary optimization (HUBO). We apply BF-DCQO to a HUBO problem featuring three-local terms in the Ising spin-glass model, validated experimentally using 156 qubits on an IBM quantum processor. In the studied instances, our results outperform standard methods such as the quantum approximate optimization algorithm, quantum annealing, simulated annealing, and Tabu search. Furthermore, we provide numerical evidence of the feasibility of a similar HUBO problem on a 433-qubit Osprey-like quantum processor. Finally, we solve denser instances of the MAX 3-SAT problem in an IonQ emulator. Our results show that BF-DCQO offers an effective path for solving large-scale HUBO problems on current and near-term quantum processors.
Kipu Quantum GmbH（基普量子有限公司）；University of the Basque Country EHU（巴斯克大学）；University of Luxembourg（卢森堡大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics
Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；Instituto de Ciencia de Materiales de Madrid (CSIC)（马德里材料科学研究所（西班牙国家研究委员会））；University of the Basque Country UPV/EHU（巴斯克地区大学）
Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits
CNR-INO（意大利国家研究委员会光学研究所）；Universita di Trento（特伦托大学）；INFN-TIFPA（意大利国家核物理研究所基础物理与应用研究所）；TECNALIA（科技联盟）；University of the Basque Country UPV/EHU（巴斯克地区大学）；Instituto de Ciencia de Materiales de Madrid (CSIC)（马德里材料科学研究所）；IKERBASQUE（伊克尔巴斯科奎）；Basque Center for Applied Mathematics BCAM（巴斯克应用数学中心）
Protein folding on a 64 qubit trapped-ion hardware via counterdiabatic quantum optimization
Kipu Quantum GmbH（Kipu Quantum有限公司）；University of the Basque Country EHU（巴斯克大学）；Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)（马德里材料科学研究所）；Universidad Autónoma de Madrid（马德里自治大学）；University of Valencia（瓦伦西亚大学）；IonQ Inc.（IonQ公司）
Large-scale portfolio optimization on a trapped-ion quantum computer
Kipu Quantum GmbH（基普量子有限公司）；Department of Physical Chemistry, University of the Basque Country EHU（巴斯克大学物理化学系）；TUM School of Management, Technische Universität München（慕尼黑工业大学管理学院）；Instituto de Ciencia de Materiales de Madrid (CSIC)（马德里材料科学研究所（西班牙国家研究委员会））；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物质理论物理系）；IDAL, Electronic Engineering Department, ETSE-UV, University of Valencia（瓦伦西亚大学电子工程学院IDAL）；IonQ Inc.（IonQ公司）；IonQ Italia（IonQ意大利分公司）
Quantum Feature Selection with Higher-Order Binary Optimization on Trapped-Ion Hardware
Kipu Quantum GmbH（Kipu量子有限公司）；IDAL, Electronic Engineering Department, ETSE-UV, University of Valencia（IDAL电子工程系，瓦伦西亚大学）；Department of Physical Chemistry, University of the Basque Country UPV/EHU（物理化学系，巴斯克大学UPV/EHU）；IonQ Inc.（IonQ公司）
