Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order
  Binary Optimization
We present an enhanced bias-field digitized counterdiabatic quantum
optimization (BF-DCQO) algorithm to address higher-order unconstrained binary
optimization (HUBO) problems. Combinatorial optimization plays a crucial role
in many industrial applications, yet classical computing often struggles with
complex instances. By encoding these problems as Ising spin glasses and
leveraging the advancements in quantum computing technologies, quantum
optimization methods emerge as a promising alternative. We apply BF-DCQO with
an enhanced bias term to a HUBO problem featuring three-local terms in the
Ising spin-glass model. Our protocol is experimentally validated using 156
qubits on an IBM quantum processor with a heavy-hex architecture. In the
studied instances, the results outperform standard methods, including the
quantum approximate optimization algorithm (QAOA), quantum annealing, simulated
annealing, and Tabu search. Furthermore, we perform an MPS simulation and
provide numerical evidence of the feasibility of a similar HUBO problem on a
433-qubit Osprey-like quantum processor. Both studied cases, the experiment on
156 qubits and the simulation on 433 qubits, can be considered as the start of
the commercial quantum advantage era, Kipu dixit, and even more when extended
soon to denser industry-level HUBO problems.
Sebastián V. Romero Anne-Maria Visuri Alejandro Gomez Cadavid Enrique Solano Narendra N. Hegade