  We introduce a method for solving combinatorial optimization problems on
digital quantum computers, where we incorporate auxiliary counterdiabatic (CD)
terms into the adiabatic Hamiltonian, while integrating bias terms derived from
an iterative digitized counterdiabatic quantum algorithm. We call this protocol
bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed
to effectively tackle large-scale combinatorial optimization problems, BF-DCQO
demonstrates resilience against the limitations posed by the restricted
coherence times of current quantum processors and shows clear enhancement even
in the presence of noise. Additionally, our purely quantum approach eliminates
the dependency on classical optimization required in hybrid classical-quantum
schemes, thereby circumventing the trainability issues often associated with
variational quantum algorithms. Through the analysis of an all-to-all connected
general Ising spin-glass problem, we exhibit a polynomial scaling enhancement
in ground state success probability compared to traditional DCQO and
finite-time adiabatic quantum optimization methods. Furthermore, it achieves
scaling improvements in ground state success probabilities, increasing by up to
two orders of magnitude, and offers an average 1.3x better approximation ratio
than the quantum approximate optimization algorithm for the problem sizes
studied. We validate these findings through experimental implementations on
both trapped-ion quantum computers and superconducting processors, tackling a
maximum weighted independent set problem with 36 qubits and a spin-glass on a
heavy-hex lattice with 100 qubits, respectively. These results mark a
significant advancement in gate-based quantum computing, employing a fully
quantum algorithmic approach.
