Benchmarking adiabatic transformation by alternating unitaries

Adiabatic transformation can be approximated as alternating unitary operators of a Hamiltonian and its parameter derivative as proposed in a gate-based approach to counterdiabatic driving [D. van Vreumingen, Phys. Rev. A 110, 052419 (2024)]. In this paper, we conduct numerical benchmarking of this alternating unitary method in a finite parameter range against adiabatic driving in a nonadiabatic timescale. We find that the alternating unitary method results in a broader distribution on energy eigenstates than that obtained by adiabatic driving, but it has the ability to sample low-energy eigenstates when an energy gap of a given Hamiltonian is small. It indicates that the alternating unitary method may be able to find good approximate solutions in quantum annealing applied to hard instances.