Adiabatic quantum computing enables the preparation of many-body ground
states. This is key for applications in chemistry, materials science, and
beyond. Realisation poses major experimental challenges: Direct analog
implementation requires complex Hamiltonian engineering, while the digitised
version needs deep quantum gate circuits. To bypass these obstacles, we suggest
an adiabatic variational hybrid algorithm, which employs short quantum circuits
and provides a systematic quantum adiabatic optimisation of the circuit
parameters. The quantum adiabatic theorem promises not only the ground state
but also that the excited eigenstates can be found. We report the first
experimental demonstration that many-body eigenstates can be efficiently
prepared by an adiabatic variational algorithm assisted with a multi-qubit
superconducting coprocessor. We track the real-time evolution of the ground and
exited states of transverse-field Ising spins with a fidelity up that can reach
about 99%.Comment: 12 pages, 4 figure