  As a valid tool for solving ground state problems, imaginary time evolution
(ITE) is widely used in physical and chemical simulations. Different ITE-based
algorithms in their quantum counterpart have recently been proposed and applied
to some real systems. We experimentally realize the variational-based quantum
imaginary time evolution (QITE) algorithm to simulate the ground state energy
of hydrogen (H2) and lithium hydride (LiH) molecules in a superconducting qubit
system. The H2 molecule is directly simulated using the 3-qubit circuit with
unitary-coupled clusters (UCC) ansatz. We also combine QITE with the cluster
mean-field (CMF) method to obtain an effective Hamiltonian. The LiH molecule is
correspondingly simulated using the 3-qubit circuit with hardware-efficient
ansatz. For comparison, the LiH molecule is also directly simulated using the
4-qubit circuit with UCC ansatz at the equilibrium point. All the experimental
results show a convergence within 4 iterations, with high-fidelity ground state
energy obtained. For a more complex system in the future, the CMF may allow
further grouping of interactions to obtain an effective Hamiltonian, then the
hybrid QITE algorithm can possibly simulate a relatively large-scale system
with fewer qubits.
