Determination of molecular energies via variational-based quantum imaginary time evolution in a superconducting qubit system

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(H_2)and lithium hydride(Li H)molecules in a superconducting qubit system.The H_2 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 Li H molecule is correspondingly simulated using the 3-qubit circuit with hardware-efficient ansatz.For comparison,the Li H 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.