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.

作为解决基态问题的有效工具，虚时间演化（ITE）广泛应用于物理和化学模拟中。最近提出了不同的基于 ITE 的量子算法，并将其应用于一些实际系统。我们通过实验实现了基于变分的量子虚时间演化（QITE）算法来模拟超导量子位系统中氢（H ₂ ）和氢化锂（LiH）分子的基态能量。使用具有酉耦合簇 (UCC) ansatz 的 3 量子位电路直接模拟H _2分子。我们还将 QITE 与簇平均场（CMF）方法结合起来以获得有效的哈密顿量。LiH 分子相应地使用具有硬件效率 ansatz 的 3 量子位电路进行模拟。为了进行比较，还使用 ​​UCC ansatz 处于平衡点的 4 量子位电路直接模拟 LiH 分子。所有实验结果均在4次迭代内收敛，并获得了高保真基态能量。对于未来更复杂的系统，CMF可能允许进一步对相互作用进行分组以获得有效的哈密顿量，那么混合QITE算法就有可能用更少的量子比特来模拟相对大规模的系统。