An Efficient Quantum Monte Carlo Method for Reducing Circuit Complexity

Quantum noise poses a severe chanllenge for variational quantum eigensolver (VQE) due to the unavoidable noise accumulation effect. To relieve the detrimental effect, shallow quantum circuit is prefered but limites the effectiveness of VQE. To address this problem, we utilize a quantum Monte Carlo-based method to effectively reduce the quantum circuit complexity of VQE, while enhancing its performance. Our simulation results demonstrate that our method can effectively solve typical 1D and 2D Heisenberg models. Furthermore, our method significantly outperforms the VQE based on conventional ansatz in terms of the circuit complexity when achieving the similar performance.