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The variational quantum eigensolver (VQE) framework has been instrumental in advancing near-term quantum algorithms. However, parameter optimization remains a significant bottleneck for VQE, requiring a large number of measurements for successful algorithm execution. In this paper, we propose sequential optimization with approximate parabola (SOAP) as an efficient and robust optimizer specifically designed for parameter optimization of the unitary coupled-cluster ansatz on quantum computers. SOAP leverages sequential optimization and approximates the energy landscape as quadratic functions, minimizing the number of energy evaluations required to optimize each parameter. To capture parameter correlations, SOAP incorporates the average direction from previous iterations into the optimization direction set. Numerical benchmark studies on molecular systems demonstrate that SOAP achieves significantly faster convergence and greater robustness to noise compared with traditional optimization methods. Furthermore, numerical simulations of up to 20 qubits reveal that SOAP scales well with the number of parameters in the ansatz. The exceptional performance of SOAP is further validated through experiments on a superconducting quantum computer using a 2-qubit model system.

TenCirChemis an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChemshows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChemsupports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem’s capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H2O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H2molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChemis capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.