We perform a systematic investigation of variational forms (wave function Ans"atze), to determine the ground state energies and properties of two-dimensional model fermionic systems on triangular lattices (with and without periodic boundary conditions), using the Variational Quantum Eigensolver (VQE) algorithm. In particular, we focus on the nature of the entangler blocks which provide the most efficient convergence to the system ground state inasmuch as they use the minimal number of gate operations, which is key for the implementation of this algorithm in NISQ computers. Using the concurrence measure, the amount of entanglement of the register qubits is monitored during the entire optimization process, illuminating its role in determining the efficiency of the convergence. Finally, we investigate the scaling of the VQE circuit depth as a function of the desired energy accuracy. We show that the number of gates required to reach a solution within an error $\epsilon$ follows the Solovay-Kitaev scaling, $𝒪({log}^c(1/\epsilon ))$, with an exponent $c = 1.31 {\rm{\pm}}0.13$.

中文翻译：

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变分量子本征求解器的纠缠产生和收敛性质

我们研究了VQE电路深度与所需能量精度之间的关系。我们证明了在错误范围内达到解决方案所需的门数$\epsilon$ 遵循Solovay-Kitaev缩放比例， $𝒪（{日志}^C（\mathrm{1个}/\epsilon ））$，指数为$ c = 1.31 {\ rm {\ pm}} 0.13 $。