论文标题
变异量子本质量的纠缠产生和收敛性
Entanglement Production and Convergence Properties of the Variational Quantum Eigensolver
论文作者
论文摘要
我们对三维模型费米子系统在三角形晶格上（有和没有周期性边界条件）上的二维模型费米式系统的基态能量和性能进行了系统研究，以确定二维模型的效率和性质，使用变量量子量子eigensolver（VQE）algorithm。特别是，我们专注于纠缠块的性质，该块为系统基态提供了最有效的收敛，因为它们使用了最小的门操作数量，这是在NISQ计算机中实现此算法的关键。使用同意度量，在整个优化过程中监视寄存器Qubits的纠缠量，从而阐明了其在确定收敛效率中的作用。最后，我们研究了VQE电路深度的缩放，这是所需能量精度的函数。我们表明，在错误$ \ varepsilon $中达到解决方案所需的门数遵循Solovay-Kitaev缩放，$ \ Mathcal {o}（\ log^c（\ log^c（1/\ varepsilon））$，带有指数$ C = 1.31 {\ rm c = 1.31 {\ rm pm pm {\ rm {\ rm {\ rm {\ rm {\ rm} 0.13} $。
We perform a systematic investigation of variational forms (wave function Ansätze), 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 $\varepsilon$ follows the Solovay-Kitaev scaling, $\mathcal{O}(\log^c(1/\varepsilon))$, with an exponent $c = 1.31 {\rm{\pm}}0.13$.
