Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conduct density-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level of tolerable depolarizing gate-errors. We find that: (i) The best-performing VQEs require gate-error probabilities between 10⁻⁶ and 10⁻⁴ (10⁻⁴ and 10⁻² with error mitigation) to predict, within chemical accuracy, ground-state energies of small molecules with 4 − 14 orbitals. (ii) ADAPT-VQEs that construct ansatz circuits iteratively outperform fixed-circuit VQEs. (iii) ADAPT-VQEs perform better with circuits constructed from gate-efficient rather than physically-motivated elements. (iv) The maximally-allowed gate-error probability, p_c, for any VQE to achieve chemical accuracy decreases with the number N_II of noisy two-qubit gates as \({p}_{c}\mathop{\propto }\limits_{\displaystyle{ \sim }}{N}_{{{{\rm{II}}}}}^{-1}\). Additionally, p_c decreases with system size, even with error mitigation, implying that larger molecules require even lower gate-errors. Thus, quantum advantage via gate-based VQEs is unlikely unless gate-error probabilities are decreased by orders of magnitude.

变分量子本征求解器（VQE）是展示近期量子优势的主要候选者。在这里，我们对一系列分子的领先的基于门的 VQE 进行密度矩阵模拟。我们对它们的可容忍去极化栅极误差水平进行了数值量化。我们发现：（i）性能最好的 VQE 需要 10 ^-6和 10 ^-4之间的门错误概率（10 ^-4和 10 ^-2具有误差缓解）才能在化学精度内预测小值的基态能量。具有 4 − 14 个轨道的分子。(ii) 迭代构建 ansatz 电路的 ADAPT-VQE 优于固定电路 VQE。(iii) ADAPT-VQE 在由门效元件而非物理激励元件构建的电路中表现更好。(iv) 任何 VQE 实现化学精度的最大允许门错误概率p _c随着噪声双量子位门的数量N _{II的增加而减小，如}\({p}_{c}\mathop{\propto } \limits_{\displaystyle{ \sim }}{N}_{{{{\rm{II}}}}}^{-1}\)。此外，即使有误差缓解，p _{c也会随着系统尺寸的增大而减小，这意味着较大的分子需要更低的门误差。}因此，除非门错误概率降低几个数量级，否则不太可能通过基于门的 VQE 获得量子优势。