Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low-rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems we consider. Although our technique requires execution of a linear-depth circuit prior to measurement, this is compensated for by eliminating challenges associated with sampling nonlocal Jordan–Wigner transformed operators in the presence of measurement error, while enabling a powerful form of error mitigation based on efficient postselection. We numerically characterize these benefits with noisy quantum circuit simulations for ground-state energies of strongly correlated electronic systems.

变分算法是利用近期量子器件对分子系统的电子状态建模的一种有前途的范例。但是，先前所需的测量时间界限表明，将这些技术应用于更大的分子可能不可行。我们提出了一种基于双电子积分张量的低阶分解的测量策略。与现有技术相比，我们的方法可大大减少术语分组的数量，并使测量时间比我们考虑的最大系统的通常参考范围所建议的测量时间小三个数量级。尽管我们的技术要求在测量之前执行线性深度电路，通过消除在存在测量误差的情况下对非本地Jordan-Wigner变换算子进行采样所带来的挑战，并基于有效的后选择实现了有效的误差缓解形式，可以弥补这一不足。我们通过对强相关电子系统的基态能量进行噪声量子电路仿真，从数值上描述了这些好处。