The still-maturing noisy intermediate-scale quantum technology faces strict limitations on the algorithms that can be implemented efficiently. In the realm of quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become ubiquitous, with many variations. Alternatively, a promising new avenue has been unraveled by the quantum variants of techniques grounded on expansions of the moments of the Hamiltonian, notably the connected moments expansion (CMX) and the Peeters–Devreese–Soldatov (PDS) energy functional. Common to those approaches is that, upon preparing an approximate ground state used to compute the necessary moments, the accuracy of the estimated ground state energy depends on the degree of overlap between the prepared state and the true ground state. Thus, we use the ADAPT-VQE algorithm to test shallow circuit construction strategies for the purpose of increasing the overlap with the exact ground state, validated by the sizable accuracy improvement herein reported in the PDS and CMX ground state energies. We also show that we can take advantage of the fact that the terms to be measured are highly recurring in different moments, incurring a substantial reduction in the number of necessary measurements. By coupling this measurement caching with a threshold that determines whether a given term is to be measured based on its associated scalar coefficient, we observe a further reduction in the number of circuit implementations while allowing for tunable accuracy.

仍在成熟的嘈杂中尺度量子技术面临着可以有效实施的算法的严格限制。在量子化学领域，变分量子本征求解器 (VQE) 算法已经变得无处不在，并且有很多变化。或者，基于哈密顿量扩展的技术的量子变体，特别是连通矩扩展 (CMX) 和 Peeters-Devreese-Soldatov (PDS) 能量泛函，开辟了一条有前途的新途径。这些方法的共同点是，在准备用于计算必要矩的近似基态时，估计基态能量的准确性取决于准备态和真实基态之间的重叠程度。因此，我们使用 ADAPT-VQE 算法来测试浅层电路构造策略，目的是增加与精确基态的重叠，本文通过 PDS 和 CMX 基态能量中报告的相当大的精度改进来验证。我们还表明，我们可以利用要测量的术语在不同时刻高度重复的事实，从而导致必要测量次数的显着减少。通过将此测量缓存与阈值相结合，该阈值确定是否要根据相关标量系数测量给定项，我们观察到电路实现的数量进一步减少，同时允许可调精度。通过本文在 PDS 和 CMX 基态能量中报告的相当大的精度改进来验证。我们还表明，我们可以利用要测量的术语在不同时刻高度重复的事实，从而导致必要测量次数的显着减少。通过将此测量缓存与阈值相结合，该阈值确定是否要根据相关标量系数测量给定项，我们观察到电路实现的数量进一步减少，同时允许可调精度。通过本文在 PDS 和 CMX 基态能量中报告的相当大的精度改进来验证。我们还表明，我们可以利用要测量的术语在不同时刻高度重复的事实，从而导致必要测量次数的显着减少。通过将此测量缓存与阈值相结合，该阈值根据相关标量系数确定是否要测量给定项，我们观察到电路实现的数量进一步减少，同时允许可调精度。