The advent of cloud quantum computing has led to the rapid development of quantum algorithms. In particular, it is necessary to study variational quantum-classical hybrid algorithms, which are executable on noisy intermediate-scale quantum (NISQ) computers. Evaluations of observables appear frequently in the variational quantum-classical hybrid algorithms for NISQ computers. By speeding up the evaluation of observables, it is possible to realize a faster algorithm and save resources of quantum computers. Grouping of observables with separable measurements has been conventionally used, and the grouping with entangled measurements has also been proposed recently by several teams. In this paper, we show that entangled measurements enhance the efficiency of evaluation of observables, both theoretically and experimentally, by taking into account the covariance effect, which may affect the quality of evaluation of observables. We also propose using a part of entangled measurements for grouping to keep the depth of extra gates constant. Our proposed method is expected to be used in conjunction with other related studies. We hope that entangled measurements would become crucial resources, not only for joint measurements but also for quantum information processing.

云量子计算的出现导致了量子算法的飞速发展。特别是，有必要研究变分量子经典混合算法，该算法可在嘈杂的中尺度量子（NISQ）计算机上执行。NISQ计算机的变分量子经典混合算法中经常出现对可观察对象的评估。通过加快对可观察物的评估，可以实现更快的算法并节省量子计算机的资源。传统上已将可观测值与可分离测量值进行分组，最近，一些团队也提出了对纠缠的测量值进行分组。在本文中，我们证明了纠缠测量在理论上和实验上都提高了可观测值的评估效率，考虑到协方差效应，这可能会影响可观测指标的评估质量。我们还建议使用纠缠测量的一部分进行分组，以使额外门的深度保持恒定。我们提出的方法有望与其他相关研究结合使用。我们希望，纠缠的测量将成为至关重要的资源，不仅用于联合测量，而且还用于量子信息处理。