论文标题
通过兼容操作员,非本地转换和协方差估计的分组量子测量的确定性改进
Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates
论文作者
论文摘要
在量子计算机上获得可观察到的可观察到的期望值是变异量子算法的关键步骤。对于复杂的可观察物,例如分子电子哈密顿量,一种共同的策略是将可观察到的可测量片段的线性组合呈现。这种方法的主要问题是精确采样可观察到的期望值所需的大量测量。我们考虑了基于通勤多数Pauli产品的分组的几种分区方案,以最大程度地减少测量数量。探索了三个主要方向:1)使用贪婪的方法对运营商进行分组,2)涉及测量的非本地统一转换,以及3)利用某些Pauli产品与几个可测量基团的兼容性。最后一个方向产生了一个通用框架,该框架不仅可以改进以前的方法,而且还将测量组方法与影子层析成像技术的最新进步联系起来。遵循这个方向,我们开发了两种新的测量方案,与以前的最新方法相比,一组模型分子的测量数量减少了几倍。
Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the observable as a linear combination of measurable fragments. The main problem of this approach is a large number of measurements required for accurate sampling of the observable's expectation value. We consider several partitioning schemes based on grouping of commuting multi-qubit Pauli products with the goal of minimizing the number of measurements. Three main directions are explored: 1) grouping commuting operators using the greedy approach, 2) involving non-local unitary transformations for measuring, and 3) taking advantage of compatibility of some Pauli products with several measurable groups. The last direction gives rise to a general framework that not only provides improvements over previous methods but also connects measurement grouping approaches with recent advances in techniques of shadow tomography. Following this direction, we develop two new measurement schemes that achieve a severalfold reduction in the number of measurements for a set of model molecules compared to previous state-of-the-art methods.