论文标题
cartan子代数方法，用于有效测量量子可观察的方法
Cartan sub-algebra approach to efficient measurements of quantum observables
论文作者
论文摘要
与当前可用的量子硬件的单个测量值无法测量与物理可观察到的任意操作员。为了获得可观察到的期望值，需要将其操作员分配到可测量的片段。但是，可观察的及其片段通常不具有任何特征状态，因此，即使准备好的波函数接近可观察到的特征态，可观察到的可观察到的期望值所需的测量数也可以迅速增长。我们提供了一个统一的谎言代数框架，用于开发量子可观察物的有效测量方案，它基于两个要素：1）将可观察到的操作员嵌入lie代数中，而2）使用单位运算符将lie代数元素嵌入cartan子代数（CSA）中。 CSA起着核心作用，因为其所有元素都是相互交换的，因此可以同时测量。我们说明了衡量在量子化学方法中出现的哈密顿量的期望值的框架。 CSA方法将许多最近提出的用于测量优化的方法在一个框架内，不仅允许减少可测量片段的数量，还可以减少测量总数。
An arbitrary operator corresponding to a physical observable cannot be measured in a single measurement on currently available quantum hardware. To obtain the expectation value of the observable, one needs to partition its operator to measurable fragments. However, the observable and its fragments generally do not share any eigenstates, and thus the number of measurements needed to obtain the expectation value of the observable can grow rapidly even when the wavefunction prepared is close to an eigenstate of the observable. We provide a unified Lie algebraic framework for developing efficient measurement schemes for quantum observables, it is based on two elements: 1) embedding the observable operator in a Lie algebra and 2) transforming Lie algebra elements into those of a Cartan sub-algebra (CSA) using unitary operators. The CSA plays the central role because all its elements are mutually commutative and thus can be measured simultaneously. We illustrate the framework on measuring expectation values of Hamiltonians appearing in the Variational Quantum Eigensolver approach to quantum chemistry. The CSA approach puts many recently proposed methods for the measurement optimization within a single framework, and allows one not only to reduce the number of measurable fragments but also the total number of measurements.
