Cian Ze-Pei, Dehghani Hossein, Elben Andreas, Vermersch Benoît, Zhu Guanyu, Barkeshli Maissam, Zoller Peter, Hafezi Mohammad
Joint Quantum Institute, College Park, Maryland 20742, USA.
The Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2021 Feb 5;126(5):050501. doi: 10.1103/PhysRevLett.126.050501.
One of the main topological invariants that characterizes several topologically ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant are conventionally based on the linear-response techniques that require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function. Remarkably, our results apply to disklike geometries that are more amenable to current quantum simulator architectures.
表征多个拓扑有序相的主要拓扑不变量之一是多体陈数（MBCN）。典型的例子包括几个分数量子霍尔相，预计在不久的将来会在不同的原子和光子量子平台中实现。该不变量的实验测量和数值计算传统上基于线性响应技术，这需要能够获取作为外部参数函数的一系列状态，而这不适用于许多量子模拟器。在此，我们提出一种无需辅助量子比特的实验方案来测量该不变量，无需任何哈密顿量知识。具体而言，我们利用随机测量的统计相关性来推断波函数的MBCN。值得注意的是，我们的结果适用于更适合当前量子模拟器架构的盘状几何结构。
