论文标题
来自模拟量子模拟器中新兴状态设计的影子层析成像
Shadow tomography from emergent state designs in analog quantum simulators
论文作者
论文摘要
我们介绍了一种方法，该方法允许人们仅利用对构成自由度的全局控制来推断量子状态的许多属性（包括非线性函数，例如Rényi熵）。在该协议中，在进行投影测量之前，首先将感兴趣的状态与固定的全球统一的一组Ancillas纠结。我们表明，当统一充分纠缠时，状态的测量结果和特性的统计数据之间会存在普遍的关系，这可以与最近发现的混乱系统中新兴量子状态设计的现象有关。由于这种关系，可以使用相同数量的实验重复来重建任意可观察物，而经典的影子层析成像[Huang等人，Nat。物理。 16，1050（2020）]。与以前的阴影层析成像方法不同，我们的协议只能使用全局操作而不是Qubit选择性逻辑门实施，这使其特别适合模拟量子模拟器，包括光学晶格中的超速原子和Rydberg Atoms的阵列。
We introduce a method that allows one to infer many properties of a quantum state -- including nonlinear functions such as Rényi entropies -- using only global control over the constituent degrees of freedom. In this protocol, the state of interest is first entangled with a set of ancillas under a fixed global unitary, before projective measurements are made. We show that when the unitary is sufficiently entangling, a universal relationship between the statistics of the measurement outcomes and properties of the state emerges, which can be connected to the recently discovered phenomenon of emergent quantum state designs in chaotic systems. Thanks to this relationship, arbitrary observables can be reconstructed using the same number of experimental repetitions that would be required in classical shadow tomography [Huang et al., Nat. Phys. 16, 1050 (2020)]. Unlike previous approaches to shadow tomography, our protocol can be implemented using only global operations, as opposed to qubit-selective logic gates, which makes it particularly well-suited to analog quantum simulators, including ultracold atoms in optical lattices and arrays of Rydberg atoms.
