利用比特串的隐藏结构证明量子态
Certification of quantum states with hidden structure of their bitstrings
摘要：
量子计算技术的快速发展已经使得操纵几十个量子比特的集体状态成为可能。这一成功对表征和验证大规模多体量子态的高效可靠的方法提出了强烈的需求。传统的方法，如量子层析成像，需要在经典计算机上存储和操作波函数，在大量自由度的情况下使用变得有问题。在本文中，我们提出了一个数值上便宜的过程来描述和区分量子态，这是基于有限数量的简单的投影测量在至少两个不同的基地和计算的跨尺度的不同的比特串模式通过粗粒化。通过这一过程获得的信息可以被看作是量子态的"散列函数"--一组简单的数字，它特定于具体的多体波函数，并可用于证明。通过对一些典型例子的研究，我们发现用这种方法可以刻画不同纠缠结构的量子态，包括混沌量子态。讨论了相异性与量子相关性的标准度量（例如冯诺伊曼熵）的联系。我们还证明了我们的方法可以用来检测多体量子磁系统中不同性质的相变。
英文摘要：
The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozen of qubits. This success poses a strong demand on efficient and reliable methods for characterization and verification of large-scale many-body quantum states. Traditional methods, such as quantum tomography, which require storing and operating wave functions on classical computers, become problematic to use in the regime of large number of degrees of freedom. In this paper, we propose a numerically cheap procedure to describe and distinguish quantum states which is based on a limited number of simple projective measurements in at least two different bases and computing inter-scale dissimilarities of the resulting bit-string patterns via coarse-graining. The information one obtains through this procedure can be viewed as a "hash function" of quantum state -- a simple set of numbers which is specific for a concrete many-body wave function and can be used for certification. By studying a number of archetypal examples, we show that it is enough to characterize quantum states with different structure of entanglement, including the chaotic quantum states. The connection of the dissimilarity to standard measures of quantum correlations such as von Neumann entropy is discussed. We also demonstrate that our approach can be employed to detect phase transitions of different nature in many-body quantum magnetic systems.
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