The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozens of qubits, which poses a strong demand on efficient methods for characterization and verification of large-scale quantum states. Here, we propose a numerically cheap procedure to distinguish quantum states which is based on a limited number of 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 wave function and can be used for certification. We show that it is enough to characterize quantum states with different structure of entanglement, including the chaotic quantum states. Our approach can also be employed to detect phase transitions in quantum magnetic systems.

量子计算技术的快速发展已经使操纵几十个量子比特的集体状态成为可能，这对大规模量子态的表征和验证的有效方法提出了强烈的需求。在这里，我们提出了一种数值便宜的程序来区分量子态，该程序基于至少两个不同基础中的有限数量的投影测量，并通过粗粒度计算得到的位串模式的尺度间差异。通过这个过程获得的信息可以看作是量子态的“散列函数”——一组简单的数字，特定于具体的波函数，可用于证明。我们表明，用不同的纠缠结构来表征量子态就足够了，包括混沌量子态。我们的方法也可用于检测量子磁系统中的相变。