Certification of quantum states with hidden structure of their bitstrings

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.