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 o
f 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.
In magnetism, skyrmions correspond to classical three-dimensional spin textures characterized by a topological invariant that keeps track of the winding of the magnetization in real space, a property that cannot be easily generalized to the quantum c
ase since the orientation of a quantum spin is in general ill-defined. Moreover, as we show, the quantum skyrmion state cannot be directly observed in modern experiments that probe the local magnetization of the system. However, we show that this novel quantum state can still be identified and fully characterized by a special local three-spin correlation function defined on neighbouring lattice sites -- the scalar chirality -- which reduces to the classical topological invariant for large systems, and which is shown to be nearly constant in the quantum skyrmion phase.
Skyrmions in condensed matter physics appear as classical topological spin structures. This nontrivial state can be obtained solving the corresponding micromagnetic model, where the magnetization is treated as a continuous classical vector field. Her
e, we introduce a new concept of quantum skyrmions of a nanoscale size. This distinct magnetic state can be formed in spin-1/2 low dimensional magnets characterized by a strong Dzyaloshinskii-Moriya interaction. This concept can also be applied to usual spin systems characterized by a nonzero exchange interaction if the quantum solution of the problem is accessible. To perform a complete characterization of such a quantum nanoskyrmion state, we analyze basis functions giving the largest contribution to the ground state at different values of external magnetic field and temperature. We observe that the quantum skyrmionic state is stabilized even when the corresponding classical skyrmionic solution has already undergone a phase transition towards the polarized ferromagnetic state.
We propose an approach for low-dimensional visualisation and classification of complex topological magnetic structures formed in magnetic materials. Within the approach one converts a three-dimensional magnetic configuration to a vector containing th
e only components of the spins that are parallel to the z axis. The next crucial step is to sort the vector elements in ascending or descending order. Having visualized profiles of the sorted spin vectors one can distinguish configurations belonging to different phases even with the same total magnetization. For instance, spin spiral and paramagnetic states with zero total magnetic moment can be easily identified. Being combined with a simplest neural network our profile approach provides a very accurate phase classification for three-dimensional magnets characterized by complex multispiral states even in the critical areas close to phases transitions. By the example of the skyrmionic configurations we show that profile approach can be used to separate the states belonging to the same phase.
