Description
Entanglement of multiqubit quantum states is examined using both analytical methods and quantum computing. Variational quantum states representing weighted and directed graphs are studied. Analytical expressions for the entanglement distance and quantum correlators are derived for different variational circuits, including that with RZZ and CZ entangling gates. We find relationships between local graph properties, circuit parameters, and the entanglement of multiqubit quantum states prepared using one- and two-layer variational circuits with entangling blocks representing different graph topologies. In addition, we study multi-qubit quantum states representing fractals. We develop scalable quantum circuits for preparing multi-qubit fractal states representing the three-dimensional Sierpinski pyramid. Analytical results show that single-qubit entanglement remains unchanged as the fractal iteration order increases, even though the Hilbert space grows. We also study how entanglement depends on the parameters of multiqubit quantum states using the IBM Kingston quantum processor and the Aer simulator, including noisy simulations. The obtained results are important for the development of quantum algorithms for studying classical complex structures. They are also of fundamental importance because entanglement is one of the key resources of quantum technologies.
