BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Entanglement in parameterized quantum circuits and its quantificat ion on quantum computers DTSTART;VALUE=DATE-TIME:20260922T122000Z DTEND;VALUE=DATE-TIME:20260922T124000Z DTSTAMP;VALUE=DATE-TIME:20260914T053314Z UID:indico-contribution-530@indico.bitp.kiev.ua DESCRIPTION:Speakers: Khrystyna Gnatenko (Ivan Franko National University of Lviv)\nEntanglement in parameterized quantum circuits and its quantific ation on quantum computers \n\nKh. P. Gnatenko\n\nIvan Franko National Un iversity of Lviv\, Professor Ivan Vakarchuk Department for Theoretical Phy sics\, 12 Drahomanov St.\, Lviv\, 79005\nSoftServe Inc.\, 2d Sadova St.\, 79021 Lviv\, Ukraine \n\n\nWe study entanglement in multi-qubit variation al quantum circuits with different structures of entangling blocks. For tw o- and multi-qubit variational states generated by circuits with $RY$ gate s and entangling $CZ$ operators\, we derive analytical expressions and rec urrence relations for quantum correlators and the entanglement distance [1 ]. For a closed one-dimensional chain of n qubits\, an explicit analytical expression for the entanglement of a qubit with the rest of the system fo r a two-layer variational protocol is obtained. It is shown that the enta nglement of a given qubit is determined not only by its local gate paramet ers but also by the parameters of the gates acting on its nearest and next -nearest neighbors [1]. We also consider multi-qubit variational states re presented by vertex- and edge-weighted graphs and constructed using single -layer circuits with $RX$ rotations and $RZZ$ gates. For quantum graph st ates of arbitrary structure\, we derive the geometric measure of entanglem ent and quantum correlators and establish their relation to the edge- and vertex-weight structure in the neighborhoods of the corresponding graph ve rtices [2]. We show that the entanglement of a qubit in quantum graph stat es is determined by the weights of the incoming and outgoing edges associa ted with the corresponding vertex\, as well as by its indegree and outdegr ee [3]. \nThe analytical results are validated using quantum computing on the IBM Marrakesh and IBM Kingston quantum processors and the Qiskit AerSi mulator\, including noisy simulations [1-3]. The corresponding quantum cir cuits are implemented to investigate the dependence of the entanglement me asures on circuit parameters and graph structure. The results of quantum c omputing are in a good agreement with the analytical results..\nIt is wort h noting that the obtained dependencies of entanglement in variational qua ntum states on the parameters of variational quantum circuits and the stru cture of their entangling blocks are of fundamental importance. At the sam e time\, they are relevant to potential applications in quantum computing. Variational quantum states and quantum graph states underly in a wide ra nge of quantum algorithms\, including quantum machine learning\, variation al quantum protocols\, and quantum error correction. The analytical charac terization of their entanglement\, together with quantum protocols for its quantification using quantum computing\, can therefore contribute to the design and improvement of quantum algorithms and to the identification of circuit architectures capable of generating and controlling a desired degr ee of entanglement. Also\, the obtained relations between entanglement of quantum graph states and structural properties of graphs\, vertex and edge weights\, open up the possibility of studying them using quantum computin g.\n\n[1] Kh. P. Gnatenko\, A. Kaczmarek Properties of multi-qubit variati onal quantum states representing weighted graphs and their computing with quantum programming\, \narXiv:2604.00958 (2026).\n[2] Kh. P. Gnatenko\, R. O. Hredil\, V. Y. Pinchuk\, M. Z. Seniak\, Y. T. Shevchuk Entanglement di stance of two- and multi-qubit variational states and its quantification w ith quantum computing\, arXiv:2605.00259 (2026).\n[3] Kh. P. Gnatenko Ent anglement of multi-qubit states representing directed networks and its det ection with quantum computing Phys. Lett. A 521\, 129815 [5 p.] (2024).\n\ nhttps://indico.bitp.kiev.ua/event/18/contributions/530/ LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall URL:https://indico.bitp.kiev.ua/event/18/contributions/530/ END:VEVENT END:VCALENDAR