Our achievements

Outstanding results

• Expressions for the geometric measure of entanglement of pure and mixed states were obtained
• Study of the geometry of the space of quantum states during evolution
• Brachistochron problem of spin systems with different types of interaction

Recent publications

• Kh. P. Gnatenko, V. M. Tkachuk Observation of spin-1 tunneling on a quantum computer // Eur. Phys. J. Plus.— 2023.— Vol. 138, No. 4.— Art. 346.— 8 p.
• Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk Geometric properties of evolutionary graph states and their detection on a quantum computer // Phys. Lett. A.— 2022.— Vol. 452.— Art. 128434.
• Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk Energy levels estimation on a quantum computer by evolution of a physical quantity // Phys. Lett. A.— 2022.— Vol. 424.— Art. 127843.— 7 p.
• Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk Detection of energy levels of a spin system on a quantum computer by probe spin evolution // Eur. Phys. J. Plus.— 2022.— Vol. 137, No. 4.— Art. 522.— 10 p.
• Kh. P. Gnatenko, V. M. Tkachuk Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computer // Phys. Lett. A.— 2021.— Vol. 396.— Art. 127248.
• Kh. P. Gnatenko, N. A. Susulovska Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer // EPL (Europhys. Lett.).— 2021.— Vol. 136, No. 4.— Art. 40003.
• A. R. Kuzmak, V. M. Tkachuk Measuring entanglement of a rank-2 mixed state prepared on a quantum computer // Eur. Phys. J. Plus.— 2021.— Vol. 136, No. 5.— Art. 564.— 12 p.
• A. V. Kryzhova, Kh. P. Gnatenko Probability of quantum state determination among N possible ones // Visnyk Lviv Univ. Ser. Phys.— 2023.— Iss. 60.— P. 18-25.
• A. R. Kuzmak, V. M. Tkachuk Preparation and study of the entanglement of the Schrödinger cat state on the ibmq-melbourne quantum computer // Condens. Matter Phys.— 2020.— Vol. 23, No. 4.— Art. 43001.— 7 p.
• A. R. Kuzmak, V. M. Tkachuk Detecting entanglement by the mean value of spin on a quantum computer // Phys. Lett. A.— 2020.— Vol. 384, No. 24.— Art. 126579.— 6 p.
• A. M. Frydryszak, M. I. Samar, V. M. Tkachuk Quantifying geometric measure of entanglement by mean value of spin and spin correlations with application to physical systems // Eur. Phys. J. D.— 2017.— Vol. 71, No. 9.— Art. 233.— 8 p.
• H. P. Laba, V. M. Tkachuk Entangled states in supersymmetric quantum mechanics // Mod. Phys. Lett. A 35, No. 34, 2050282 [9 p.] (2020)
• A. R. Kuzmak, V. M. Tkachuk Detecting the Lee-Yang zeros of a high-spin system by the evolution of probe spin // EPL (Europhysics Letters) 125, No. 1, 10004 [7 p.] (2019)
• H. P. Laba, V. M. Tkachuk Geometric characteristics of quantum evolution: curvature and torsion // Condens. Matter Phys. 20, No. 1, 13003 [7 p.] (2017)
• H. P. Laba, V. M. Tkachuk Geometric measure of mixing of quantum state // Condens. Matter Phys. 21, No. 3, 33003 [4 p.] (2018)
• A. R. Kuzmak, V. M. Tkachuk Geometry of a two-spin quantum state in evolution // J. Phys. A: Math. Theor. 49, No. 4, 045301 [8 p.] (2016)
• A. R. Kuzmak, V. M. Tkachuk The quantum brachistochrone problem for an arbitrary spin in a magnetic field // Phys. Lett A 379, No. 18-19, 1233–1239 (2015)
• A. R. Kuzmak, V. M. Tkachuk Preparation of quantum states of two spin-½ particles in the form of the Schmidt decomposition // Phys. Lett. A 378, No. 21, 1469-1474 (2014)
• A. R. Kuzmak, V. M. Tkachuk The quantum brachistochrone problem for two spins-½ with anisotropic Heisenberg interaction // J. Phys. A: Math. Theor. 46, 155305 [12 p.] (2013)
• V. M. Tkachuk Nonuniform Zeno effect // J. Phys. Stud. 15, No. 1, 1001 [3 p.] (2011)
• V. M. Tkachuk, S. I. Vakarchuk Supersymmetry of Pauli Hamiltonian and entanglement // J. Phys. Stud. 12, No. 4, 4004 [3 p.] (2008)
• A. M. Frydryszak, V. M. Tkachuk Quantum brachistochrone problem for a spin-1 system in a magnetic field // Phys. Rev. A 77, No. 1, 014103 [4 p.] (2008)