Detection characteristics of networks and properties of spin systems on a quantum computer
ORAL
Abstract
Multi-qubit quantum states representing directed networks are studied. These states are considered to be evolutionary quantum states of spin systems described by the Ising model with spatially anisotropic interactions. The geometric measure of entanglement for these states has been calculated for arbitrary structures of weighted and directed graphs [1]. A relationship has been established between the entanglement of quantum network states and the properties of the corresponding networks, including the weights of incoming and outgoing arcs, as well as the outdegree and indegree of vertices [1].
Additionally, a relationship has been identified between the properties of spin systems, their quantum states (energy fluctuations, coupling constants, velocity of quantum evolution, and geometric characteristics of evolutionary quantum states) and graph properties, including the sum of the weighted degrees of nodes, the sum of products of edge weights forming triangles and squares, the number of triangles and squares in the graph [2,3]. Quantum algorithms for detecting network properties have been proposed. Based on these findings, the properties of specific network cases and their corresponding quantum network states were calculated on IBM's quantum devices [2,3].
A quantum algorithm for detecting the energy levels of spin systems, based on the study of the evolution of a probe spin, has been proposed. The energy levels of spin systems described by the Ising model were determined using quantum programming on IBM's quantum computers [4].
References:
[1] Kh. P. Gnatenko, Physics Letters A 521, 129815 (2024).
[2] Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk, Physics Letters A 452, 128434 (2022).
[3] Kh. P. Gnatenko, Relation of curvature and torsion of weighted graph states with graph properties and its studies on a quantum computer, arXiv:2408.01511 (2024).
[4] Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk, Eur. Phys. J. Plus 137(4), 522 (2022).
Additionally, a relationship has been identified between the properties of spin systems, their quantum states (energy fluctuations, coupling constants, velocity of quantum evolution, and geometric characteristics of evolutionary quantum states) and graph properties, including the sum of the weighted degrees of nodes, the sum of products of edge weights forming triangles and squares, the number of triangles and squares in the graph [2,3]. Quantum algorithms for detecting network properties have been proposed. Based on these findings, the properties of specific network cases and their corresponding quantum network states were calculated on IBM's quantum devices [2,3].
A quantum algorithm for detecting the energy levels of spin systems, based on the study of the evolution of a probe spin, has been proposed. The energy levels of spin systems described by the Ising model were determined using quantum programming on IBM's quantum computers [4].
References:
[1] Kh. P. Gnatenko, Physics Letters A 521, 129815 (2024).
[2] Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk, Physics Letters A 452, 128434 (2022).
[3] Kh. P. Gnatenko, Relation of curvature and torsion of weighted graph states with graph properties and its studies on a quantum computer, arXiv:2408.01511 (2024).
[4] Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk, Eur. Phys. J. Plus 137(4), 522 (2022).
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Presenters
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Khrystyna Gnatenko
Ivan Franko National University of Lviv
Authors
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Khrystyna Gnatenko
Ivan Franko National University of Lviv