Registration Number
0223U004835,
(0120U104801)
, R & D reports
Title
Studies of physical systems and effects of space quantization on quantum computers
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Моделювання квантованого простору та дослідження його властивостей на квантовому комп’ютері. Моделювання систем з гамільтоніанами з комплексними параметрами. Властивості фізичних систем у квантованому просторі та їх дослідження на квантовому комп’ютері. Квантове обчислення нулів статистичної суми спінових систем.
Head
Tkachuk Volodymyr M., Доктор фізико-математичних наук
Registration Date
05-12-2023
Organization
Ivan Franko National University of Lviv
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The aim of the project is to model quantum systems to establish their properties on quantum computers. Namely, finding a bipartite geometric measure of entanglement of mixed states of systems with an arbitrary number of spins analytically and using quantum computers from IBM. Writing quantum protocols for the formation of graph states generated by operators of evolution with different spin Hamiltonians (Ising and Heisenberg Hamiltonians). Calculate the measure of entanglement of such graph spin states and establish its connection with the characteristics of the corresponding graphs. Writing quantum protocols for operators of the evolution of spin systems with different types of interaction. Determination of geometrical characteristics such as curvature and torsion for the evolution states of spin systems, that are described by the Ising and Heisenberg models using quantum computers. Establishing the relationship between curvature and torsion with the entanglement of quantum states. Modeling of spin physical systems described by Hamiltonians with complex parameters. Finding zeros of time correlation functions of spin systems and zeros of the partition functions using quantum calculations. Modeling a spin network that describes quantized space on quantum computers and establishing the effects of space quantization on the properties of spin systems using quantum computing.
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Graph states that are generated by the operator of evolution with Ising and Heisenberg Hamiltonians are studied. Relation of properties of spin systems in graph states with characteristics of graphs is found. The geometric measure of entanglement of graph states is detected on IBM’s quantum computers and its relation with degree of vertexes of corresponding graphs is found. Geometric measure of entanglement of
continuous variable is obtained. A method for detection of energy levels of arbitrary spin system on a quantum computer based on studies of evolution of only one probe spin is proposed. It opens a possibility to achieve quantum supremacy in solving eigenvalue problem with development of multi-qubit quantum computers.
Product Description
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Gnatenko Khrystyna P.
Kuzmak Andrij R.
Laba Hanna P
Samar Mykola I.
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2023-12-05
