Studies of spin systems on a quantum computer | QSD2023

Quantum Science Days is an annual, international, and virtual scientific conference organized by QWorld (Association) to provide opportunities to the quantum community to present and discuss their research results at all levels (from short projects to thesis work to research publications), and to get to know each other. The third edition (QSD2023) included 7 invited speakers, 10 thematic talks on “Building an Open Quantum Ecosystem”, 31 contributed talks, an industrial demo session by Classiq, and a career talk on quantum. QSD2023 was sponsored by Unitary Fund & Classiq and supported by Latvian Quantum Initiative.

Studies of spin systems on a quantum computer
Speaker: Volodymyr Tkachuk
Abstract: In this talk I will mainly present the results published in [1-4]. We propose a method and the corresponding quantum protocol for determining energy levels of spin systems on a quantum computer. The method is based on studies of the evolution of the mean value of operator anticommuting with Hamiltonian. In this case the evolution of the mean value of the corresponding physical quantity is related with the energy levels of a quantum system. It is in the contrast to the general case when time dependence of the mean value of a physical quantity is related to the transition energies of a quantum system. Therefore proposed method allows us to nd just energy levels on a quantum computer [1]. It is interesting to note that the structure of energy spectrum in this case is related to the supersymmetric properties of the system. Note that this method is restricted to the Hamiltonians for which anticommuting operators exist and the corresponding energy spectrum is symmetric with respect to inversion of the energy. We generalize this method to the case of an arbitrary spin system by adding to the system one probe (ancilla) spin [2]. Studies of the probe spin evolution allow us to determine energy levels of the system. The energy levels of various spin systems are found on IBM’s quantum computer. The results of quantum calculations are in good agreement with the theoretical ones.
The proposed method is applied to studies of the single spin-1 tunneling on IBM’s quantum computer, ibmq-bogota [3]. The spin-1 is realized with two spins-1/2 [3,4]. On the basis of studies of the time dependence of the mean value of z-component of spin-1 on the quantum device we detect oscillations of spin-1 between the states |1⟩ and |-1⟩ in the result of tunneling. The eigenvalues of Hamiltonian which describe the spin tunneling and the energy level splitting are observed on the IBM’s quantum computer.
[1] Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk, Phys. Lett. A 424, 127843 (2022).
[2] Kh. P. Gnatenko, H. P. Laba, V. M. Tkachuk, Eur. Phys. J. Plus 137, 522 (2022).
[3] K. P. Gnatenko, V. M. Tkachuk, Observation of spin-1 tunneling on a quantum computer, arXiv preprint arXiv:2201.08872 (2022), (to be published in Eur. Phys. J. Plus).
[4] A. R. Kuzmak, V. M. Tkachuk, Probing mean values and correlations of high-spin systems on a quantum computer, arXiv preprint arXiv:2205.10800 (2022).

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