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Variational Quantum Eigensolver for the Analysis of High-Resolution NMR Spectra: Applications to AB and AB2 Spin Systems

Murat Kurt, Ayda Kaltehei, Selçuk Çakmak, Azmi Gençten

Abstract

The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is based on the variational method of quantum mechanics and it is used to find the ground state energy of a quantum system. In this study, VQE is used for the analysis of NMR spectra for the AB and AB2 spin systems. The frequencies and the spin coupling values are obtained from the sample spectra for these spin systems. Then the Hamiltonians are written in terms of pauli spin operators and transformed into a suitable forms for quantum computer. By employing VQE the ground state energies are obtained for the related spin systems. They are found to be in good agreement with the results obtained from the known variation method.

Variational Quantum Eigensolver for the Analysis of High-Resolution NMR Spectra: Applications to AB and AB2 Spin Systems

Abstract

The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is based on the variational method of quantum mechanics and it is used to find the ground state energy of a quantum system. In this study, VQE is used for the analysis of NMR spectra for the AB and AB2 spin systems. The frequencies and the spin coupling values are obtained from the sample spectra for these spin systems. Then the Hamiltonians are written in terms of pauli spin operators and transformed into a suitable forms for quantum computer. By employing VQE the ground state energies are obtained for the related spin systems. They are found to be in good agreement with the results obtained from the known variation method.
Paper Structure (9 sections, 27 equations, 5 figures, 3 tables)

This paper contains 9 sections, 27 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Quantum Information Processing
  4. VQE
  5. The Variational Method in NMR
  6. Results and Discussion
  7. VQE for AB Spin System
  8. VQE for AB$_2$ Spin System
  9. Conclusion

Figures (5)

  • Figure 1: The VQE workflow.
  • Figure 2: The full VQE process with ansatz part for the AB spin system.
  • Figure 3: Cost function for the VQE circuit of the AB spin system.
  • Figure 4: The full VQE process with ansatz part for the AB$_2$ spin system.
  • Figure 5: Cost function for the VQE circuit of the AB$_2$ spin system.