Document Type : Original Article
Authors
Department of theoretical and astrophysics, Faculty of Physics, University of Tabriz, Tabriz, Iran
Abstract
The one-dimensional quantum Ising model is used to describe many physical systems, therefore the calculation of ground and excited state energies of Ising model that has many applications in statistical mechanics, has been paid attention. We obtain the ground and excited states of this model by using the Quantum Approximate Optimization Algorithm(QAOA), which is a kind of hybrid quantum-classical algorithms. For this purpose, first, we find the ground state with quantum approximate optimization algorithm, then we generalize this algorithm by adding an overlap term to obtain excited states. We calculated ground state energy and excited states energies for different coupling coefficients which is compatible with exact calculation.
Keywords
- S Sachdev, Physics world 12, 4 (1999)
- M L Frazier, et al., Biophysical journal 92, 7 (2007) 2422.
- A R Honerkamp-Smith et al., Biophysical journal 95, 1 (2008) 236.
- Y Liu and J P Dilger, Biophysical journal 64, 1 (1993) 26.
- S Miyazima, Progress of Theoretical Physics 40, 3 (1968)
- J Strecka and M Jascur, A brief account of the Ising and Ising-like models: Mean-field, effective-field and exact results. arXiv preprint arXiv:1511.03031, 2015.
- R P Feynman, J. Theor. Phy 21 (1982) 467.
- A Peruzzo, et al., Nature communications 5 (2014) 4213.
- P J O’Malley, et al., Physical Review X 6, 3 (2016)
- Y Li and S C Benjamin, Physical Review X 7, 2 (2017) 021050.
- O Higgott, D Wang, and S Brierley, Quantum 3 (2019) 156.
- E Farhi, J Goldstone, and S Gutmann, A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014.
- R Somma, et al., International Journal of Quantum Information 1, 2 (2003)189.
- J R Johansson, P D Nation and, F Nori, Computer Physics Communications, 184, 4 (2013) 1234.
- R S Smith, M J Curtis and W J Zeng, A practical quantum instruction set architecture. arXiv preprint arXiv:1608.03355, 2016.
)