Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910718428708864 |
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| author | Javanmard, Younes Liaubaite, Ugne Osborne, Tobias J. Xu, Xusheng Yung, Man-Hong |
| author_facet | Javanmard, Younes Liaubaite, Ugne Osborne, Tobias J. Xu, Xusheng Yung, Man-Hong |
| contents | The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries Javanmard, Younes Liaubaite, Ugne Osborne, Tobias J. Xu, Xusheng Yung, Man-Hong Quantum Physics Strongly Correlated Electrons The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices. |
| title | Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2401.02355 |