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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.07600 |
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| _version_ | 1866915121188569088 |
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| author | Sumeet Hörmann, M. Schmidt, K. P. |
| author_facet | Sumeet Hörmann, M. Schmidt, K. P. |
| contents | We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit. This is done by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE). Here, the VQE algorithm is used as a cluster solver within the NLCE. We test our hybrid quantum-classical algorithm (NLCE$+$VQE) for the ferromagnetic transverse-field Ising model on the one-dimensional chain and the two-dimensional square lattice. The calculation of ground-state energies on each open cluster demands a modified Hamiltonian variational ansatz for the VQE. One major finding is convergence of NLCE$+$VQE to the conventional NLCE result in the thermodynamic limit when at least $N/2$ layers are used in the VQE ansatz for each cluster with $N$ sites. Our approach demonstrates the fruitful connection of techniques known from correlated quantum many-body systems with hybrid algorithms explored on existing quantum-computing devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit Sumeet Hörmann, M. Schmidt, K. P. Quantum Physics Statistical Mechanics Strongly Correlated Electrons We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit. This is done by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE). Here, the VQE algorithm is used as a cluster solver within the NLCE. We test our hybrid quantum-classical algorithm (NLCE$+$VQE) for the ferromagnetic transverse-field Ising model on the one-dimensional chain and the two-dimensional square lattice. The calculation of ground-state energies on each open cluster demands a modified Hamiltonian variational ansatz for the VQE. One major finding is convergence of NLCE$+$VQE to the conventional NLCE result in the thermodynamic limit when at least $N/2$ layers are used in the VQE ansatz for each cluster with $N$ sites. Our approach demonstrates the fruitful connection of techniques known from correlated quantum many-body systems with hybrid algorithms explored on existing quantum-computing devices. |
| title | Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.07600 |