An occupation number quantum subspace expansion approach to compute the single-particle Green function: an opportunity for noise filtering
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917823623725056 |
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| author | Gauthier, B. Rosenberg, P. Foley, A. Charlebois, M. |
| author_facet | Gauthier, B. Rosenberg, P. Foley, A. Charlebois, M. |
| contents | We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a non-orthogonal excitation basis composed of a set of single-particle excitations generated by occupation number operators. The excited sectors of the Hamiltonian in this basis can then be measured on the quantum device and a classical post-processing procedure yields the Green function in the Lehmann representation. The technique allows for noise filtering, a useful feature for NISQ devices. To validate the approach, we carry out a set of proof-of-principle calculations on the single-band Hubbard model on IBM quantum hardware. For a 2 site system we find good agreement between the results of quantum simulations and the exact result for the local spectral function. This proof-of-principle also shows that the noise filtering provides a reliable way to get rid of satellite peaks present in the spectral weight obtained from a NISQ device. A simulation of a 4 site system carried out on classical hardware suggests that the approach can achieve similar accuracy for larger systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_13497 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An occupation number quantum subspace expansion approach to compute the single-particle Green function: an opportunity for noise filtering Gauthier, B. Rosenberg, P. Foley, A. Charlebois, M. Strongly Correlated Electrons Quantum Physics We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a non-orthogonal excitation basis composed of a set of single-particle excitations generated by occupation number operators. The excited sectors of the Hamiltonian in this basis can then be measured on the quantum device and a classical post-processing procedure yields the Green function in the Lehmann representation. The technique allows for noise filtering, a useful feature for NISQ devices. To validate the approach, we carry out a set of proof-of-principle calculations on the single-band Hubbard model on IBM quantum hardware. For a 2 site system we find good agreement between the results of quantum simulations and the exact result for the local spectral function. This proof-of-principle also shows that the noise filtering provides a reliable way to get rid of satellite peaks present in the spectral weight obtained from a NISQ device. A simulation of a 4 site system carried out on classical hardware suggests that the approach can achieve similar accuracy for larger systems. |
| title | An occupation number quantum subspace expansion approach to compute the single-particle Green function: an opportunity for noise filtering |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2312.13497 |