Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver
Lana Mineh,Ashley Montanaro +1 more
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TLDR
In this article, a detailed study into how density matrix embedding theory (DMET) could be implemented on a quantum computer to solve the Hubbard model was carried out, where the variational quantum eigensolver (VQE) was used as the solver for the embedded Hamiltonian within the DMET algorithm.Abstract:
Calculating the ground state properties of a Hamiltonian can be mapped to the problem of finding the ground state of a smaller Hamiltonian through the use of embedding methods. These embedding techniques have the ability to drastically reduce the problem size, and hence the number of qubits required when running on a quantum computer. However, the embedding process can produce a relatively complicated Hamiltonian, leading to a more complex quantum algorithm. In this paper we carry out a detailed study into how density matrix embedding theory (DMET) could be implemented on a quantum computer to solve the Hubbard model. We consider the variational quantum eigensolver (VQE) as the solver for the embedded Hamiltonian within the DMET algorithm. We derive the exact form of the embedded Hamiltonian and use it to construct efficient ansatz circuits and measurement schemes. We conduct detailed numerical simulations up to 16 qubits, the largest to date, for a range of Hubbard model parameters and find that the combination of DMET and VQE is effective for reproducing ground state properties of the model.read more
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References
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Journal ArticleDOI
Electron correlations in narrow energy bands
TL;DR: In this paper, the Hartree-Fock approximation of the correlation problem for the d-and f-bands was applied to a simple, approximate model for the interaction of electrons in narrow energy bands.
Journal ArticleDOI
Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future as mentioned in this paper, which will be useful tools for exploring many-body quantum physics, and may have other useful applications.
Journal ArticleDOI
Quantum Computing in the NISQ era and beyond
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future, and the 100-qubit quantum computer will not change the world right away - but it should be regarded as a significant step toward the more powerful quantum technologies of the future.
Journal ArticleDOI
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
Abhinav Kandala,Antonio Mezzacapo,Kristan Temme,Maika Takita,Markus Brink,Jerry M. Chow,Jay M. Gambetta +6 more
TL;DR: The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2.
Journal ArticleDOI
Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
Elliott H. Lieb,F. Y. Wu +1 more
TL;DR: In this paper, the short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case, and the ground-state energy, wave function, and chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.