A hybrid quantum-classical method for electron-phonon systems

• Published in: Communications physics Vol. 6; no. 1; pp. 233 - 10
• Main Authors: Denner, M. Michael, Miessen, Alexander, Yan, Haoran, Tavernelli, Ivano, Neupert, Titus, Demler, Eugene, Wang, Yao
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 28.08.2023; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119/995; 639/766/483/3926; Algorithms; Antiferromagnetism; Charge density waves; Computers; Correlation; Electron phonon interactions; Electrons; Fermions; Hilbert space; Hybrid systems; Methods; Phonons; Physics; Physics and Astronomy; Qubits (quantum computing)
• ISSN: 2399-3650; 2399-3650
• DOI: 10.1038/s42005-023-01353-3

Interactions between electrons and phonons play a crucial role in quantum materials. Yet, there is no universal method that would simultaneously accurately account for strong electron-phonon interactions and electronic correlations. By combining methods of the variational quantum eigensolver and the variational non-Gaussian solver, we develop a hybrid quantum-classical algorithm suitable for this type of correlated systems. This hybrid method tackles systems with arbitrarily strong electron-phonon coupling without increasing the number of required qubits and quantum gates, as compared to purely electronic models. We benchmark our method by applying it to the paradigmatic Hubbard-Holstein model at half filling, and show that it correctly captures the competition between charge density wave and antiferromagnetic phases, quantitatively consistent with exact diagonalization. Quantum simulation of fermion-boson systems is significant in material applications, while limited by the unbounded boson states. By merging variational non-Gaussian transformations and variational quantum Eigensolvers, the authors design a hybrid quantum-classical algorithm suitable for the simulation of strongly correlated electrons coupled to phonons.