A Hybrid Quantum-Classical Method for Electron-Phonon Systems*

Abstract

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 the new 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. *M.M.D. and T.N. acknowledge support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (ERC-StG-Neupert-757867-PARATOP). M.M.D. was further funded by a Forschungskredit of the University of Zurich, Grant No. FK-22-085. H.Y. and Y.W. acknowledge support from the National Science Foundation (NSF) awards DMR-2038011 and DMR-2337930 E.D. acknowledges support from the ARO grant number W911NF-20-1-0163 and from the Swiss National Science Foundation under Division II. Simulation results were obtained using the Frontera computing system at the Texas Advanced Computing Center. IBM, the IBM logo, and ibm.com are trademarks of International Business Machines Corp., registered in many jurisdictions worldwide. Other product and service names might be trademarks of IBM or other companies.