Quantum circuits for digital quantum simulation of nonlocal electron-phonon coupling

Motivated by the compelling need to understand the nonequilibrium dynamics of small-polaron formation following an electron-phonon interaction quench, in this work we propose a digital quantum simulator of a one-dimensional lattice model describing an itinerant fermionic excitation (e.g. an electron) nonlocally coupled to zero-dimensional bosons (e.g. Einstein-type phonons). Quantum circuits implementing the dynamics of this model, which includes Peierls- and breathing-mode-type excitation-boson interactions, are designed here, their complexity scaling linearly with the system size. A circuit that generates the natural initial (pre-quench) state of this system - a bare-excitation Bloch state, equivalent to a W state of a qubit register - is also presented. To facilitate comparisons with the proposed simulator, once experimentally realized, the system dynamics are also evaluated numerically and characterized through the Loschmidt echo and various correlation functions.