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

TL;DR

This paper proposes a scalable digital quantum circuit model to simulate the nonequilibrium dynamics of a one-dimensional electron-phonon system with nonlocal coupling, including initial state preparation and analysis tools.

Contribution

It introduces a quantum circuit design for simulating nonlocal electron-phonon interactions with linear complexity and provides methods for initial state preparation and dynamic analysis.

Findings

Circuit complexity scales linearly with system size.

Initial state can be prepared as a Bloch state using a quantum circuit.

Numerical evaluation of system dynamics using Loschmidt echo and correlation functions.

Abstract

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.