Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities

TL;DR

This paper develops and benchmarks adaptive variational quantum algorithms for calculating Green's functions and nonlinear susceptibilities, demonstrating their feasibility on classical simulators for small quantum systems.

Contribution

It introduces adaptive variational quantum approaches for real-time response functions, enabling accurate calculations with compact circuits on classical simulators.

Findings

Accurate Green's functions for Fermi-Hubbard chains and LiH molecule.

Feasibility of calculating third-order nonlinear susceptibilities.

Use of compact, automatically generated circuits for long-time evolution.

Abstract

We present and benchmark quantum computing approaches for calculating real-time single-particle Green's functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation. Using automatically generated compact circuits, the dynamical evolution is performed over sufficiently long times to achieve adequate frequency resolution of the response functions. We showcase accurate Green's function calculations using a statevector simulator on classical hardware for Fermi-Hubbard chains of 4 and 6 sites, with maximal ansatz circuit depths of 65 and 424 layers, respectively, and for the molecule LiH with a maximal ansatz circuit depth of 81 layers. Additionally, we consider an antiferromagnetic quantum spin-1 model that incorporates the Dzyaloshinskii-Moriya interaction to illustrate calculations of the third-order nonlinear susceptibilities, which can be measured in two-dimensional coherent spectroscopy experiments. These results demonstrate that real-time approaches using adaptive parameterized circuits to evaluate linear and nonlinear response functions can be feasible with near-term quantum processors.