Quantum Simulation of Dynamical Response Functions of Equilibrium States

TL;DR

This paper introduces a quantum computing method to compute dynamical response functions in equilibrium states without needing to prepare those states, using energy filtering and classical postprocessing, demonstrated on a free-fermion model.

Contribution

The work presents a novel quantum algorithm that bypasses the need for equilibrium state preparation by employing energy filter techniques and classical postprocessing.

Findings

Successfully computed dynamical conductivity of a free-fermion model

Revealed energy-dependent localization properties of the model

Demonstrated the method's effectiveness through numerical simulations

Abstract

The computation of dynamical response functions is central to many problems in condensed matter physics. Owing to the rapid growth of quantum correlations following a quench, classical methods face significant challenges even if an efficient description of the equilibrium state is available. Quantum computing offers a promising alternative. However, existing approaches often assume access to the equilibrium state, which may be difficult to prepare in practice. In this work, we present a method that circumvents this by using energy filter techniques, enabling the computation of response functions and other dynamical properties in both microcanonical and canonical ensembles. Our approach only requires the preparation of states that have significant weight at the desired energy. The dynamical response functions are then reconstructed from measurements after quenches of varying duration by classical postprocessing. We illustrate the algorithm numerically by applying it to compute the dynamical conductivity of a free-fermion model, which unveils the energy-dependent localization properties of the model.