A linear response framework for simulating bosonic and fermionic correlation functions illustrated on quantum computers

TL;DR

This paper introduces a linear response framework for simulating bosonic and fermionic correlation functions on quantum computers, linking experimental observables directly to quantum states and enabling frequency- and momentum-selective measurements.

Contribution

It presents a novel, ancilla-free linear response method that directly connects quantum simulations with experimental response functions, applicable to both bosonic and fermionic systems.

Findings

Successfully simulated Green's functions for bosons and fermions

Demonstrated application on a charge-density-wave material

Provided a robust framework for quantum and classical response function calculations

Abstract

Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for obtaining response functions in linear response has no direct link to experiment. Within the context of quantum computing, and by using a linear response framework, we restore this link by making the experiment an inextricable part of the quantum simulation. This method can be frequency- and momentum-selective, avoids limitations on operators that can be directly measured, and is ancilla-free. As prototypical examples of response functions, we demonstrate that both bosonic and fermionic Green's functions can be obtained, and apply these ideas to the study of a charge-density-wave material on ibm_auckland. The linear response method provides a robust framework for using quantum computers to study systems in physics and chemistry. It also provides new paradigms for computing response functions on classical computers.