# Analyzing the spectral density of a perturbed analog quantum simulator using Keldysh formalism

## TL;DR

This paper investigates how decoherence affects the spectral density in analog quantum simulators by mapping them onto fermionic systems and applying Keldysh formalism, revealing the limits of spectral feature resolution.

## Contribution

It introduces a diagrammatic Keldysh approach to analyze the spectral density of noisy quantum simulators, bridging quantum simulation and many-body physics.

## Key findings

- Features stronger than the decoherence rate are resolvable.
- Weaker spectral features are washed out by noise.
- Keldysh approach agrees with master-equation calculations for small systems.

## Abstract

Simulation of interacting electron systems is one of the great challenges of modern quantum chemistry and solid state physics. Controllable quantum systems offer the opportunity to create artificial structures which mimic the system of interest. An interesting quantity to extract from these quantum simulations is the spectral function. We map a noisy quantum simulator onto a fermionic system and investigate the influence of decoherence on the simulation of the spectral density using a diagrammatic approach on Keldysh contour. We show that features stronger than the single-qubit decoherence rate can be resolved, while weaker features wash out. For small systems, we compare our Keldysh approach to master-equation calculations.