Open systems with error bounds: spin boson model with spectral density variations

TL;DR

This paper establishes error bounds for predictions in open quantum systems, specifically the spin-boson model, accounting for uncertainties in spectral density and demonstrating their application to the Hierarchical Equations of Motion method.

Contribution

It introduces two error bounds for expectation values considering spectral density variations in the spin-boson model, enhancing prediction reliability.

Findings

Derived two error bounds for spectral density uncertainties.

Provided a sufficient condition for the applicability of the strongest bound.

Applied bounds to assess errors in Hierarchical Equations of Motion simulations.

Abstract

In the study of open quantum systems, one of the most common ways to describe environmental effects on the reduced dynamics is through the spectral density. However, in many models this object cannot be computed from first principles and needs to be inferred on phenomenological grounds or fitted to experimental data. Consequently, some uncertainty regarding its form and parameters is unavoidable; this in turn calls into question the accuracy of any theoretical predictions based on a given spectral density. Here, we focus on the spin-boson model as a prototypical open quantum system, and find two error bounds on predicted expectation values in terms of the spectral density variation considered, and state a sufficient condition for the strongest one to apply. We further demonstrate an application of our result, by bounding the error brought about by the approximations involved in the Hierarchical Equations of Motion resolution method for spin-boson dynamics.