Coupled Lindblad pseudomode theory for simulating open quantum systems

TL;DR

This paper introduces a scalable coupled Lindblad pseudomode approach for simulating non-Markovian quantum dynamics, with theoretical guarantees on the number of modes needed and a robust numerical construction method.

Contribution

It provides a theoretical bound on the number of pseudomodes scaling polylogarithmically with simulation parameters and develops a robust algorithm for mode construction, improving the coupled Lindblad framework.

Findings

Efficient simulation of non-Markovian dynamics demonstrated on spin-boson model.

The number of pseudomodes scales polylogarithmically with simulation time and accuracy.

The new algorithm avoids non-convex optimization, enhancing computational robustness.

Abstract

Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as $\mathrm{polylog}(T/\varepsilon)$ in the simulation time $T$ and precision $\varepsilon$. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoids the non-convex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. This work provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.