Convergence guarantees for discrete mode approximations to non-Markovian quantum baths

TL;DR

This paper proves that approximating non-Markovian quantum environments with discrete modes converges to the true dynamics under certain conditions, providing a rigorous foundation for simulation algorithms.

Contribution

It establishes convergence guarantees and error bounds for discrete mode approximations of non-Markovian quantum systems, which was previously lacking.

Findings

Finite-time dynamics converge with enough modes

Approximation error decreases polynomially with modes

Provides rigorous foundation for simulation algorithms

Abstract

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.