Nonnormality and Dissipation in Markovian Quantum Dynamics: Implications for Quantum Simulation

TL;DR

This paper introduces a structural framework for Markovian open quantum systems, highlighting how nonnormality and dissipation influence dynamics and impact quantum simulation stability.

Contribution

It characterizes Lindbladian generators using dissipative strength and nonnormality, revealing their roles in stability and transient amplification in quantum simulations.

Findings

Normal generators allow exact decoupling and exponential decay.

Nonnormality is intrinsically dissipative and affects transient behavior.

Transient amplification due to nonnormality can increase simulation costs.

Abstract

Understanding the structure and stability of open quantum dynamics is increasingly important for both fundamental studies of nonequilibrium quantum systems and the development of quantum simulation algorithms. In this work, we introduce a structural framework for Markovian open quantum systems that characterizes Lindbladian generators in terms of two scalar quantities: the dissipative strength and the nonnormality. We show that normal generators admit an exact decoupling between dissipative and norm-preserving dynamics, leading to purely exponential behavior governed by the dissipative scale. In contrast, nonnormality is an intrinsically dissipative feature: it vanishes in the absence of dissipation but is not implied by it. Moreover, it is structurally constrained by the interplay between the Hermitian and anti-Hermitian components of the generator. For generic Markovian open quantum systems, we identify parametric regimes controlled by a dimensionless ratio between nonnormality and dissipative strength, governing the onset of transient amplification. These structural features have direct implications for quantum simulation. While Hamiltonian and normal dissipative dynamics exhibit stable evolution with standard scaling behavior, nonnormal generators can induce transient growth that amplifies numerical errors and increases simulation cost. Our results provide a unified generator-level perspective on irreversibility, stability, and quantum simulation of open quantum systems.