# Prethermal Strong Zero Modes and Topological Qubits

## TL;DR

This paper demonstrates that certain topological zero modes, like Majorana modes, can protect quantum information for exponentially long times even at infinite temperature, due to a prethermalization phenomenon that obstructs their equilibration with the bulk.

## Contribution

It provides a non-perturbative proof that topological zero modes exhibit long-lived protection in closed systems, extending the understanding of quantum information stability.

## Key findings

- Protection time scales exponentially with system parameters.
- Protection persists even at infinite temperature.
- Numerical simulations confirm theoretical predictions.

## Abstract

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This non-equilibrium dynamical phenomenon is a form of prethermalization, and occurs because of obstructions to the equilibriation of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a non-perturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes, and on trapped ion chains.