# Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures

## TL;DR

This paper investigates relaxation and decoherence timescales for qubits encoded in collective states of magnetic atoms on surfaces, highlighting the benefits of decoherence-free subspaces for quantum coherence preservation.

## Contribution

It generalizes $T_{1}$ and $T_{2}$ definitions for collective atomic states and analyzes their behavior across various atomic configurations.

## Key findings

- Decoherence-free subspaces enhance qubit coherence times.
- Relaxation and decoherence rates vary with atomic structure.
- Generalized $T_{1}$ and $T_{2}$ provide better understanding of quantum state stability.

## Abstract

The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of $T_{1}$ and $T_{2}$ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.