Generalized Toric Codes Coupled to Thermal Baths

TL;DR

This paper investigates the finite-temperature dynamics of generalized toric codes based on qudits, revealing unique thermal processes for qutrits and deriving decay rates and relaxation behaviors.

Contribution

It introduces a master equation for qudit-based toric codes at finite temperature, highlighting new anyonic processes for qutrits and analyzing their thermal relaxation properties.

Findings

Qutrits exhibit new anyonic creation, annihilation, and diffusion processes.

Decay rates depend on the qudit dimension and temperature.

Qutrits show a unique initial decay rate behavior above a certain temperature.

Abstract

We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. As a consequence, we find that for qutrits new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension $d$ of the qudits. Although we provide an explicit proof that the system relax to the Gibbs state for arbitrary qudits, we also prove that above a certain crossing temperature, qutrits initial decay rate is smaller than the original case for qubits. Surprisingly this behavior only happens with qutrits and not with other qudits with $d>3$.