Shuttling of $\mathbb{Z}_4$ parafermions in an electronic ladder model

TL;DR

This paper studies the real-time dynamics of $ ext{Z}_4$ parafermion shuttling in an electronic ladder model, crucial for topological quantum computing, using advanced numerical methods to analyze transport and speed limits.

Contribution

It provides the first detailed analysis of the controlled shuttling process of $ ext{Z}_4$ parafermions, including adiabatic speed limits, in a realistic model.

Findings

Analyzed the transport of $ ext{Z}_4$ parafermion edge states.

Assessed the adiabatic speed limit for shuttling under experimental conditions.

Demonstrated the feasibility of controlled parafermion manipulation.

Abstract

Parafermions with non-Abelian statistics have been proposed as a promising platform for quantum computation, potentially enabling a broader set of topologically protected gates than Majorana fermions. The experimental and theoretical exploration of these exotic quasiparticles remains challenging, as their stability is linked to strong electron-electron interactions. A key step toward practical applications is the controlled shuttling of parafermionic modes, which is required for implementing geometric braiding operations. In the present work, we investigate the real-time dynamics of the elementary shuttling process by applying a combination of the density matrix renormalization group and the time-dependent variational principle approaches. We analyze the transport of $\mathbb{Z}_4$ parafermion edge states and assess the corresponding adiabatic speed limit under experimentally relevant conditions.