Finite-Time Braiding Dynamics within Topological Nanowire Qubits

TL;DR

This paper analyzes the finite-time dynamics of Majorana-based topological qubits in nanowires, providing time-dependent gate models to aid in realistic quantum computing implementations.

Contribution

It extends the understanding of Majorana shuttling beyond adiabatic limits by developing finite-time gate representations for practical qubit operations.

Findings

Finite-time gate models for Majorana shuttling

Analysis of two shuttling methods in nanowires

Insights for experimental topological qubit implementations

Abstract

Topological Quantum Computing has largely evolved towards a paradigm of manipulating edge localized Majorana within $p$-wave topological superconducting nanowires. To bridge the gap between physical qubit systems and quantum algorithms, we perform a dynamical analysis to extend what is known in the adiabatic regime, providing time-dependent gate elements for further qubit and algorithm modeling efforts. Our analysis covers dynamical considerations for two methods of shuttling domain edge bound Majoranas in a single nanowire system which both function by applying spatiotemporally dependent onsite and hopping parameters within the system's Hamiltonian. We then complicate this model by converting it into the T-qubit to calculate the finite-time gate representation of the shuttling techniques used in a more practical setting. These contributions provide insight for realistic experimental setups in the next-generation of qubit implementation and will hopefully facilitate fault tolerant scalable systems and universal gate design.