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We propose a scheme to braid Majorana zero modes (MZMs) through steering the spin degree of freedom, without moving, measuring, or more generically fusing the modes. For a spinful Majorana system, we show that braiding two MZMs is achieved…
The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana…
Braiding of Majorana zero modes provides a promising platform for quantum information processing, which is topologically protected against errors. Strictly speaking, however, the scheme relies on infinite braiding times as it utilizes the…
Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional…
Discrete time crystals have attracted considerable theoretical and experimental studies but their potential applications have remained unexplored. A particular type of discrete time crystals, termed "Majorana time crystals", is found to…
This is a tutorial review of methods to braid the world lines of non-Abelian anyons (Majorana zero-modes) in topological superconductors. That "Holy Grail" of topological quantum information processing has not yet been reached in the…
We propose a realization of the one-dimensional Kitaev topological superconductor in classical mechanical metamaterials. By designing appropriate braiding protocols, we demonstrate that the system's mid-gap vibrational modes, termed…
After a decade of intense theoretical and experimental efforts, demonstrating braiding of Majorana modes remains an unsolved problem in condensed matter physics due to platform specific challenges. In this work, we propose topological…
Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated…
Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been…
Majorana zero modes are localized quasiparticles that obey non-Abelian exchange statistics. Braiding Majorana zero modes forms the basis of topologically protected quantum operations which could in principle significantly reduce qubit…
Topological quantum computation using non-Abelian Majorana zero modes localized in proximitized semiconductor nanowires requires careful electrostatic control of wire-junctions so as to manipulate and braid the zero modes enabling anyonic…
We propose a simple approach to realize two-dimensional Floquet topological superfluid by periodically tuning the depth of square optical lattice potentials. We show that the periodic driving can induce topological phase transitions between…
One promising avenue to study one-dimensional ($1$D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a $1$D number-conserving system…
Majorana zero modes in superconductor-nanowire hybrid structures are a promising candidate for topologically protected qubits with the potential to be used in scalable structures. Currently, disorder in such Majorana wires is a major…
The Majorana code is an example of a stabilizer code where the quantum information is stored in a system supporting well-separated Majorana Bound States (MBSs). We focus on one-dimensional realizations of the Majorana code, as well as…
Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. However, the complexity of the braiding manipulation hinders its experimental realization. Here we propose an experimental setup composing of…
Qubits built out of Majorana zero modes (MZMs) constitute the primary path towards topologically protected quantum computing. Simulating the braiding process of multiple MZMs corresponds to the quantum dynamics of a superconducting…
We propose a protocol to realize synthetic $p_x+ip_y$ superconductors in one-dimensional topological systems that host Majorana fermions. By periodically driving a localized Majorana mode across the system, our protocol realizes a…
Recent advances in quantum dot platforms have opened new pathways for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological…