Majorana Bound States (MBS) have emerged as promising candidates for robust quantum computing due to their non-Abelian statistics and topological protection. In this study, we focus on the dynamical transport of MBS in the semiconductor-superconductor (SM-SC) heterostructure via the piano key-type setup, wherein each of the keys of the wire can be tuned from topological to trivial phases. We focus on the transport of MBS under noisy conditions and evaluate the feasibility for realistic scenarios. The central emphasis of our work lies in using both numerical and analytical techniques to understand the effect of noise in inducing diabatic errors during transport and to establish scaling laws that relate these errors to the drive time. To achieve this, we derive an effective model that captures the scaling behavior in both noise-free and noisy scenarios, providing a unified framework for analyzing the transport dynamics. We investigate the optimal number of keys for both noisy and noiseless scenarios. Additionally, we explore the effects of disorder on transport dynamics, highlighting its impact on error scaling and robustness.
Majorana Bound States (MBS) have emerged as promising candidates for robust quantum computing due to their non-Abelian statistics and topological protection. In this study, we focus on the dynamical transport of MBS in the semiconductor-superconductor (SM-SC) heterostructure via the piano key-type setup, wherein each of the keys of the wire can be tuned from topological to trivial phases. We focus on the transport of MBS under noisy conditions and evaluate the feasibility for realistic scenarios. The central emphasis of our work lies in using both numerical and analytical techniques to understand the effect of noise in inducing diabatic errors during transport and to establish scaling laws that relate these errors to the drive time. To achieve this, we derive an effective model that captures the scaling behavior in both noise-free and noisy scenarios, providing a unified framework for analyzing the transport dynamics. We investigate the optimal number of keys for both noisy and noiseless scenarios. Additionally, we explore the effects of disorder on transport dynamics, highlighting its impact on error scaling and robustness.
Majorana zero modes (MZMs) appear as edge states in topological superconductors and are envisioned as promising candidates for application towards fault-tolerant quantum computation. Quantum information may be stored in a degenerate ground state subspace constructed from MZMs while quantum gates may be performed by braiding MZMs and exploiting their non-Abelian properties. While the topological protection of MZMs ensures that they are robust against decoherence, their dynamical manipulation can nonetheless induce undesirable transitions to excited states, manifesting as a “diabatic error.”This thesis studies the diabatic error accumulated as MZMs are transported across a superconducting wire, which is an essential building block for physical braiding schemes. The transport protocol considered relies on appropriately tuning sections (“piano keys”) of a wire between distinct topological phases via electric gates to control local chemical potentials. First, the diabatic error is examined for transport which uses multiple piano keys. The error is calculated through numerical simulation of the transport protocol and is complemented by approximate analytical expressions calculated using an effective, low-energy model. It is found that an optimal number of keys can be used to reduce the error. Furthermore, this thesis explores transport protocols performed on wires which feature disorder on the chemical potential and noise in the piano key tuning. The rise in the diabatic error due to these additional effects with respect to parameters-of-interest including the disorder strength, disorder correlation length, noise amplitude, and noise frequency cut-offs is characterized using numerical methods. For disorder, it is found that the error’s behaviour is principally controlled by the statistics of the minimum bulk energy gap. Spatially correlated disorder is also studied which presents non-monotonic behaviour for the error. Finally, for noise, it is found that optical transitions can cause a substantial increase in the error as the frequency modes within the noise approach the minimum energy gap.
This thesis aims to investigate the novel physics around Majorana bound states (MBSs). MBSs are quasiparticle excitations predicted to exist in topological superconductors. Due to the inherent protection they obtain from their topology, they have long been regarded as a promising setup to build a topologically protected quantum computer. Apart from this very practical application, they continue to fascinate as platforms built with MBS exhibit unique effects like nonabelian braiding and non-Fermi liquid behaviour in the topological Kondo effect.The thesis starts with a general introduction to quantum computing, highlighting both the promises and challenges of that field. Afterwards follows an introduction to systems that are candidates to host MBSs. It focuses on the theoretical proposals and experimental realizations that are most relevant to the presented work. We continue with a summary of the most fundamental effects and the setups that make the physics of MBSs accessible. The author's contributions in this field are theoretical. However, each publication comes with the explicit goal of investigating setups that make the unique physics of MBSs directly accessible in experiments. The first three papers have been peer-reviewed and were published in scientific journals. The fourth one is currently under peer review. The first two papers investigate DC transport setups connecting to a qubit based on MBSs called the MBS tetron. We show that via an effect called parity blockade, it is possible to initialize the qubit, quantify its lifetime, and determine whether it holds MBSs or trivial (normal fermionic) states. Also employing parity blockade, the second paper establishes a transport setup that enables access to MBS fusion rules, an effect directly related to nonabelian braiding. The third paper translates the concept of a MBS tetron into the newly experimentally established approach of MBSs in quantum dot-based Kitaev chains. We denote this system the poor man's Majorana tetron. We find that the poor man's Majorana tetron in a transport setup with appropriate tuning exhibits the famed topological Kondo effect. Paper~IV focuses on nonabelian braiding. It investigates the hybridization-based braiding protocol and accounts for imperfections in MBS localization, breaking the ground state degeneracy. This detrimental effect is corrected by the introduction of a correction term, followed by a full analytical solution of the transformation induced by this generalized braiding protocol.
Majorana bound states (MBSs), with their non-Abelian statistics and topological protection, are key candidates for fault-tolerant quantum computation. However, their unambiguous identification in solid-state systems remains a fundamental challenge. Here, we present a theoretical study demonstrating that drag transport in a capacitively coupled double quantum dot system offers a robust and nonlocal probe of weakly coupled MBSs. Using the master equation approach, we investigate both steady-state and transient dynamics and uncover a distinctive signature of MBSs, namely the emergence of pronounced split peaks in the drag transconductance, directly linked to inter-MBS coupling. We further show that the dynamics of quantum coherence is correlated with the emergence and enhancement of MBS-induced split peaks in the drag transconductance. A comparative analysis with trivial subgap states reveals key differences, that is, MBS-induced transconductance peaks are symmetric and exhibit characteristic splitting, while trivial-state features are generally asymmetric and lack such robust splitting behavior. These findings establish experimentally accessible criteria for distinguishing MBSs from trivial subgap states and provide a practical framework for probing Majorana physics through nonlocal transport.
Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which are naturally immune to microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum systems from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana edge modes storing qubits to investigate the effects of classical noise in the crossover from the quasistatic to the fast fluctuation regime. We present detailed results for the Majorana edge correlations, and fidelity of braiding operations for both global and local noise sources preserving parity symmetry, such as random chemical potentials and phase fluctuations. While in general noise will induce heating and dephasing, we identify examples of long-lived quantum correlations in the presence of fast noise due to motional narrowing, where external noise drives the system rapidly between the topological and nontopological phases.
Majorana zero modes have emerged as one of the most promising platforms for topological quantum computation, since their non-Abelian braiding statistics allow quantum information to be encoded nonlocally and manipulated through braiding operations that are, in principle, protected against local perturbations. In practice, however, a braid is only as robust as its physical implementation: finite-time operation, residual couplings, and environmental noise can all convert local excitations into logical errors during the exchange process. Here, we address this question through a microscopic comparison of two representative braiding architectures, a nanowire trijunction and a quantum-dot-assisted setup, simulating the full time-dependent Bogoliubov--de Gennes dynamics under both noiseless and noisy conditions. We show that the dot-assisted architecture consistently achieves a lower error over a shorter timescale than the trijunction, owing to its more localized exchange mechanism. This advantage persists in the presence of noise, and a spatially resolved analysis further reveals that, in the dot-assisted geometry, fast noise localized on the dot produces a smaller error than equivalent noise on the wires, whereas slow, quasi-static noise on the dot becomes the dominant limitation. Taken together, these findings link the different error contributions directly to device geometry, pointing to concrete design principles for noise-resilient Majorana-based quantum gates.