arXiv subjects

Themba Hodge

Publications and source records attributed to Themba Hodge.

9 recordsLinked to original sources

arXiv2026

Negative Hybridization: a Potential Cure for Braiding with Imperfect Majorana Modes

Majorana zero modes, the elementary building blocks for the quantum bits of topological quantum computers, are known to suffer from hybridization as their wavefunctions begin to overlap. This breaks the ground state degeneracy, splitting their energy levels and leading to an accumulation of error when performing topological quantum gates. Here we show that the energy splitting of the Majorana zero modes can become negative, which can be utilized to reduce the average hybridization energy of the total gate. We present two illustrative examples where negative hybridization suppresses gate errors to such an extent that they remain below the fault-tolerance threshold. As an intrinsic property of Majorana zero modes, negative hybridization enables systems based on imperfect Majorana zero modes to regain functionality for quantum information processing.

cond-mat.mes-hall↗

arXiv2025

Projective Measurements: Topological Quantum Computing with an Arbitrary Number of Qubits

Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a critical yet often overlooked challenge arises when scaling beyond two qubits: the naive extension of braiding based gates fails to support even the full Clifford group. To overcome this limitation, we incorporate projective measurements that enable transitions between different qubit encodings, thus restoring computational universality. We perform many-body simulations of braiding dynamics augmented with measurement-based switching, explicitly preparing the Bell state and GHZ state for systems of two and five qubits, respectively. Furthermore, we execute a random unitary circuit on five qubits, achieving a fidelity exceeding 99%. We analyze the circuit's robustness by studying its fidelity dependence on total braid duration and static potential disorder. Our results show that the fidelity remains above 99% for moderate disorder, underscoring the intrinsic fault tolerance of the architecture. Finally, we demonstrate a random circuit on a ten qubit system to showcase the scalability of our techniques.

quant-ph↗

arXiv2025

Majorana braiding simulations with projective measurements

We summarize the key ingredients required for universal topological quantum computation using Majorana zero modes in networks of topological superconductor nanowires. Particular emphasis is placed on the use of both sparse and dense logical qubit encodings, and on the transitions between them via projective parity measurements. Combined with hybridization, these operations extend the computational capabilities beyond braiding alone and enable universal gate sets. In addition to outlining the theoretical foundations-including the algebra of Majorana operators, along with the stabilizer formalism-we introduce an efficient numerical method for simulating the time-dependent dynamics of such systems. This method, based on the time dependent Pfaffian formalism, allows for the classical simulation of realistic device architectures that incorporate braiding, projective measurements, and disorder. The result is a semi-pedagogical overview and computational toolbox designed to support further exploration of topological quantum computing platforms.

quant-ph↗

arXiv2025

Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes

Topological quantum computation, featuring qubits built out of anyonic excitations known as Majorana zero modes (MZMs), have long presented an exciting pathway towards scalable quantum computation. Recently, the advent of altermagnetic materials has presented a new pathway towards localized MZMs on the boundary of two-dimensional materials, consisting of an altermagnetic film, subject to a superconducting proximity effect from a superconducting substrate. In this work, we demonstrate the possibility for an altermagnet-superconductor heterostructure, to not only harbor MZMs, but also freely manipulate their position along the topological boundary of the material, via rotation of the N\'eel vector. Using this mechanism, on a square platform, we utilize a time-dependent method to simulate the Z-gate via braiding, and then extend this to a larger H-junction, where we implement the $\sqrt{{\rm X}}$ and $\sqrt{{\rm Z}}$ gate on a single-qubit system. Further, this structure is eminently scalable to many-qubit systems, thus providing the essential ingredients towards universal quantum computation.

cond-mat.mes-hall↗

arXiv2025

Fusion Dynamics of Majorana Zero Modes

Braiding and fusion of Majorana zero modes are key elements of any future topological Majorana-based quantum computer. Here, we investigate the fusion dynamics of Majorana zero modes in the spinless Kitaev model, as well as in a spinful model describing magnet-superconductor hybrid structures. We consider various scenarios allowing us to reproduce the fusion rules of the Ising anyon model. Particular emphasis is given to the charge of the fermion obtained after fusing two Majorana zero modes: as long as it remains on the superconductor, charge quantization is absent. When moving the fermion to a non-superconducting region, such as a quantum dot, nearly-quantized charge can be measured. Our findings confirm for both platforms that fusion dynamics of Majorana zero modes can indeed be used for the readout of Majorana qubits.

cond-mat.mes-hall↗

arXiv2025

Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing

Qubits built out of Majorana zero modes (MZMs) have long been theorized as a potential pathway toward fault-tolerant topological quantum computation. Almost unavoidable in these processes is Majorana wavefunction overlap, known as hybridization, which arise throughout the process when Majorana modes get close to each other. This breaks the ground state degeneracy, leading to qubit errors in the braiding process. This work presents a simple but precise method to predict qubit errors for dynamic hybridization which varies in space and time. This includes hybridization between four or more MZMs through topological or trivial regions, or both of them. As an illustration, we characterize qubit-errors for an X-gate. We demonstrate how to utilize the hybridization to implement not only arbitrary one-qubit rotations but also a two-qubit controlled variable phase gate, providing a demonstration of universal quantum computing.

cond-mat.mes-hall↗

arXiv2024

Effect of impurities and disorder on the braiding dynamics of Majorana zero modes

Impurities and random disorder are known to affect topological superconducting phases and their Majorana zero modes (MZMs). In particular, it is a common assumption that disorder negatively influences the braiding dynamics of MZMs. Recently, it was shown, however, that random disorder can also stabilize or even increase topological phases. Here, we investigate quantitatively how a single impurity can lead to braiding errors. We show that the impurity increases, in most scenarios, the dynamical hybridization of the MZMs, reducing the braiding performance. In addition, we show how random disorder, i.e., impurities on all lattice sites but with different strengths, affects braiding. As for the static case, we observe a window of opportunity where random disorder decreases the average energy of a braid, and thus improves braiding outcomes. This window of opportunity is, however, limited due to an increase of diabatic effects in the presence of disorder. Nevertheless and contrary to physical intuition, disorder can in certain situations be beneficial and improve braiding outcomes.

cond-mat.mes-hall↗

arXiv2023

Many-body Majorana braiding without an exponential Hilbert space

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 many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wavefunctions as well as their expectation values, correlators and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. We show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our work opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any non-interacting superconductor.

quant-ph↗

arXiv2023

Implementation of Topological Quantum Gates in Magnet-Superconductor Hybrid Structures

The creation of topological quantum gates using Majorana zero modes -- an outstanding problem in the field of topological quantum computing -- relies on our ability to control the braiding process of these particles in time and space. Here, we demonstrate the successful implementation of topologically protected $\sqrt{\sigma_z}$-, $\sigma_z$- and $\sigma_x$-quantum gates using Majorana zero modes in two-dimensional magnet-superconductor hybrid structures. We propose a braiding protocol that makes use of recent advances in the ability to control the spin of individual atoms using electron-spin-resonance techniques. We visualize the braiding process in time and space by computing the non-equilibrium local density of states, which is proportional to the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments.

cond-mat.mes-hall↗