Themba Hodge

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 , which can be utilized to reduce the average hybridization energy of the total gate. We present two illustrative examples where 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.

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 Greenberger–Horne–Zeilinger 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.

Topological quantum computation, featuring qubits built out of anyonic excitations known as Majorana zero modes (MZMs), have long presented an exciting route toward scalable quantum computation. Recently, the advent of altermagnetic materials has presented a pathway toward 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 Néel vector. Using this mechanism, on a square platform, we utilize a time-dependent method to simulate the Z gate via , and then extend this to a larger H junction, where we implement the X and Z gates on a single-qubit system. Further, this structure is eminently scalable to many-qubit systems, thus providing the essential ingredients toward universal quantum computation.

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 wave function overlap, known as hybridization, which arises 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.

Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes 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 wave functions 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 Letter 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 noninteracting superconductor.