Stephan Rachel

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.

The p-wave magnet has emerged as a new type of magnetism exhibiting odd-parity, time-reversal-symmetric spin splitting in momentum space, and has attracted considerable interest as a promising platform for spintronic applications. However, the theoretical understanding of the fundamental mechanism responsible for stabilizing this phase remains limited. In this Letter, we identify a microscopic interacting model that realizes the p-wave magnet as its ground state. We first introduce a Hubbard model and derive the corresponding low-energy spin Hamiltonian. At the classical level, we find that the p-wave magnet is stabilized but remains energetically degenerate with competing noncoplanar states. Quantum fluctuations lift this degeneracy, selecting the p-wave magnet as the unique ground state. The resulting electronic structure exhibits finite spin accumulation via the Edelstein effect, highlighting the potential of p-wave magnetism for spintronic applications. We further discuss the relevance of our theory to quasi-two-dimensional honeycomb magnets such as Ni_{2}Mo_{3}O_{8}. Our findings establish the possibility of spontaneous p-wave magnetism.

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.

Majorana modes offer great potential for fault-tolerant quantum computation due to their topological protection. However, intrinsic disorder makes the unambiguous detection of Majorana modes difficult in the commonly used hybrid superconductor–semiconductor nanowire platform. By contrast, for magnet–superconductor hybrid systems, Majorana modes were theoretically predicted to be very robust against disorder, but no experimental confirmation of this has been reported so far. Here we demonstrate that these modes are indeed robust in one-dimensional spin chains constructed from individual iron atoms on a Rashba surface alloy with proximity-induced superconductivity. Although the chains exhibit perfect crystalline order, we observe nanoscale potential disorder of the BiAg ₂ /Ag(111)/Nb(110) heterostructure by scanning tunnelling microscopy. However, this does not prevent the emergence of zero-energy modes at both ends of the atomic chains, in agreement with tight-binding calculations showing that these modes are only found in the topologically non-trivial regime of the phase diagram. Our results explain the earlier observation of zero-energy Majorana modes in disordered Fe chains on other superconducting substrates, and may provide an avenue for the realization of Majorana qubits.