Optimising the exchange of Majorana zero modes in a quantum nanowire network

Tomasz Maciazek; Mia Conlon

Home/Archive/arXiv

arXiv · 2310.13634

Optimising the exchange of Majorana zero modes in a quantum nanowire network

Tomasz Maciazek·Mia Conlon

View original source ↗Read source document ↗Export metadata ↓

Abstract

Determination of optimal control protocols for Majorana zero modes during their exchange is a crucial step towards the realisation of the topological quantum computer. In this paper, we study the finite-time exchange process of Majorana zero modes on a network formed by coupled p-wave superconducting one-dimensional nanowires. We provide scalable computational tools for optimising such an exchange process relying on deep learning techniques. To accomplish the scalability, we derive and implement an analytic formula for the gradient of the quantum infidelity which measures the error in the topological quantum gate generation in the Majorana zero modes exchange. Our optimisation strategy relies on learning the optimised transport protocol via a neural net which is followed by direct gradient descent fine tuning. The optimised exchange protocols in the super-adiabatic regime discover the fact that the Majorana zero modes must necessarily stop before crossing a junction point in the network. We explain that this is caused by fast changes in the energy gap of the system whenever one of the Majorana zero modes approaches a junction point. In particular, the energy gap exhibits oscillations followed by a sharp jump. We explain this phenomenon analytically in the regime where the Majorana zero modes are completely localised. Finally, we study how the disorder in the quantum nanowire affects the exchange protocols. This shows that understanding the disorder pattern would allow one to improve quantum gate fidelity by one to two orders of magnitude.

Explore related subjects

cond-mat.mes-hall

Keep this discovery

BibTeX RIS

Tomasz Maciazek, Mia Conlon. 2023-10-20. Optimising the exchange of Majorana zero modes in a quantum nanowire network. https://arxiv.org/abs/2310.13634

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Emergence of spin-orbit coupling among spin, atomic orbital, and Bloch dynamics in Janus double-transition-metal MXenes

We found a spin-orbit coupling to cause a simultaneous correlation among three degrees of freedom, the electronic spin, orbital, and Bloch dynamics in an investigation into the electronic structure of Janus double-transition-metal MXenes, Mo$_2$HfC$_2$OS and W$_2$HfC$_2$OS. In this paper, it is also revealed that the spin-orbit coupling causes a staggered spin configuration with a trigonal pattern around the $\Gamma$ point near the insulating gap. We developed a reduced Hamiltonian describing the electronic states and show that the spin-orbit coupling cannot be equated with conventional forms for a single electron in solids, LS, Rashba, and Dresselhaus couplings, even in the approximation under the low-energy and small wave number condition. Because of the intrinsic shape of the conduction band, a trigonally alternating spin-momentum locking emerges with the spin axis perpendicular to the layer plane. The theoretical analysis shows that these Janus materials can provide a platform for exploring the spin-related phenomena due to the trigonal spin-momentum locking other than Rashba and Dresselhaus types.

cond-mat.mes-hall↗

arXiv2026

A substrate booster for P-type 2D ferromagnetic semiconductor

Spin transistors with its both charge and spin properties tuned via electrostatic gating are believed capable for widespread use, which however have proven challenging due to the extreme rareness of their physical base -- magnetic semiconductors. The latter are limited within very few systems including diluted magnetic semiconductors (DMS) and two-dimensional ferromagnetic semiconductors (2D-FMS), and known to suffer from inadequate gate-tunability of their electric and/or magnetic properties. Here, we show a substrate engineering paradigm by interfacing few-layered Cr$_{2}$Ge$_{2}$Te$_{6}$ (FL-CGT) with an antiferromagnetic insulator CrOCl. Owing to the subtle interfacial charge transfer couplings, CGT can be drastically turned from an ambipolar semiconductor into a high performance P-type semiconductor. When cooled below the Curie temperature, the ON-OFF ratio in such substrate-boosted FMS field-effect transistor (FET) reaches 10$^{5}$ with its coercive field $H_{c}$ of magnetic hysteresis loop tunable by a factor of more than 200$\%$, enabling {gate-assisted magnetic switching in the prototype semiconducting spin transistor architecture}. A crossover from critical power-law scaling to a dual power-law behaviour under heavy hole doping was further observed. Our findings {signify} an efficient interfacial charge transfer and electrically modulated magnetic anisotropy energy supported by calculations. This high performance P-type FMS-FET system suggests that active substrate-boosting paradigm might be a powerful path for the investigation of future gate-tunable spintronic devices.

cond-mat.mes-hall↗

arXiv2026

In-plane magnetic field control of anomalous Hall response enabled by magnetic anisotropy engineering

Engineering magnetic anisotropy provides a powerful route to control magnetization orientation and unlock emerging functionalities in opto-spintronic and current-driven devices. Beyond its role in magnetization reversal, the effective anisotropy can strongly influence the magnetotransport response, offering an additional degree of freedom to tune new device functionalities. In this work, we report a magnetotransport study of a ferrimagnetic [Tb/Co]$_{\times 5}$ multilayer grown with a Tb thickness gradient, whose wedge-shaped tilts the uniaxial anisotropy axis slightly away from the film normal. Anomalous Hall resistivity measurements from 80 K to 300 K reveal a spin reorientation transition, while the angular dependence of the magnetotransport responses exposes the crucial role of the tilted anisotropy. A simplified macrospin model reproduces the full angular response across the transition and shows that the observed anomalous Hall effect when the in-plane magnetic field is applied originates from the tilt of the uniaxial anisotropy axis, which supplies a built-in symmetry-breaking mechanism, enabling in-plane field control over the out-of-plane anomalous Hall response, sign included. These findings establish tilted magnetic anisotropy as a promising route toward Hall effect-based sensor applications and highlight Tb/Co multilayers as a versatile platform for anisotropy-engineered spintronic devices.

cond-mat.mes-hall↗