[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123868-en":3,"doc-seo-123868-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123868,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Topological gap protocol based machine learning optimization of Majorana hybrid wires","Majorana zero modes in superconductor–nanowire hybrid structures offer a route to topologically protected qubits, but disorder can destroy the topological phase and reduce device yield. The work presents a machine-learning optimization scheme for a gate array near a grounded Majorana wire, enabling reliable compensation even under strong disorder. A metric inspired by the topological gap protocol is introduced, implementable via measurements of non-local conductance, avoiding interferometry while restoring the topological phase and localized modes.","arXiv :2305 . 16230v1 [ cond-mat .mes-hall ] 25 May 2023  \nTopological gap protocol based machine learning optimization of Majorana hybrid  \nwires  \nMatthias Thamm 1 and Bernd Rosenow 1  \n1 Institut f¨ur Theoretische Physik, Universit¨at Leipzig, Br¨uderstrasse 16, 04103 Leipzig, Germany  \n(Dated: May 26, 2023)  \nMajorana zero modes in superconductor-nanowire hybrid structures are a promising candidate for topologically protected qubits with the potential to be used in scalable structures. Currently, disorder in such Majorana wires is a major challenge as it can destroy the topological phase and thus reduce the yield in the fabrication of Majorana devices. We study machine learning optimization of a gate array in proximity to a grounded Majorana wire, which allows us to reliably compensate even strong disorder. We propose a metric for optimization that is inspired by the topological gap protocol, and which can be implemented based on measurements of the non-local conductance through the wire.  \nI. INTRODUCTION  \nA promising avenue towards achieving scalable quantum computing involves the utilization of Majorana zero modes (MZMs) [1–3], which emerge as bound states within topological superconductors [4–12] . Their occurrence is a consequence of the topological properties of the underlying phase, and they manifest as zero-energy states located within the excitation gap of the system. Due to this topological protection, MZMs exhibit robustness against external perturbations and decoherence. Furthermore, the ability to manipulate MZMs through anyonic braiding allows for the implementation of faulttolerant qubit operations [4–7, 13] .  \nMZMs can occur in hybrid systems of conventional superconductors and semiconductors with strong spin-orbit coupling [4, 14–17] . However, disorder in these systems turns out to be a major problem [18–23], as it can destroy the topological phase [24] and induce trivial Andreev bound states (ABSs) [25–43], which can mimic signatures of MZMs [18, 20, 40, 44–46] . These ABSs complicate the verification of MZMs in experiments as they make more complex measurements and devices necessary [22, 47] . To distinguish MZMs from ABSs, signatures based on coherent transport using electron interferometers [47–50] are suitable, but experimentally challenging [47] . Another method to detect MZMs is the so-called topological gap protocol [51], which can be applied to agrounded wire contacted with leads at both ends. Here, all elements of the conductance matrix between the two leads are measured to ensure that zero-bias conductance peaks occur simultaneously at both ends and that the excitation gap closes at the boundaries of the topological phase [51] .  \nNumerous experimental studies have confirmed the predicted signatures of Majorana zero modes (MZMs)[52–57] . Compelling evidence exists for the presence of MZMs in hybrid wires, demonstrated through interferometry [47] and the application of the topological gap protocol [22] . Theoretical investigations have also identified strategies for enhancing MZMs in clean Majorana wires, including the use of magnetic field textures [58–61],  \nFIG. 1. Majorana hybrid wire consisting of a grounded superconductor (orange) and a semiconductor with strong spin orbit coupling (blue) connected to two leads L and R separated from the wire by a potential Vconf created by pinch-off gates. The full conductance matrix Gαβ = dIα /dVβ can be measured as a function of an applied bias voltage VR −VL and external Zeeman field Ez based on which voltages of an array of gates (green) are optimized using the CMA-ES algorithm [67] to cancel disorder effects in the hybrid wire.  \nharmonic potential profiles [59], and optimized geometries for Majorana Josephson junctions [62] . However, the presence of disorder in the fabrication process significantly affects the yield of Majorana devices [22], which poses a major limitation for the realization of large-scale qubit systems. Several approaches have b","cbCaiiWWu9i8vhY8","https://ap.wps.com/l/cbCaiiWWu9i8vhY8","pdf",3105292,1,13,"English","en",105,"# Introduction\n## Majorana zero modes and topological protection\n## Disorder effects and experimental verification challenges\n## Topological gap protocol\n## Related optimization and machine learning approaches\n# Setup","[{\"question\":\"What problem does the document address in Majorana hybrid wires?\",\"answer\":\"Disorder in superconductor–nanowire hybrid systems can destroy the topological phase and lower fabrication yield, often inducing trivial Andreev bound states that mimic Majorana signatures.\"},{\"question\":\"How does the proposed method optimize the device?\",\"answer\":\"It uses a CMA-ES machine learning algorithm to tune voltages on a gate array near a grounded Majorana wire, aiming to minimize an optimization metric tied to topological behavior.\"},{\"question\":\"What measurement is used to implement the optimization metric?\",\"answer\":\"The metric can be implemented using measurements of the non-local conductance through the wire, following an inspiration from the topological gap protocol rather than requiring interferometry.\"}]","Topological gap protocol based machine learning optimization of Majorana hybrid wires | 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problem does the document address in Majorana hybrid wires?","Question",{"text":75,"@type":76},"Disorder in superconductor–nanowire hybrid systems can destroy the topological phase and lower fabrication yield, often inducing trivial Andreev bound states that mimic Majorana signatures.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method optimize the device?",{"text":80,"@type":76},"It uses a CMA-ES machine learning algorithm to tune voltages on a gate array near a grounded Majorana wire, aiming to minimize an optimization metric tied to topological behavior.",{"name":82,"@type":73,"acceptedAnswer":83},"What measurement is used to implement the optimization metric?",{"text":84,"@type":76},"The metric can be implemented using measurements of the non-local conductance through the wire, following an inspiration from the topological gap protocol rather than requiring 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