EAGER: BRAIDING: Parity control and braiding of Majorana fermions in S-TI-S Josephson junction networks

摘要：随着一系列拓扑绝缘体、具有隐藏有序和导电表面态的奇异材料的制造取得快速进展，所谓的“拓扑量子计算”的令人兴奋的前景正成为人们关注的焦点。整合超导体和拓扑绝缘体的技术为实验实现马约拉纳费米子提供了一个舞台，马约拉纳费米子曾被认为是一种基本粒子，现在已成为固态拓扑量子比特的候选材料，有望对环境干扰具有弹性。这项拨款支持的项目需要创建一个模式超导体拓扑绝缘体混合结构，该结构支持量子漩涡，其核心预计将驻留马约拉纳费米子。这项研究的目标是在这个体系结构中确定这种马约拉纳费米子的存在，并执行备受追捧的量子计算协议所需的关键步骤。实现这一目标的一系列步骤包括：设计合适的图形通道和磁场配置来形成漩涡并移动漩涡；应用所需的脉冲电流和局部场来执行量子位操作；使用单电子晶体管读取量子位状态。该项目跨越基础物理、凝聚态物质和量子计算的跨学科性质，以及实验家和理论家之间的合作，为培养受该基金支持的研究生提供了丰富而肥沃的智力环境。从技术角度来看，该项目的结果与固态量子器件的未来发展，阐明纳米尺度和中尺度的量子行为，以及评估拓扑结结构作为拓扑量子计算的候选者高度相关。技术摘要：作为实现拓扑量子计算的重大进展，社区的一个紧迫目标是成功演示基于马约拉纳费米子（MF）的拓扑量子比特的功能。这些MFs预计将以束缚态的形式存在于拓扑超导体中，是承载拓扑量子比特的主要候选者。非局域费米子对共享一种电子状态，这种电子状态既可以被占据，也可以是空的，使这样的一对成为奇偶量子位。半导体奈米线，以及最近的铁磁原子链，因其能使磁偶联态成核而备受关注。与传统的量子计算一样，在材料系统中实现拓扑量子计算可以通过研究多条路径来实现。这个合作实验理论项目的目标是横向超导体-拓扑绝缘体-超导体约瑟夫森结的网络架构，作为另一个可行的、非常有前途的候选网络，它在支持基于mf的拓扑量子比特方面有几个优势。目标是演示拓扑量子计算协议中的关键组件MF编织，并在该系统中执行相关的电子奇偶量子位读出。该结构由长约瑟夫森结组成，该结夹在单线对超导体之间的拓扑绝缘体中。通过结的外加磁通量使相滑移（约瑟夫森结涡）以受控的方式携带MF束缚态。脉冲电流和局部场的动态应用沿着特定的结路径诱导运动。通过旋涡操纵编织包括i)交换三结几何形状的mf， ii)将四个mf阵列中的一对mf聚集在一起并分离出来。奇偶量子比特读出是通过耦合到量子点和单电子晶体管的隧穿和传感电子来完成的。建立这些步骤可能会对量子计算和量子信息处理的固态量子比特的实现产生潜在的变革，特别是在评估拓扑系统中相干性的作用以及比较不同拓扑体系结构的优势方面。该项目跨越基础物理、凝聚态物质和量子计算的跨学科性质，以及实验家和理论家之间的合作，为培养受该基金支持的研究生提供了丰富而肥沃的智力环境。

Non-technical Abstract: The exciting prospect of so-called "topological quantum computation" is taking center stage with the rapid progress in fabrication of a range of topological insulators, exotic materials possessing hidden order and conducting surface states. Technologies integrating superconductors and topological insulators have provided an arena for experimentally realizing the Majorana fermion, once proposed as an elementary particle, now a candidate for forming the building blocks for solid-state topological qubits, which are expected to be resilient to environmental disturbances. The project supported by this grant entails creation of a patterned superconductor-topological insulator hybrid architecture that supports quantum vortices in whose cores Majorana fermions are expected to reside. The goal of the research is to establish the existence of such Majorana fermions within this architecture and to perform the key steps required for much sought-after quantum computational protocols. A tight combination of steps to achieve the goals involves designing appropriate patterned channels and configurations of magnetic fields to nucleate and move vortices, applying the desired pulsed currents and local fields to perform qubit operations, and employing single-electron transistors to read out qubit states. The transdisciplinary nature of this project spanning fundamental physics, condensed matter, and quantum computation and the collaboration between experimentalists and theorists involved provides a rich and fertile intellectual environment for training the graduate students who are supported by this grant. From a technological perspective, the results of the project are highly relevant to the future development of solid-state quantum devices, to elucidating quantum behavior at the nanoscale and mesoscale, and to assessing topological junction architectures as candidates for topological quantum computation. Technical Abstract:As a significant advance towards implementing topological quantum computation, a pressing goal for the community is to successfully demonstrate the functioning of Majorana fermion (MF)-based topological qubits. These MFs, expected to exist as bound states in topological superconductors, are prime candidates for hosting topological qubits. Non-local pairs of such fermions share an electronic state that can be either occupied or empty, making such a pair a parity qubit. Semiconducting nanowires, and more recently, chains of ferromagnetic atoms, have received prominent attention for their ability to nucleate MF bound states. As with conventional quantum computing, implementing topological quantum computation in a materials system can be best achieved by investigating multiple routes. The collaborative experiment-theory project targets network architectures of lateral superconductor-topological insulator-superconductor Josephson junctions as another viable, highly promising candidate that has several advantages for supporting MF-based topological qubits. The goal is to demonstrate MF braiding, a key component in topological quantum computational protocols, and to perform associated electron parity qubit read-outs in this system. The architecture consists of long Josephson junctions that sandwich topological insulators between singlet-paired superconductors. Applied magnetic flux through the junction nucleates phase slips (Josephson junction vortices) carrying MF bound states in a controlled fashion. Pulsed currents and dynamic applications of local fields induce motion along specific junction pathways. Braiding via vortex manipulation consists of i) exchange of MFs in tri-junction geometries and ii) involves bringing together and separating out a pair of MFs in an array of four MFs. Parity qubit read-outs are performed by tunneling and sensing electrons through coupling to quantum dots and single-electron transistors. Establishing these steps may potentially be transformative to the implementation of solid-state qubits for quantum computing and quantum information processing, particularly in assessing the role of coherence in topological systems and in comparing the strengths of different topological architectures. The transdisciplinary nature of this project spanning fundamental physics, condensed matter, and quantum computation and the collaboration between experimentalists and theorists involved provides a rich and fertile intellectual environment for training the graduate students who are supported by this grant.