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

非技术摘要：随着一系列拓扑绝缘体、具有隐藏有序的奇异材料和导电表面态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占据中心舞台。集成超导体和拓扑绝缘体的技术为实验实现Majorana费米子提供了一个舞台，Majorana费米子曾经被认为是一种基本粒子，现在是形成固态拓扑量子比特的候选粒子，预计它将对环境干扰具有弹性。由这笔赠款支持的项目需要创建一种图案化的超导体-拓扑绝缘体混合体系结构，该体系结构支持量子涡旋，其核心预计将驻留Majorana费米子。这项研究的目标是确定这种结构中存在这种Majorana费米子，并执行非常受欢迎的量子计算协议所需的关键步骤。实现这些目标的步骤的紧密结合包括设计适当的图案化通道和磁场配置以成核和移动涡旋，施加所需的脉冲电流和局部场来执行量子比特操作，以及使用单电子晶体管来读出量子比特态。这个项目跨越基础物理、凝聚态物质和量子计算的跨学科性质，以及参与其中的实验者和理论家之间的合作，为培养由这笔拨款支持的研究生提供了一个丰富而肥沃的知识环境。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高度相关，有助于阐明纳米和介观尺度上的量子行为，并评估作为拓扑量子计算候选者的拓扑结结构。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Majorana Fermion(MF)的拓扑量子比特的功能。这些有望以束缚态存在于拓扑超导体中的金属原子，是托管拓扑量子比特的主要候选者。这种费米子的非局域对共享一种电子态，这种电子态既可以被占据，也可以是空的，这使得这种对成为奇偶量子比特。半导体纳米线，以及最近的铁磁原子链，因其成核MF束缚态的能力而受到显著关注。与传统的量子计算一样，在材料系统中实现拓扑量子计算最好的方法是研究多条路径。该合作实验-理论项目将横向超导体-拓扑绝缘体-超导体约瑟夫森结的网络结构作为另一个可行的、非常有希望的候选方案，它在支持基于MF的拓扑量子比特方面具有几个优势。我们的目标是演示拓扑量子计算协议中的关键组件MF辫子，并在该系统中执行相关的电子宇称量子比特读出。该体系结构由长长的约瑟夫森结组成，它们夹在单线对超导体之间的拓扑绝缘体之间。通过结的外加磁通以受控的方式形成携带MF束束态的相移(约瑟夫森结涡旋)。脉冲电流和局域场的动态应用会沿特定的结路径诱导运动。通过涡旋操纵进行编织包括：i)交换三结几何结构中的MF；ii)将四个MF阵列中的一对MF组合在一起并分离出来。奇偶量子比特读出是通过耦合到量子点和单电子晶体管来隧道和感测电子来执行的。建立这些步骤可能会对用于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，特别是在评估相干性在拓扑系统中的作用以及比较不同拓扑结构的优势方面。这个项目跨越基础物理、凝聚态物质和量子计算的跨学科性质，以及参与其中的实验者和理论家之间的合作，为培养由这笔拨款支持的研究生提供了一个丰富而肥沃的知识环境。

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.