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、具有隐藏有序性和导电表面态的奇异材料的快速制备，所谓的“拓扑量子计算”的令人兴奋的前景正占据中心舞台。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竞技场，马约拉纳费米子曾被认为是基本粒子，现在是形成固态拓扑量子比特的构建模块的候选者，预计它对环境干扰具有弹性。 由该资助支持的项目需要创建一个模式化的超导体-拓扑绝缘体混合架构，该架构支持量子涡旋，其核心中预期存在Majorana费米子。这项研究的目标是在这种架构中建立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。实现这些目标的步骤的紧密组合包括设计适当的图案化通道和磁场配置以使涡旋成核和移动，施加所需的脉冲电流和局部场以执行量子位操作，以及采用单电子晶体管来读出量子位状态。该项目的跨学科性质跨越基础物理学，凝聚态物质和量子计算以及实验学家和理论家之间的合作，为培养受此资助的研究生提供了丰富而肥沃的智力环境。 从技术的角度来看，该项目的结果与固态量子器件的未来发展高度相关，以阐明纳米尺度和介观尺度的量子行为，并评估拓扑结架构作为拓扑量子计算的候选者。 技术摘要：作为实现拓扑量子计算的一个重大进展，社区的一个紧迫目标是成功地证明基于马约拉纳费米子（MF）的拓扑量子比特的功能。 这些MF，预计存在于拓扑超导体中的束缚态，是托管拓扑量子比特的主要候选者。这种费米子的非定域对共享一个可以被占据或为空的电子状态，使这样的一对成为奇偶校验量子比特。半导体纳米线，以及最近的铁磁原子链，因其使MF束缚态成核的能力而受到突出的关注。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线来实现。该合作实验-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、非常有前途的候选者，它在支持基于MF的拓扑量子比特方面具有几个优势。我们的目标是证明MF编织，拓扑量子计算协议的关键组成部分，并在这个系统中执行相关的电子奇偶校验量子位读出。 该架构由长约瑟夫森结组成，这些结将拓扑绝缘体夹在单态对超导体之间。施加的磁通量通过结核相位滑移（约瑟夫森结涡旋）携带MF束缚态在一个受控的方式。脉冲电流和局部场的动态应用引起沿沿着特定结路径的运动。经由涡旋操纵的编织包括i）在三结几何结构中交换MF，以及ii）涉及在四个MF的阵列中将一对MF聚集在一起并分离出。奇偶校验量子位读出是通过耦合到量子点和单电子晶体管来隧穿和感测电子来执行的。建立这些步骤可能对量子计算和量子信息处理的固态量子比特的实现具有潜在的变革性，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架构的优势方面。该项目的跨学科性质跨越基础物理学，凝聚态物质和量子计算以及实验学家和理论家之间的合作，为培养受此资助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.