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

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

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.