Nontechnical Abstract: Quantum statistics is central to the quantum mechanical understanding of the world. All known particles have so-called Abelian statistics, meaning that result of several consecutive particle exchanges does not depend on the order of the exchanges. Recently it has been proposed that particles with non-Abelian statistics can be realized in some exotic systems, and signatures of simplest such non-Abelian particles - Majorana fermions - have been reported. The main driving force in the search for these elusive excitations, apart from scientific curiosity, is a possibility to realize a fault tolerant quantum computer. Qubits based on Majorana fermions have their limitations, and the main objective on this proposal is to develop a new system where more computationally useful higher order non-Abelian excitations can be realized.
main objective of the proposed research is to develop a system where high-order non-Abelian excitations can be realized and manipulated. The non-Abelian statistics (the notion that a result of consecutive exchanges of several identical particles depends on the order of the exchanges) is at the heart of a revolutionary concept to realize a fault-tolerant quantum computer. Current efforts are focused on the development of Majorana-based qubits, the simplest non-Abelian particles. Majorana-based qubits are not computationally universal, though, and higher order non-Abelions are required to realize a universal gate. Specifically, spin transitions in the fractional quantum Hall effect regime will be explored to realize a reconfigurable network of helical channels with fractionalized charged excitations. Demonstration of induced superconductivity in these channels will be the major milestone. Quantum statistics of excitations formed at a boundary of trivial and topologically non-trivial superconductors will be investigated in multi-gate devices, where network of topological channels can be reconfigured within a two-dimensional plane.
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