EAGER: BRAIDING: Multi-terminal Josephson circuits supporting nontrivial Chern topologies for anyonic qubits

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Nontechnical Abstract: This research project aims to exploit the physical laws of quantum mechanics to create a new tool for superfast information processing, known as quantum computation. Researchers will encode information in identical subatomic particles, known as non-Abelian particles, which can "remember" the history of their mutual positions and how they have exchanged positions. Practical quantum information processing hardware is expected to allow the encoded information to be read out and will provide transformative advances in several areas, including the design of new, functional materials and complex, multi-dimensional information-processing operations. The quantum materials and devices to be developed in this project are important for enabling very precise measurements in science and technology. Furthermore, the project has important implications for fundamental science; for example, cosmological models of the Universe could be mimicked using these new methods of quantum information processing. Under this project, students will receive extensive training in advanced scientific methods, materials science and nanotechnology and, also, in applying scientific methods for critical thinking and problem solving. Technical Abstract: This work focuses on demonstrating the superior potential of multi-terminal superconducting Josephson circuits and qubits as a braiding platform for non-Abelian particles and as emulators of novel higher-dimensional topological states and their possible use in applications for topologically protected computing. The vortices are created in two-dimensional arrays of superconducting nano-islands placed on a topological insulator. Such vortices are predicted to carry non-Abelian Majorana zero modes. The studied qubit device is a cross-current meissneron transmon qubit, which is able to supply a circularly polarized supercurrent allowing circular braiding trajectories of vortex-antivortex pairs. In this project, a quantum-superposition Lorentz force is generated by means of the two qubits coupled to a multi-terminal superconducting junction having the array of superconducting nano-islands. The goal is to achieve a superposition of two-dimensional braiding trajectories in order to store quantum information. At the first stage, a two-dimensional multi-terminal superconducting proximity junction, decorated with an array of superconducting nano-islands, is being used to stabilize and permit two-dimensional translocation of vortices and antivortices. The parity of the Majorana states affects the qubit excitation energy and thus can be measured by qubit spectroscopy. Combining vortices and antivortices serves the purpose of simplifying braiding algorithms, because the Lorentz force acting on antivortices under a given supercurrent is opposite to the Lorentz force acting on vortices. The two-dimensional nature of the proximity arrays, serving as nonlinear inductors in transmon qubits, is the key factor allowing vortices and antivortices to be present simultaneously in the junction and to move around each other to achieve braiding operations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.