The development of “fault-tolerant” quantum computers, unaffected by noise and decoherence, is one of the fundamental challenges in quantum technology. One of the approaches currently followed is the realization of “topologically protected” qubits which make use of quantum systems characterized by a degenerate ground state of composite particles, known as “non-Abelian anyons”, able to encode and manipulate quantum information in a non-local manner. In this paper, we discuss the potential of quasi-two-dimensional electron gas (q2DEG) at the interface between band insulating oxides, like LaAlO3 and SrTiO3, as an innovative technological platform for the realization of topological quantum systems. Being characterized by a unique combination of unconventional spin-orbit coupling, magnetism, and 2D-superconductivity, these systems naturally possess most of the fundamental characteristics needed for the realization of a topological superconductor. These properties can be widely tuned by electric field effect acting on the orbital splitting and occupation of the non-degenerate 3dxy and 3dxz,yz bands. The topological state in oxide q2DEGs quasi-one-dimensional nanochannels could be therefore suitably controlled, leading to conceptual new methods for the realization of a topological quantum electronics based on the tuning of the orbital degrees of freedom.

The interface between two wide band-gap insulators, LaAlO₃ and SrTiO₃ (LAO/STO), hosts a quasi-two-dimensional electron gas (q2DEG), two-dimensional superconductivity, ferromagnetism, and giant Rashba spin-orbit coupling. The co-existence of two-dimensional superconductivity with gate-tunable spin-orbit coupling and multiband occupation is of particular interest for the realization of unconventional superconducting pairing. To investigate the symmetry of the superconducting order parameter, phase sensitive measurements of the Josephson effect are required. We describe an approach for the fabrication of artificial superconducting weak links at the LAO/STO interface using direct high-resolution electron beam lithography and low-energy argon ion beam irradiation. The method does not require lift-off steps or sacrificial layers. Therefore, resolution is only limited by the electron beam lithography and pattern transfer. We have realized superconducting weak links with a barrier thickness of 30–100 nm. The barrier transparency of the weak links can be controlled by the irradiation dose and further tuned by a gate voltage. Our results open up new possibilities for the realization of quantum devices in oxide interfaces.