  Oxide heterostructures are versatile platforms with which to research and
create novel functional nanostructures. We successfully develop one-dimensional
(1D) quantum-wire devices using quantum point contacts on MgZnO/ZnO
heterostructures and observe ballistic electron transport with conductance
quantised in units of 2e^{2}/h. Using DC-bias and in-plane field measurements,
we find that the g-factor is enhanced to around 6.8, more than three times the
value in bulk ZnO. We show that the effective mass m^{*} increases as the
electron density decreases, resulting from the strong electron-electron
interactions. In this strongly interacting 1D system we study features matching
the 0.7 conductance anomalies up to the fifth subband. This paper demonstrates
that high-mobility oxide heterostructures such as this can provide good
alternatives to conventional III-V semiconductors in spintronics and quantum
computing as they do not have their unavoidable dephasing from nuclear spins.
This paves a way for the development of qubits benefiting from the low defects
of an undoped heterostructure together with the long spin lifetimes achievable
in silicon.
