Electrostatic gate-controlled quantum interference in a high-mobility two-dimensional electron gas at the (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)O$_3$/SrTiO$_3$ interface

We report quantum oscillations in magnetoresistance that are periodic in magnetic field ($B$), observed at the interface between (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)O$_3$ and SrTiO$_3$. Unlike Shubnikov-de Haas oscillations, which appear at magnetic fields $>7$ T and diminish quickly as the temperature rises, these $B$-periodic oscillations emerge at low fields and persist up to 10 K. Their amplitude decays exponentially with both temperature and field, specifying dephasing of quantum interference. Increasing the carrier density through electrostatic gating results in a systematic reduction in both the amplitude and frequency of the oscillations, with complete suppression beyond a certain gate voltage. We attribute these oscillations to the Altshuler-Aronov-Spivak effect, likely arising from naturally formed closed-loop paths due to the interconnected quasi-one-dimensional conduction channels along SrTiO$_3$ domain walls. The relatively long phase coherence length ($\sim$ 1.8 $\mu$m at 0.1 K), estimated from the oscillation amplitude, highlights the potential of complex oxide interfaces as a promising platform for exploring quantum interference effects and advancing device concepts in quantum technologies, such as mesoscopic interferometers and quantum sensors.