  We report Aharonov-Bohm (AB)-type quantum interference in simply-connected
devices created at the LaAlO$_3$/SrTiO$_3$ interface using conductive-atomic
force microscope (c-AFM) lithography. The oscillations are multi-periodic
functions of magnetic field strength, and they exhibit a substantial magnetic
hysteresis with frequencies that depends on the magnetic sweep direction. The
oscillation amplitude for the lowest two frequencies approaches $e^2/h$,
consistent with the theoretical maximum for the AB effect, and harmonics up to
third order are observable. Broadband quasiperiodic behavior is reported in a
fraction of simply-connected electron waveguide devices that exhibit magnetic
asymmetries. Curiously, nanoscale ring devices that are multiply-connected lack
signatures of AB quantum interference. The interference phenomena are
associated with an inhomogeneous magnetic landscape within the
LaAlO$_3$/SrTiO$_3$ nanostructures.
