Qubit reset is a basic prerequisite for operating quantum devices,
requiring the export of entropy. The fastest and most accurate way
to reset a qubit is obtained by coupling the qubit to an ancilla
on demand. Here, we derive fundamental bounds on qubit reset in
terms of maximum fidelity and minimum time, assuming control over
the qubit and no control over the ancilla. Using the Cartan
decomposition of the Lie algebra of qubit plus two-level ancilla,
we identify the types of interaction and controls for which the
qubit can be purified. For these configurations, we show that a
time-optimal protocol consists of purity exchange between qubit
and ancilla brought into resonance, where the maximum fidelity
is identical for all cases but the minimum time depends on the
type of interaction and control. Furthermore, we find the maximally
achievable fidelity to increase with the size of the ancilla Hilbert
space, whereas the reset time remains constant.