  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.
