Fundamental Bounds on Qubit Reset.

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 ancilla, we identify the types of interaction and controls for which the qubit can be purified. For these cases, we show that a time-optimal protocol is resonant purity exchange between qubit and ancilla, where the maximum fidelity is identical for all cases but the minimum time strongly depends on the type of interaction and control.