  Leakage errors damage a qubit by coupling it to other levels. Over the years,
several theoretical approaches to dealing with such errors have been developed
based on perturbation arguments. Here we propose a different strategy: we use a
sequence of finite rotation gates to exactly eliminate leakage errors. The
strategy is illustrated by the recently proposed charge quadrupole qubit in a
triple quantum dot, where there are two logical states to support the qubit and
one leakage state. We have found an su(2) subalgebra in the three-level system,
and by using the subalgebra we show that ideal Pauli x and z rotations, which
are universal for single-qubit gates, can be generated by two or three
propagators of experimentally-available Hamiltonians. The proposed strategy
does not require additional pulses, is independent of error magnitude, and
potentially reduces experimental overheads. In addition, the magnitude of
detuning fluctuation can be estimated based on the exact solution.
