  A triple-quantum-dot system can be operated as either an exchange-only qubit
or a resonant-exchange qubit. While it is generally believed that the decisive
advantage of the resonant-exchange qubit is the suppression of charge noise
because it is operated at a sweet spot, we show that the leakage is also an
important factor. Through molecular-orbital-theoretic calculations, we show
that when the system is operated in the exchange-only scheme, the leakage to
states with double electron occupancy in quantum dots is severe when rotations
around the axis 120$^\circ$ from $\hat{z}$ is performed. While this leakage can
be reduced by either shrinking the dots or separating them further, the
exchange interactions are also suppressed at the same time, making the gate
operations unfavorably slow. When the system is operated as a resonant-exchange
qubit, the leakage is 3-5 orders of magnitude smaller. We have also calculated
the optimal detuning point which minimizes the leakage for the
resonant-exchange qubit, and have found that although it does not coincide with
the double-sweet-spot for the charge noise, they are rather close. Our results
suggest that the resonant-exchange qubit has another advantage that leakage can
be greatly suppressed compared to the exchange-only qubit, and operating at the
double-sweet-spot point should be optimal both for reducing charge noise and
suppressing leakage.
