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A triple-quantum-dot system can be operated as either an exchange-only qubitor a resonant-exchange qubit. While it is generally believed that the decisiveadvantage of the resonant-exchange qubit is the suppression of charge noisebecause it is operated at a sweet spot, we show that the leakage is also animportant factor. Through molecular-orbital-theoretic calculations, we showthat when the system is operated in the exchange-only scheme, the leakage tostates with double electron occupancy in quantum dots is severe when rotationsaround the axis 120$^\circ$ from $\hat{z}$ is performed. While this leakage canbe reduced by either shrinking the dots or separating them further, theexchange interactions are also suppressed at the same time, making the gateoperations unfavorably slow. When the system is operated as a resonant-exchangequbit, the leakage is 3-5 orders of magnitude smaller. We have also calculatedthe optimal detuning point which minimizes the leakage for theresonant-exchange qubit, and have found that although it does not coincide withthe double-sweet-spot for the charge noise, they are rather close. Our resultssuggest that the resonant-exchange qubit has another advantage that leakage canbe greatly suppressed compared to the exchange-only qubit, and operating at thedouble-sweet-spot point should be optimal both for reducing charge noise andsuppressing leakage.

Leakage and sweet spots in triple-quantum-dot spin qubits: A molecular-orbital study