Leakage Suppression via Simultaneous Exchange in a Triangular Exchange-Only Qubit

Exchange-only (EO) spin qubits use three spins to encode a qubit in a decoherence-free subspace that can protect against global fluctuations in the magnetic field. However, due to the enlarged Hilbert space associated with encoded qubits, EO qubits are susceptible to leakage out of the computational subspace, which can be detrimental to the performance of quantum error correcting codes. Here, in an all-to-all connected triangular quantum dot array [1, 2], we show that by simultaneously turning on exchange interactions between all three spins, we open an energy gap that suppresses leakage out of the qubit subspace. We present procedures to optimize this leakage suppression and for measuring the strength of the simultaneous exchange interaction. Although activating multiple exchange interactions simultaneously increases the effects of charge noise, we find that for a certain range of simultaneous exchange energies, this is not the dominant factor in limiting coherence times.