A reset-if-leaked procedure for encoded spin qubits

The spin of electrostatically confined electrons in semiconductor heterostructures has proven to be a promising candidate for hosting long-lived quantum information. Single and two spin qubit realizations rely on manipulation using (engineered) magnetic fields, but universal control using exclusively pairwise Heisenberg exchanges becomes possible when encoding the qubit in the spin-1/2 subspace of three electrons. While such qubits have proven to be operable with high fidelity [1], an issue is the presence of the spin-3/2 leakage subspace which tends to be occupied under sustained operation and has to be actively depopulated via so called Leakage Reduction Units.
We show, based on group-theoretic reasoning, that 2 ancillary spins are sufficient to perform such leakage reduction and present sequence accomplishing this task within 14 exchange gates, less than half than previously reported [2].
We further discuss the resilience with respect to noise as well as the possibility and implications of flagging leakage via such gadgets.

[1] R. W. Andrews et al., Nat. Nanotechnol. 14, 747–750 (2019)
[2] B. H. Fong and S. M. Wandzura, Quantum Inf. Comput. 11 1003-1018 (2011)