  We consider the effects of leakage on the ability to realize a discrete time
crystal (DTC) in a semiconductor quantum dot linear array being operated as a
chain of singlet-triplet (ST) qubits. This system realizes an Ising model with
an effective applied magnetic field, plus additional terms that can cause
leakage out of the computational subspace. We demonstrate that, in the absence
of these leakage terms, this model theoretically realizes a DTC phase over a
broad parameter regime for six and eight qubits, with a broader parameter range
for the eight-qubit case. We then reintroduce the leakage terms and find that
the DTC phase disappears entirely over the same parameter range if the system
is only subject to a uniform magnetic field, which does not suppress leakage.
However, we find that the DTC phase can be restored if the system is instead
subject to a magnetic field that alternates from qubit to qubit, which
suppresses leakage. We thus show that leakage is a serious problem for the
realization of a DTC phase in a chain of ST qubits, but is by no means
insurmountable. Our work suggests that experiments manifesting small-system
stable DTC should be feasible with currently existing quantum dot spin qubits.
