  Recent work has demonstrated a new route to discrete time crystal physics in
quantum spin chains by periodically driving nearest-neighbor exchange
interactions in gate-defined quantum dot arrays [arXiv:2006.10913]. Here, we
present a detailed analysis of exchange-driven Floquet physics in small arrays
of GaAs quantum dots, including phase diagrams and additional diagnostics. We
also show that emergent time-crystalline behavior can benefit the protection
and manipulation of multi-spin states. For typical levels of nuclear spin noise
in GaAs, the combination of driving and interactions protects spin-singlet
states beyond what is possible in the absence of exchange interactions. We
further show how to construct a time-crystal-inspired CZ gate between
singlet-triplet qubits with high fidelity. These results show that periodically
driving exchange couplings can enhance the performance of quantum dot spin
systems for quantum information applications.
