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Abstract Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit \(\sqrt{\mathrm{SWAP}}\) gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times.
We demonstrate that a state-of-the-art multigrid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal retraining on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as communication avoidance are straightforward to implement in this framework.
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