I want to point out that the experiment was at Harvard in the Lukin group. There is a proposal for constant-rate encodings using large quantum low-density parity check codes via atom rearrangement which could in principle achieve such high encoding rate. That said, it's certainly not mainstream yet. https://arxiv.org/abs/2308.08648
Yes, good point (apologies to the Lukin group). That's an interesting proposal, but it seems from a cursory read that you would need still need very many physical qubits to approach that asymptotic rate, and also you would be forced to take a very large slow down due to serializing all of your logical operations through a smaller set of conventionally encoded logical qubits. That said, I'm not current on SOA LDPC QEC proposals, so I'll moderate my claim a bit to "the first actually useful logical qubits will almost certainly have an encoding rate lower than 1/5".
