[drkevorkian]

Don't get me wrong, their (QuEra's) demonstration is incredibly impressive, but it seems you've been misled by inconsistent nomenclature around the phrase "logical qubit". They've demonstrated a 5/1 encoding scheme, yes, but that scheme is not anywhere close to being sufficiently redundant to allow for deep quantum circuits. When people talk about needing 1000 physical qubits, they mean to make a logical qubit with sufficiently low error rate to run interesting algorithms. In the QuEra device, when they say they "made 48 logical qubits out of 240 physical qubits", they simply meant that they used an encoding, and made no claim about the error rate on those qubits being low enough. There is no hope (that I know of) for a 5-1 encoding scheme to make error rates low enough. The QuEra device would just as well need many more physical qubits per logical qubit.

[s1dev]

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

[drkevorkian]

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".

[rubberband]

"Peanut Gallery" here... These types of conversations are the reason I'm still addicted to HN.

Thank you both. And /hattip