IBM releases first-ever 1k-qubit quantum chip
nature.com
nature.com
> Researchers have generally said that state-of-the-art error-correction techniques will require more than 1,000 physical qubits for each logical qubit. A machine that can do useful computations would then need to have millions of physical qubits.
> But in recent months, physicists have grown excited about an alternative error-correction scheme called quantum low-density parity check (qLDPC). It promises to cut that number by a factor of 10 or more, according to a preprint by IBM researchers
One of the first example is the experiment of Egan et al where they demonstrated a fault-tolerant QEC measurement using 13 physical qubits. https://arxiv.org/abs/2009.11482 They show improvements in the logical performance on the codes, but it is still a pretty small improvement (factor of 2).
Another example is the experiment we performed at Google https://arxiv.org/abs/2207.06431 where we used superconducting qubits. In that experiment we showed that we were able to go from a small code to a slightly larger code and that the error got "slightly better" as you scaled things up.
Other groups have also demo-ed small scale logical qubits. Notable ones include those done by Quantinuum (trapped ion qubits) and ETH Zurich (superconducting qubits). But all of these show very small improvements in error rates. To truly build "logical" qubits one would hope to get suppression of errors by factors of like 100-1000, and no one is really close to that right now.