[da-bacon]

This chip has 0 logical qubits, for any reasonable definition of logical qubit: it’s not good enough (yet) to offer substantial error suppression by using a quantum error correcting code. (Disclosure: work for Google’s quantum effort)

[vlovich123]

Since you probably know, has anyone managed to create a logical qbit yet?

[da-bacon]

Yes, for some definition of logical qubit.

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.