Let me break this down.<p>* In an error correction code, you encode a logical bit/qubit into a set of physical bits/qubits.<p>* Error correcting codes come in families, parameterized by integer distance d. Incrementing d, leads to a code with more physical bits/qubits, n, but also the ability to correct errors on a larger number of bits/qubits, j.<p>* If the error probability on each qubit is p, then on a code of size n, there will be on average n*p errors. It should be immediately clear that if p is small, then n*p<j and the code can correct errors that occur, but if p is large then n*p>j and there will be errors that the code can't correct.<p>* If the code corrects any physical errors that do occur, then there won't be a logical error (value of logical bit/qubit unchanged), otherwise there will be a logical error. In summary, given a p, you have to pick the right sized code from your family so that n*p<j, and you don't incur any logical errors.<p>* Another way of saying the same thing is that if p in your hardware becomes small enough, then as you increase your distance d, your logical error rate will go down.<p>These guys are claiming that their p is small enough that the distance 5 code has a smaller logical error rate then the distance 3 code, which is indeed a breakthrough (if correct). No one has done something like this before to my knowledge.<p># Criticism<p>* The results are limited to storage errors. All they are doing is initializing the logical qubit in some initial state and repeatedly doing error-correction on it, to simulate a qubit at rest while the computation is happening elsewhere on some hypothetical other logical qubits. They have not attempted to do any experiments with applying gates to the qubits. Those will likely yield a much larger error rate. In particular, they are only testing a single logical qubit here, but the interesting gates would be two-qubit gates between two logical qubits, which are necessary to do any non-trivial computation.<p>* The experiment is limited to 25 cycles of error-detection. This means that their experiment shows that their device could hypothetically implement a depth ~25 circuit. As you might realize, useful circuits have depth many orders of magnitude larger, so this continues to be toy device.<p>The above is what immediately springs to mind, but I am sure the actual experts will soon chime in. My subjective opinion is that the technical achievements of just running the experiment are very impressive. This is a long journey to useful QCs, but this is nice milestone along the way.