Yes, I was certainly confused. When IBM announced they are building a 7x7 = 49 qubit machine, I naturally assumed they meant logical qubits, not physical ones. Using surface codes, they can probably get one logical bit. But what confuses me are past records where they used Shor's algorithm to factor small integers on a quantum computer. How is this possible if we haven't even built a single logical qubit yet? It's surely necessary to have ~2N logical qubits to factor an integer of N bits.
I have an idea that might help though: if logical qubits are so difficult to build and require thousands of times more physical qubits, and physical qubits are also difficult to build, perhaps we can simulate physical qubits with thousands of times more "ultra-physical" qubits.
Regarding claims of factoring small numbers: First note that error correction becomes exponentially more important for longer computations. Second, see this
Regarding building a tower of ever less noisy qubits: it turns out there is something called a threshold theorem which requires a certain minimal level of noise before concatenating error correction schemes makes things better rather than worse.
That first article you cite certainly puts the whole thing in perspective. I was tempted to put an article on Arxiv announcing a new architecture for billions of "super-physical" qubits, but you've convinced me that not only would the real experts see right through this, but that it might bring me down to the level of some of the qubit measuring contests currently on display from the likes of IBM, Google and Microsoft. Thanks for the genuinely interesting answers, especially to the not completely serious question!
I have an idea that might help though: if logical qubits are so difficult to build and require thousands of times more physical qubits, and physical qubits are also difficult to build, perhaps we can simulate physical qubits with thousands of times more "ultra-physical" qubits.