What are they doing about error correction? Not that it makes this any less impressive (everything starts somewhere ), are they simply ignoring the problem?
It's a bit too early for quantum computers to do fault-tolerant (error corrected) computation. This is because you need more than one physical qubit to make a logical (error corrected) qubit. You need 7 physical qubits to encode a logical qubit if you use the Steane code [0]. So with 50 qubits, they could theoretically make 7 error corrected qubits. [0]: https://en.wikipedia.org/wiki/Steane_code
But that's not right. At least two more qubits are needed for fault-tolerant error correction. So that means you could fit nine codewords into 50 qubits (since 9x5+2=47 But that's not right. There exist more efficient codes that put multiple encoded qubits into a single code block. [2] For example, three qubits can be encoded into eight, still with distance three. [3] Six of these could fit into 50 qubits (since 6x8+2=50), giving 18 encoded qubits.
But that's not right. The IBM systems are superconducting qubits, with very constrained interactions. Not every qubit can talk directly to every other qubit. So you'd probably want every code block to have its own extra qubits dedicated to error correction. If you need 8+2 qubits per code block, then you could fit five code blocks, for 15 encoded qubits, into 50.
Obviously this is really complicated.
[1] https://en.wikipedia.org/wiki/Stabilizer_code#Example_of_a_s...