> We implemented the algorithm on IBM quantum processors using only 5 qubits
Last December, a team based out of Harvard demonstrated the ability to scale up to 48 logical qubits: https://arxiv.org/abs/2312.03982
It has been shown that, to factor an integer with n bits, Shor's algorithm requires ~2n logical qubits: https://arxiv.org/pdf/quant-ph/0205095.pdf
The core issue why Schor algorithm is hard is that it requires exponential supppression of error with number of qubits to produce meaningful results. Therefore we don’t actually see much results here as the error rates have not yet reached thresholds to do it with more qubits. The error correction would not be a panacea either because it would necessitate it’s repeated application to get necessary threshold to run Schor algorithm. This would require unreasonable amount of physical qubits.