This paper [1] claims that with their implementation they can get an AQFT (approximate QFT) with sufficient precision to factor RSA-2048 with < 0.01% error prob

This paper [1] claims that with their implementation they can get an AQFT (approximate QFT) with sufficient precision to factor RSA-2048 with < 0.01% error probability using 2083 qubits, 364,510 CNOT gates and 196,234 T gates, both of which can be error corrected. [1] https://www.nature.com/articles/s41534-020-0257-5 https://www.nature.com/articles/s41534-020-0257-5 Just because textbook QFT requires ever increasingly precise gates does not mean that this can't be worked around. If you want to do useful quantum computation you have to embrace error bounds, precision loss and probabilistic computing, which makes it quite difficult. But not impossible.