How to factor 2048 bit RSA integers with less than a million noisy qubits

Craig Gidney estimates that a 2048 bit RSA integer could be factored in less than a week by a quantum computer with less than a million noisy qubits, down from the roughly 20 million qubits his 2019 co-authored estimate required. He attributes the qubit reduction mainly to approximate residue arithmetic from Chevignard, Fouque and Schrottenloher (2024), to yoked surface codes, and to magic state cultivation. The longer runtime comes mainly from more Toffoli gates and fewer magic state factories, though the paper reports a Toffoli count over 100 times lower than Chevignard, Fouque and Schrottenloher's 2024 method. The estimates assume a square grid of qubits, a 0.1% gate error rate, and a 1 microsecond surface code cycle time.