IIRC none of those uses of shor's algorithm were real (well maybe the 2019 one was, but that failed).
There's a threshold you need to reach for quantum error correction to work and we are approaching it pretty steadily on a log scale.
There's a threshold you need to reach for quantum error correction to work and we are approaching it pretty steadily on a log scale.
> Of course this should not be considered a serious demonstration of Shor’s algorithm. It does, however, illustrate the danger in “compiled” demonstrations of Shor’s algorithm. To varying degrees, all previous factorization experiments have benefited from this artifice. While there is no objection to having a classical compiler help design a quantum circuit (indeed, probably all quantum computers will function in this way), it is not legitimate for a compiler to know the answer to the problem being solved. To even call such a procedure compilation is an abuse of language.
I have never seen a result like that. Do you have a citation?
A recent result considers a generic error model and a subclass for particular kinds of prime numbers [1]. The important result is $epsilon > cn^{−1/3}$ where epsilon represents qubit error rate and n number of bits in the factorised number. As $n = 2^N$ where N is a number of qubits, the result:
error_rate < const/2^{N/3}
Therefore, the error rate must decrease exponentially with the number of logical qubits with which the computation is made.