The result you cite: they don't even consider those early NMR "computers" to be quantum in any meaningful sense. They're avogadro computers.
you said the number 15 was never factored on a quantum computer - this is false.
You can run as many gates as you want - go ahead and run 4608 gates in qiskit right now - the measurements will be random but you can do it.
IDK where you got that equation for the number of gates but it's probably for the general case - doesn't take into account the fact that different gate sets can be used to reduce the total.
Also confused on the error correction part - the whole point of error correction is to make the coherence time independent of the number of 'gates' in your circuit - so yeah with error correction you get more gates but you also get an effectively infinite coherence time...
I guess it depends what you mean by "factored" and "quantum computer" -using the generally accepted definitions, the number 15 has never been factored on a quantum computer using the Shor algorithm.
Yes, I am talking about the general case where you don't leave out the gates for 2 and 7 being factors of 15. That's what most people mean by factoring. Stating the answer because you know it already isn't useful. LARPing by running the algo through the "right" gates also isn't useful.
And you failed to consider quantum annealing as an alternative to Shor.
Besides, the empirical data shows otherwise. It takes 12 qubits to factor 15. We're up to 53 now.
With quantum annealing, a 20 bit number has been factored with 97 qubits. Not on a real quantum computer yet, of course.
So I have no idea what you are talking about.
Erm, OK. I guess we agree that nobody has factored the number 15 on a quantum computer yet.
Maybe you should read the paper I helpfully linked you above.
I was referring to the quantum annealing example, because no 97 qubit quantum computer exists yet.
Did you read the nature article, or just the press releases?
Both methods requires 饾挭(log2(饾憗)) qubits in total, where N is the number to be factored. The novelty of our demonstration of quantum annealing for prime factorization is based on the reduction in quantum resources required to execute factoring and the experimental verification of the algorithmic accuracy using currently available hardware. As a proof-of-concept, we have demonstrated these methods by factoring integers using the D-Wave 2000Q quantum annealing hardware, but these methods may be used on any other quantum annealing system with a similar number of qubits, qubit degree of connectivity, and hardware parameter precision. Assuming that quantum annealing hardware systems will continue to grow both in the number of qubits and bits of precision capabilities, our methods offer a promising path toward factor much larger numbers in the future.
And there is this too: https://link.springer.com/article/10.1007%2Fs11433-018-9307-...
Are you just going to sit there and lob lame insults or do you have anything meaningful to contribute?
"RSA cryptography is based on the difficulty of factoring large integers, which is an NP-hard (and hence intractable) problem for a classical computer."
That is incorrect: there is no proof that factoring is NP-hard. Anyway, you can hardly expect me to take anything they say after this seriously.
I just... I can't.