Peter Gutmann and Stephan Neuhaus have a new paper—I think it’s new, even though it has a March 2025 date—that makes the argument that we shouldn’t trust any of the quantum factorization benchmarks, because everyone has been cooking the books:
Similarly, quantum factorisation is performed using sleight-of-hand numbers that have been selected to make them very easy to factorise using a physics experiment and, by extension, a VIC-20, an abacus, and a dog. A standard technique is to ensure that the factors differ by only a few bits that can then be found using a simple search-based approach that has nothing to do with factorisation…. Note that such a value would never be encountered in the real world since the RSA key generation process typically requires that |p-q| > 100 or more bits [9]. As one analysis puts it, “Instead of waiting for the hardware to improve by yet further orders of magnitude, researchers began inventing better and better tricks for factoring numbers by exploiting their hidden structure” [10].
A second technique used in quantum factorisation is to use preprocessing on a computer to transform the value being factorised into an entirely different form or even a different problem to solve which is then amenable to being solved via a physics experiment…
Lots more in the paper, which is titled “Replication of Quantum Factorisation Records with an 8-bit Home Computer, an Abacus, and a Dog.” He points out the largest number that has been factored legitimately by a quantum computer is 35.
I hadn’t known these details, but I’m not surprised. I have long said that the engineering problems between now and a useful, working quantum computer are hard. And by “hard,” we don’t know if it’s “land a person on the surface of the moon” hard, or “land a person on the surface of the sun” hard. They’re both hard, but very different. And we’re going to hit those engineering problems one by one, as we continue to develop the technology. While I don’t think quantum computing is “surface of the sun” hard, I don’t expect them to be factoring RSA moduli anytime soon. And—even there—I expect lots of engineering challenges in making Shor’s Algorithm work on an actual quantum computer with large numbers.
