The “JVG algorithm” only wins on tiny numbers

Sorry to interrupt your regular programming about the AI apocalypse, etc., and return to the traditional beat of this blog’s very earliest years … but I’ve now gotten multiple messages asking me to comment on something called the “JVG (Jesse–Victor–Gharabaghi) algorithm” (yes, the authors named it after themselves). This is presented as a massive improvement over Shor’s factoring algorithm, which could (according to popular articles) allow RSA-2048 to be broken using only 5,000 physical qubits.

On inspection, the paper’s big new idea is that, in the key step of Shor’s algorithm where you compute x^r mod N in a superposition over all r’s, you instead precompute the x^r mod N’s on a classical computer and then load them all into the quantum state.

Alright kids, why does this not work? Shall we call on someone in the back of the class—like, any undergrad quantum computing class in the world? Yes class, that’s right! There are exponentially many r’s. Computing them all takes exponential time, and loading them into the quantum computer also takes exponential time. We’re out of the n²-time frying pan but into the 2ⁿ-time fire. This can only look like it wins on tiny numbers; on large numbers it’s hopeless.

If you want to see people explaining the same point more politely and at greater length, try this from Hacker News or this from Postquantum.com.

Even for those who know nothing about quantum algorithms, is there anything that could’ve raised suspicion here?

1. The paper didn’t appear on the arXiv, but someplace called “Preprints.org.” Come to think of it, I should add this to my famous Ten Signs a Claimed Mathematical Breakthrough is Wrong! It’s not that there isn’t tons of crap on the arXiv as well, but so far I’ve seen pretty much only crap on preprint repositories other than arXiv, ECCC, and IACR.
2. Judging from a Google search, the claim seems to have gotten endlessly amplified on clickbait link-farming news sites, but ignored by reputable science news outlets—yes, even the usual quantum hypesters weren’t touching this one!

Often, when something is this bad, the merciful answer is to let it die in obscurity. In this case, I feel like there was a sufficient level of intellectual hooliganism, just total lack of concern for what’s true, that those involved deserve to have this Shtetl-Optimized post as a tiny bit of egg on their faces forever.

This entry was posted on Saturday, March 7th, 2026 at 9:06 pm and is filed under Complexity, Quantum, Rage Against Doofosity, Speaking Truth to Parallelism. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.