IonQ published a very good and interesting THEORETICAL RESEARCH paper regarding Shor's algorithm. Congrats to Chris Ballance and his #quantumcomputing team. Before people start claiming that Q-Day is tomorrow, I want to point out a few things. The company doesn't have anything close to the 13,000 qubits to factor 1,071,514,531 in less than a day. Moreover, while this is a big jump for what quantum computers can do today with factoring, that number is trivial to factor classically on a desktop machine: Number: 1,071,514,531 Factors: {32719: 1, 32749: 1} Time elapsed: 0.000650 seconds The Python code and a link to the IonQ paper are in the comments. So, this is solid quantum architectural progress with reasonable performance estimates, but RSA and ECCC are safe for a bit longer. Marin Ivezic
I cover some of the classical factoring methods in my book Dancing with Qubits, Second Edition, in section 10.2. (4.8) ⭐ ⭐⭐⭐⭐ https://amzn.to/4u07Z1l
The number of logical qubits required to run Shor's algorithm on an n-bit number scales linearly in n. If we assume that the physical qubits scale in roughly the same way, then that would suggest that factoring a 2048-bit number (with 68 times as many bits) would require roughly 900,000 physical qubits - almost exactly the same physical qubit count that Google estimated last year.
https://www.hstoday.us/subject-matter-areas/cybersecurity/no-chinese-did-not-crack-rsa-with-quantum-yet/ "More recently, in 2025, the same group announced factoring a 90-bit RSA number using an improved hybrid approach. That 90-bit demo is the largest quantum-assisted factorization to date – still far smaller than any RSA keys used in practice, but an impressive academic milestone. " Annealing with hybrid method is new oil.
Laurent Prost I guess I am too much of an applied researcher and fail to understand the euphoria/alarming of purely theoretical statements. Theoretical papers are needed but the practical application is always problematic, simply because many theoretical prerequisites don't hold. We are far from practical evaluations, I am not convinced that euphoria based on theoretical results helps the field.
Somehow we see an inflation of papers being used to create an alarming/euphoric atmosphere regarding Shor and other features (streaming, QML .. ) and to promote developments in HW companies. Not really sure what to think about that.
Robert, thanks for the ping. You're right on every count. This paper won't break anything. But I'd encourage people to actually read this paper, and not because of Shor's. The factoring example is just briefly mentioned in the last pages of this 110-page doc. The real substance is in this being the best, so far, complete fault-tolerant blueprint from a QC vendor. Built entirely on qLDPC codes. And you are right to start debunking it. As always (so predictable!) when a serious paper drops, curious people start asking "what does this mean for CRQC?". And then the ethically challenged vendors fire up their newsletters: "new paper brings quantum threat closer, buy our solution now." I got two of those today. By Friday this will be in three sales decks with the word "imminent" somewhere on the first slide. RSA-2048 is not under threat from this paper. Neither is ECC-256. But it is a paper that pushes the field forward.
That number can be factored by hand by Fermat's method, since the factors are so close together. Someone skilled in mental arithmetic could do it in their head. 1071514531 = 32734² – 15² = (32734–15)×(32734+15)
Phew 😅 ! In seriousness, thx for the coverage dear Bob!
https://arxiv.org/abs/2604.19481