Yeah there's a reason that the quantum computing field has moved away from attempting factorisations. Not that there's not still hype and misleading claims being punished, but the hardware has improved a ton since 2001 and ever closer to actual useful quantum computation (such as large size quantum chemistry calculations).
Are those useful computations in the room with us right now? No, but seriously, I feel like factorization is the one application that could justify those massive investments QC is receiving (even though it would probably make the world strictly worse...).
All those other applications, no matter how neat, I feel are quite niche. Like, "simulate pairs of electrons in the Ising model". Cool. Is that a multi-billion dollars industry though?
"Just as a thought experiment, what's the most gutless device that could
perform this "factorisation"? There's an isqrt() implementation that uses
three temporaries so you could possibly do the square root part on a ZX81, but
with 1k of RAM I don't think you can do the verification of the guess unless
you can maybe swap the values out to tape and load new code for the multiply
part. A VIC20 with 4k RAM should be able to do it... is there a programmable
calculator that does arbitrary-precision maths? A quick google just turns up
a lot of apps that do it but not much on physical devices.
>Similarly, we refer to an abacus as “an abacus” rather than a
digital computer, despite the fact that it relies on digital manipulation to effect its computations.
> In the Callas Normal Form, the factors are integers p = 2^{n-1}
and q = 2^{m+1}, where n ≤ m, and p and q are ideally prime, but don’t have to be.
The paper's formatting clearly went wrong here, as it should have read p = 2^n - 1 and q = 2^m + 1.
The "Proposed Quantum Factorisation Evaluation Criteria" are excellent, but for measuring progress, the required minimum factor size of 64 bits is too large. A good milestone would be a quantum circuit that can factor the product of any pair of 5-bit primes {17,19,23,29,31}.
I think 8 bit primes is probably a better minimum. 5 bits is still small enough that randomly choosing a 5 bit factor will succeed 40% of the time. This is especially problematic since Shor's algorithm only has a 50% success probability per round, so you need some extra bits to be able to distinguish a correctly working quantum computer from a random number generator.
I checked in with Scribble as he did the typesetting. He apologizes for the error but says working without opposable thumbs makes the work more challenging.
Somewhat related is the work done in "Falling with Style: Factoring up to 255 “with” a Quantum Computer" published in the proceedings of SIGBOVIK 2025 [1]. The author, Craig Gidney [2], successfully factored all odd composite numbers up to 255 using Shor's algorithm, even though the quantum circuits involved were such that any meaningful output would be overwhelmed by noise (and indeed, performance was maintained when the circuits were replaced by a random number generator).
> To my knowledge, no one has cheated at factoring in this way before. Given the shenanigans pulled by past factoring experiments, that’s remarkable.
[2] Who has previous experience in cheating at quantum factoring: see "Factoring the largest number ever with a quantum computer", posted April Fools' Day 2020 at https://algassert.com/post/2000
>...6502 microprocessor from 1975. Since this processor uses transistors, and transistors work by using quantum effects, a 6502 is as much a quantum device as is a D-Wave “quantum computer”.
I'm not sure that is true in the way it is intended. The NMOS transistors used in the 6502 were quite large and worked on the basis of electrostatic charges ... as opposed to bipolar transistors that are inherently quantum in operation.
Of course it is now understood that everything that does anything is at some level dependent on quantum effects. That would include the dog...
17 comments
[ 3.8 ms ] story [ 59.7 ms ] threadThe dog is funny but it just means, pick actually "random" numbers from a bigger range than the staged phony numbers quantum factorisation uses.
All those other applications, no matter how neat, I feel are quite niche. Like, "simulate pairs of electrons in the Ising model". Cool. Is that a multi-billion dollars industry though?
It starts here: https://www.metzdowd.com/pipermail/cryptography/2025-Februar...
This part is from farther down thread:
"Just as a thought experiment, what's the most gutless device that could perform this "factorisation"? There's an isqrt() implementation that uses three temporaries so you could possibly do the square root part on a ZX81, but with 1k of RAM I don't think you can do the verification of the guess unless you can maybe swap the values out to tape and load new code for the multiply part. A VIC20 with 4k RAM should be able to do it... is there a programmable calculator that does arbitrary-precision maths? A quick google just turns up a lot of apps that do it but not much on physical devices.
Peter."
Brilliant.
>Similarly, we refer to an abacus as “an abacus” rather than a digital computer, despite the fact that it relies on digital manipulation to effect its computations.
The paper's formatting clearly went wrong here, as it should have read p = 2^n - 1 and q = 2^m + 1.
The "Proposed Quantum Factorisation Evaluation Criteria" are excellent, but for measuring progress, the required minimum factor size of 64 bits is too large. A good milestone would be a quantum circuit that can factor the product of any pair of 5-bit primes {17,19,23,29,31}.
> To my knowledge, no one has cheated at factoring in this way before. Given the shenanigans pulled by past factoring experiments, that’s remarkable.
[1] https://sigbovik.org/2025/; standalone paper is also available in the code repository https://github.com/strilanc/falling-with-style
[2] Who has previous experience in cheating at quantum factoring: see "Factoring the largest number ever with a quantum computer", posted April Fools' Day 2020 at https://algassert.com/post/2000
I really hope he eventually gets the recognition he deserves, outside of just experts in the field.
I'm not sure that is true in the way it is intended. The NMOS transistors used in the 6502 were quite large and worked on the basis of electrostatic charges ... as opposed to bipolar transistors that are inherently quantum in operation.
Of course it is now understood that everything that does anything is at some level dependent on quantum effects. That would include the dog...
(Beware of typo pointed out by tromp here.)