Pretending to factor large numbers on a quantum computer · HackerPapers discussions

Pretending to factor large numbers on a quantum computer — mentioned by Strilanc

Thu, 08 Jan 2026 05:59:34 GMT

> By late 2024 the biggest numbers that had been factored by an actual digital quantum computer had 35 bits (citing https://arxiv.org/pdf/2410.14397v1 ) This is incorrect. The cited reference says "N <= 35". That N is the number being factored, not the number of bits in the number. Also, footnote a of that paper points out (correctly) that the circuits that were used likely needed knowledge of the factors to create (e.g. as explained in https://arxiv.org/abs/1301.7007 ). As far as I know, only N=15 has been factored on a quantum computer in a no-shenanigans way. It's conceivable that current…

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Pretending to factor large numbers on a quantum computer — mentioned by tromp

Tue, 28 May 2024 15:22:14 GMT

They were illegitimate instances of Shor according to [1]: > Of course this should not be considered a serious demonstration of Shor’s algorithm. It does, however, illustrate the danger in “compiled” demonstrations of Shor’s algorithm. To varying degrees, all previous factorization experiments have benefited from this artifice. While there is no objection to having a classical compiler help design a quantum circuit (indeed, probably all quantum computers will function in this way), it is not legitimate for a compiler to know the answer to the problem being solved. To even call such a…

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Pretending to factor large numbers on a quantum computer — mentioned by iamawacko

Tue, 02 Jan 2024 03:20:44 GMT

Factoring 15 with quantum computers happened nearly 22 years ago[1]. The current record for factoring, with just Shor's and no minimization, is 21. Like you said, a lot of the hyped ones aren't practical. It's not that hard to pretend to factor large numbers on a quantum computer [2]. There have been a few newer algorithms can work with larger numbers, but they have scaling issues and so aren't useful for cryptography. [1]https://research.ibm.com/blog/factor-15-shors-algorithm [2]https://arxiv.org/abs/1301.7007

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Pretending to factor large numbers on a quantum computer — mentioned by Strilanc

Thu, 20 May 2021 15:14:50 GMT

It depends how much circuit optimization you consider to be cheating. The hard part of Shor's algorithm is computing `pow(g, e, modulus=N)` where g is a uniformly random number, e is a uniformly superposed number, and N is the number you want to factor. But note that 15 is one less than a power of 2, so modular arithmetic mod 15 can use special circuits that are surprisingly efficient. Since it's easy to check if a number is one less than a power of 2, there's no obstacle to using this optimization on a "real" problem. On the other hand, most products of two primes aren't one less than a…

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Pretending to factor large numbers on a quantum computer — mentioned by acqq

Wed, 18 Sep 2019 21:37:35 GMT

For those who are interested in the papers about this topic: https://arxiv.org/abs/1301.7007 "Pretending to factor large numbers on a quantum computer (2013)" "Of course this should not be considered a serious demonstration of Shor’s algorithm. It does, however, illustrate the danger in “compiled” demonstrations of Shor’s algorithm. To varying degrees, all previous factorization experiments have benefited from this artifice. While there is no objection to having a classical compiler help design a quantum circuit (indeed, probably all quantum computers will function in this way), it is not…

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Pretending to factor large numbers on a quantum computer — mentioned by jessriedel

Mon, 18 Dec 2017 20:50:23 GMT

Two excellent questions. Regarding claims of factoring small numbers: First note that error correction becomes exponentially more important for longer computations. Second, see this https://arxiv.org/abs/1301.7007 Regarding building a tower of ever less noisy qubits: it turns out there is something called a threshold theorem which requires a certain minimal level of noise before concatenating error correction schemes makes things better rather than worse. https://en.m.wikipedia.org/wiki/Quantum_threshold_theorem Reaching this threshold for physical qubits in the laboratory is perhaps the…

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Pretending to factor large numbers on a quantum computer — mentioned by jessriedel

Sun, 07 Apr 2013 23:28:35 GMT

> For the record, this is also true for every quantum computer in existence. Yes, I'm well aware. The difference from D-wave is that the labs at IBM, UCSB, and Yale haven't claimed they've built a quantum computer (mostly). > What is clear though, is that quantum computers have already solved problems in fewer steps than classical computers. This is statement is false and probably not even interpretable in a sensible way. See, for instance, my esteemed colleagues on why some labs' claims to have factored small numbers like 15 are bogus: http://arxiv.org/abs/1301.7007 > And to be fair, it's…

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