How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits · HackerPapers discussions

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by upofadown

Tue, 31 Mar 2026 21:14:39 GMT

You can save time by first looking at the required noise performance of these schemes. From the abstract of the paper: >On superconducting architectures with 10−3 physical error rates... So good old 0.1% noise performance again. That seems to have come from the "20 million noisy qubits to break RSA" scheme[1] from back in 2019. That level of noise performance is still wildly out of reach and for all we know might be physically impossible. [1] https://arxiv.org/abs/1905.09749

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by Strilanc

Sat, 01 Nov 2025 20:02:25 GMT

> The precision in phase needed to perform an accurate QFT scales EXPONENTIALLY with the number of qubits you're trying to transform. This is false. The gates that appear in the textbook QFT circuit (such as the one shown on wikipedia [1]) do mention angles that are exponentially small in N (the number of qubits being operated upon). That may be what's confusing you. But it's well known that the tolerance on those rotations is high, meaning that simply skipping all the exponentially tiny rotations introduces negligible error [2][3]. Here's a simple model. Each time you get a rotation off by…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by ryao

Tue, 22 Apr 2025 17:06:09 GMT

> Is there some minimum number of qubits at which some minimum viable quantum-supreme task can theoretically be achieved? That is a very broad range of possibilities, so allow me to narrow it to cryptography. I am by no means an expert on this, but I spent the weekend reading about quantum motivations to change the cryptographic algorithms society uses and as at as I can tell, nobody knows what the hard lower bound is for breaking hardness assumptions in classical cryptography. The best guess is that it is many orders of magnitude higher than what current machines can do. We are so far from…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by wzeng

Sun, 19 Jan 2025 00:16:04 GMT

We don’t need exponentially more physical qubits because we have quantum error correction schemes that exponentially decrease the logical error rate with only a polynomial increase in the number of qubits. There are in fact many schemes for this (https://errorcorrectionzoo.org/) with the surface code mentioned in the blog being a leading approach. Details for how this could work for factoring are here: https://arxiv.org/abs/1905.09749 There will be engineering challenges to scale up these implementations but in principal you shouldn’t need exponential resources (unless there is something…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by qnleigh

Mon, 09 Dec 2024 20:55:19 GMT

You need to distinguish between "physical qubits" and "logical qubits." This paper creates a single "first-of-a-kind" logical qubit with about 100 physical qubits (using Surface Code quantum error correction). A paper from Google in 2019 estimates needing ~20 million physical qubits ("How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits" - https://arxiv.org/abs/1905.09749), though recent advances probably brought this number down a bit. That's because to run Shor's algorithm at a useful scale, you need a few thousand very high quality logical qubits. So despite this…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by amirhirsch

Fri, 13 Sep 2024 00:28:37 GMT

https://scottaaronson.blog/?p=8310 suggests perhaps the next decade for useful quantum computer. this suggests the scale for RSA2048: https://arxiv.org/pdf/1905.09749 The thing about this bet is you don't have to pay until 2048 whereas I have to pay as soon as it happens and accounting for savings rates the bet will cost about a dime a day.

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by archgoon

Tue, 19 Sep 2023 17:52:53 GMT

> If current quantum computers were scaled up to more qubits That depends on what you mean by "scaled up". There is a concept of "Quantum Volume" that exists, which basically means the depth of the longest qubit circuit you can pull off. https://en.wikipedia.org/wiki/Quantum_volume 'Simply' (it's never simple ;) ) adding qubits to a machine does not necessarily increase its Quantum Volume. Decreasing the noise typically will. However, there is a threshold at which point you can scale up mostly indefinitely. This is what the whole Quantum Error Correction is all about.…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by upofadown

Mon, 19 Jun 2023 16:29:12 GMT

Related: https://arxiv.org/abs/1905.09749 | How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Wed, 18 Jan 2023 13:27:50 GMT

I think publick key encryption is already broken in secret

What are the odds you think encryption is already broken behind closed doors? Do you think governments would even announce it first before spying? https://www.forbes.com/sites/arthurherman/2021/06/07/q-day-is-coming-sooner-than-we-think/ https://arxiv.org/abs/1905.09749

1 point; 1 discussion reply on HN. Paper and source history. A submission is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by reikonomusha

Tue, 03 Jan 2023 20:32:12 GMT

A 5-qubit code corrects against single qubit errors. You could say a factor of 5 is a lower bound. In more technical terms, this scheme fixes all weight-1 errors. More realistically [1], you'd have a factor of around 1,600 for a distance-27 code. [1] https://arxiv.org/pdf/1905.09749.pdf

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by bnjemian

Tue, 16 Nov 2021 21:03:55 GMT

Gidney and Ekerå have you covered: https://arxiv.org/abs/1905.09749 Short answer, this probably won't even register as a pitstop on the technical pathway.

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by Strilanc

Fri, 29 May 2020 19:51:03 GMT

In hardware this would be called a carry save adder [1]. One interesting fact about carry save adders is that the carry part of the register can be extended in order to avoid any carrying between words for very long periods of time. Instead of using 53 bits to represent 52 bits, use 60 bits, and now you can perform 256 sequential additions with no carrying between words before the carry part saturates and needs to be handled. Somewhat surprisingly, it's even possible to use this construction in the context of a quantum computation [2][3]. The reason it's surprising is because tacking on…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by nabla9

Fri, 10 Jan 2020 20:40:33 GMT

Google's new quantum supremacy device has 1,113 single-qubit gates and 430 two-qubit gates. Article "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits" https://arxiv.org/abs/1905.09749 shows how to significantly reduce the cost of factoring integers and computing discrete logarithms. Implementation of the efficient device mentioned in the article requires 2.7 billion Toffoli gates for 2048 bit input. It could factor one key in 8 hours. Microprocessors reached that high MOS transistor count less than 10 years ago. For example, 8-core Core i7 Haswell-E has 2.6 billion…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by nabla9

Thu, 24 Oct 2019 17:31:05 GMT

You are way off. Google's new quantum supremacy device has 1,113 single-qubit gates and 430 two-qubit gates. Consider recent improvement in RSA factorization "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits" https://arxiv.org/abs/1905.09749 Actual implementation of the device mentioned above requires 2.7 billion Toffoli gates gates for 2048 bit input and it could factor just one key in 8 hours. Microprocessors reached that high MOS transistor count less than 10 years ago. For example, 8-core Core i7 Haswell-E has 2.6 billion transistors (2014). If quantum…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by grubles

Wed, 23 Oct 2019 19:59:34 GMT

"How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits" https://arxiv.org/abs/1905.09749

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Thu, 17 Oct 2019 18:59:28 GMT

How to factor 2048 bit RSA integers in 8 hours using 20M noisy qubits

3 points; 1 discussion reply on HN. Paper and source history. A submission is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Wed, 16 Oct 2019 02:59:52 GMT

How to factor 2048 bit RSA integers in 8 hours using 20M noisy qubits

3 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Tue, 15 Oct 2019 11:57:45 GMT

How to factor 2048 bit RSA integers in 8 hours using 20M noisy qubits

3 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Sat, 08 Jun 2019 16:29:25 GMT

How to factor 2048 bit RSA integers in 8 hours using 20M noisy qubits

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Mon, 03 Jun 2019 02:51:35 GMT

How to factor 2048 bit RSA integers in 8 hours using 20M noisy qubits

6 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — mentioned by kristianp

Fri, 24 May 2019 05:35:21 GMT

https://arxiv.org/abs/1905.09749

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits — HN submission

Fri, 24 May 2019 02:38:45 GMT

How to factor 2048 bit RSA integers in 8 hours using 20M noisy qubits

174 points; 67 discussion replies on HN. Paper and source history. A submission is not an endorsement.