So how many gates are we talking to factor some "cryptographically useful" number? Is there some pathway that makes quantum computers useful this century?
Strilanc · 3h ago
> So how many gates are we talking to factor some "cryptographically useful" number?
Table 5 of [1] estimates 7 billion Toffoli gates to factor 2048 bit RSA integers.
> Is there some pathway that makes quantum computers useful this century?
The pathway to doing billions of gates is quantum error correction. [1] estimates distance 25 surface codes would be sufficient for those 7 billion gates (given the physical assumptions it lists). This amplifies the qubit count from 1400 logical qubits to a million physical noisy qubits.
Samuel Jacques had a pretty good talk at PQCrypto this year, and he speculates about timelines in it [2].
It's not just quantum error correction that is required, it's also hard to make devices small enough due to cooling, to allow thousands of qubits let alone billions.
lisper · 5h ago
> So how many gates are we talking to factor some "cryptographically useful" number?
That is a hard question to answer for two reasons. First, there is no bright line that delineates "cryptographically useful". And second, the exact design of a QC that could do such a calculation is not yet known. It's kind of like trying to estimate how many traditional gates would be needed to build a "semantically useful" neural network back in 1985.
But the answer is almost certainly in the millions.
[UPDATE] There is a third reason this is hard to predict: for quantum error correction, there is a tradeoff between the error rate in the raw qbit and the number of gates needed to build a reliable error-corrected virtual qbit. The lower the error rate in the raw qbit, the fewer gates are needed. And there is no way to know at this point what kind of raw error rates can be achieved.
> Is there some pathway that makes quantum computers useful this century?
This century has 75 years left in it, and that is an eternity in tech-time. 75 years ago the state of the art in classical computers was (I'll be generous here) the Univac [1]. Figuring out how much less powerful it was than a modern computer makes an interesting exercise, especially if you do it in terms of ops/watt. I haven't done the math, but it's many, many, many orders of magnitude. If the same progress can be achieved in quantum computing, then pre-quantum encryption is definitely toast by 2100. And it pretty much took only one breakthrough, the transistor, to achieve the improvement in classical computing that we enjoy today. We still don't have the equivalent of that for QC, but who knows when or if it will happen. Everything seems impossible until someone figures it out for the first time.
It's not an eternity because QC is a low-headroom tech which is already pushing its limits.
What made computing-at-scale possible wasn't the transistor, it was the precursor technologies that made transistor manufacturing possible - precise control of semiconductor doping, and precision optical lithography.
Without those the transistor would have remained a lab curiosity.
QC has no hint of any equivalent breakthrough tech waiting to kick start a revolution. There are plenty of maybe-perhaps technologies like Diamond Defects and Photonics, but packing density and connectivity are always going to be huge problems, in addition to noise and error rate issues.
Basically you need high densities to do anything truly useful, but error rates have to go down as packing densities go up - which is stretching optimism a little.
Silicon is a very forgiving technology in comparison. As long as your logic levels have a decent headroom over the noise floor, and you allow for switching transients (...the hard part) your circuit will be deterministic and you can keep packing more and more circuitry into smaller and smaller spaces. (Subject to lithography precision.)
Of course it's not that simple, but it is basically just extremely complex and sophisticated plumbing of electron flows.
Current takes on QC are the opposite. There's a lot more noise than signal, and adding more complexity makes the problem worse in non-linear ways.
lisper · 21m ago
I'm sympathetic to this argument, but nearly every technological breakthrough in history has been accompanied by plausible-sounding arguments as to why it should have been impossible. I myself left my career as an AI researcher about 20 years ago because I was convinced the field was moribund and there would be no major breakthroughs in my lifetime. That was about as well-informed a prediction as you could hope to find at the time and it was obviously very wrong. It is in the nature of breakthroughs that they are rare and unpredictable. Nothing you say is wrong. I would bet against QC is 5 years (and even then I would not stake my life savings) but not 75.
fhdkweig · 5h ago
>> Is there some pathway that makes quantum computers useful this century?
> This century has 75 years left in it, and that is an eternity in tech-time.
As a comparison, we went from first heavier than air flight to man walking on the moon in only 66 years.
manquer · 31m ago
> walking on the moon in only 66 years.
Yet it has been 53 years since we have been able to send a manned mission to the moon . No other program has or likely to come close in the next 13 years including the current US one. By 2038 the moon landings would be closer to Wright brothers than future us.
The curve of progress is only smooth and exponential when you squint hard .
It is a narrow few decades of exponential growth hardly can reasonably be expected to last for 100+ years .
It is for the same reason you cannot keep doubling grains on a chess board just because you did it 10-20 steps quickly.
Fusion power, quantum computing are all always two decades away for a reason despite the money being spent . AI has gone through 3-4 golden ages in living memory and yet too many keep believing this one would last.
Reality is when the conditions are right, I.e. all the ground work has been done for decades or centuries before there can be rapid innovation for a short(few decades at best) time
thechao · 4h ago
My great grandmother, who was born in 1891, asserted ca. 1990 that her favorite invention was large print novels. More importantly: the social right to read trashy novels. But, yeah, computers, planes, starships, nuclear power, etc etc.
sokoloff · 1h ago
Amara’s Law – “We tend to overestimate the effect of a technology in the short run and underestimate the effect in the long run.”
Related to your observation: A piece of the original Wright Flyer was landed on Mars just a bit over 117 years after the first flight.
saati · 22m ago
That's only true if you totally ignore hot air balloons, the actual first manned flight was in 1783.
lisper · 18m ago
The comment you're responding to specified heaver-than-air. (And it should have been even more constrained: the real milestone was heavier-than-air powered flight.)
eastbound · 3h ago
> to man walking on the moon in only 66 years
And that was before Epoch (1969, unix time started in 1970). We went from calculator to AI in 55 years, which is, actually, extremely long. It took exactly the time to miniaturize CPUs enough that you would hold as many gates in a GPU as neurones in a human’s brain. The moment we could give enough transistors to a single program, AI appeared. It’s like it’s just an emergent behavior.
galangalalgol · 18m ago
It just seems that way because people had been researching neural networks from before the time they had floating point units in processors. So there were all these ideas people were waiting tp try when we finally had the speed. Then it was a matter of trying them all to see which worked the best. But yes, there is the point that even a bad ai model can learn most anything if you give it enough parameters. So the emergent property isn't far off either.
jacquesm · 36m ago
> We went from calculator to AI in 55 years, which is, actually, extremely long.
I think it is insanely fast.
Think about it: that planet has been here for billions of years. Modern humanity has been here for 200,000 years, give or take. It took 199700 years and change to get to a working steam engine. 266 years later men were walking on the moon and another 55 years and we had a good facsimile of what an AI looks like in practice. That's insane progress. The next 75 years are going to be very interesting, assuming we don't fuck it all up, the chances of which are right now probably 50/50 or so.
ted_dunning · 2h ago
Good reminder on the time scale.
On the other hand, the Univac could do more useful work than current quantum computers.
nabla9 · 5h ago
For RSA 4096 10^7 qubits with 10^-4 error rate (order of magnitude).
You can do useful and valuable quantum chemistry calculations already with few 100s of qubits with that low error rates, while post-quantum algorithms are becoming more common everyday removing incentives to build crypto cracking quantum computers.
I think the quantum computing will advance fastest in directions that are not easy to use in cryptography.
HappyPanacea · 2h ago
Which valuable quantum chemistry calculations you can do with few 100s of qubits with that low error rates?
nabla9 · 14m ago
The general idea is that with N fault-tolerant qubits, you can find the ground-state energy of an electronic system with N spin orbitals. 100 spin orbitals is the practical upper limit of current computers, so when you get into several hundred qubits, you can start seeing gains.
In some special problems hybrid methods start giving gains in 100 qubits or below.
As a layman the pathway seems to exist behind multiple massive materials science breakthroughs
andrewflnr · 5h ago
How is it that we need to build logical qubits out of physical qubits for error correction purposes, but then still need to blow out our logic qubit numbers for error correction purposes, again? It seems like there's something missing from this explanation, at least.
adgjlsfhk1 · 1h ago
the blow-up is in physical qbits
gjrq · 3h ago
Latest numbers are about 1e6 qubits with 1e-4 error rate: https://arxiv.org/abs/2505.15917. Gates (in the sense the OP means) is harder to quantify in the error corrected context once you compile to the operations that are native to your code. Total compute time of about a week assuming a 1MHz "clock" (code cycle time, for the experts). In some ways this is the harder metric to meet than the qubit numbers.
Note that the magic of quantum error correction (exponential improvement in the error rate goes both ways): if you could get another 9 in qubit fidelity, you get a much larger improvement in qubit numbers. On the other hand, if you need to split your computation over several systems, things get much worse.
adgjlsfhk1 · 1m ago
given the correct state of gate noise progress, it seems likely that we might get an extra order of magnitude of error before we get the 3 orders of magnitude in gates.
tripplyons · 5h ago
Not sure about the gate count, but if you look at the number of logical qubits required, we are still very far away from factoring numbers that traditional computing has already factored like the 829-bit RSA-250 number.
Legend2440 · 5h ago
Realistically, you want millions to billions of qubits to compete with classical computers that already have trillions of transistors.
jameshart · 4h ago
Ah - this helped me understand the numbers in quantum computing a little more clearly. I had been under the impression (based on my naive interpretation of the naming) that the number of qubits in a quantum processor might be something analogous to the number of bits of register state in a regular CPU; that qubits should be thought of more as analogous to transistors or maybe even gates makes it a little clearer why you need so many more qubits to perform more complex operations.
adgjlsfhk1 · 59m ago
the difference is that you need millions of 1 qbits to factor rsa 4096, but you only need 10s of millions to factor rsa 32k. qbits and quantum time scale almost linearly with factor size, but super-polynomially for regular computers
AceJohnny2 · 7h ago
What does this mean about the size (and thus feasibility) of a circuit required to factor a cryptographically interesting number, say, to be generous, RSA1024?
Strilanc · 2h ago
Estimates of the cost of RSA1024 use explicit circuit constructions at the target size, rather than extrapolating from the 4 bit case. So they implicitly account for the discontinuity being pointed out in the post. So this post has no impact on those costs.
add-sub-mul-div · 7h ago
"(Quick aside: the amount of optimization that has gone into this factoring-21 circuit is probably unrepresentative of what would be possible when factoring big numbers. I think a more plausible amount of optimization would produce a circuit with 500x the cost of the factoring-15 circuit… but a 100x overhead is sufficient to make my point. Regardless, special thanks to Noah Shutty for running expensive computer searches to find the conditional-multiplication-by-4-mod-21 subroutine used by this circuit.)"
Davidzheng · 7h ago
Off topic, but are cryptographers convinced that on the new gigawatt data centers RSA1024 is infeasible to factor? I gather that the fastest known algorithms are still too slow to factor it in reasonable time. But is consensus that there will not be improvements to these algorithms in near future?
rwmj · 7h ago
Number Field Sieves are still the best method, and the techniques are three or more decades old with only incremental improvements. (Of course there might be an incredible breakthrough tomorrow.)
tiahura · 6h ago
best published method
consp · 5h ago
Are the bitcoins in the first wallets gone? No? I will assume it's still the best method without any irrefutable evidence.
tripplyons · 5h ago
Bitcoin uses ECDSA to sign transactions, not RSA.
In addition, selling information to a government on how to break either system would be more valuable than the amount of bitcoin you would able to sell before exchanges stop accepting deposits or the price crashes.
aleph_minus_one · 5h ago
> In addition, selling information to a government on how to break either system would be more valuable
Honest question because one can find such claims very often on forums like HN:
Does there really exist a "feasible" way how some "lone hacker" could sell such information to some government and become insanely rich?
I know that people who apparently have some deep knowledge about how exploit markets work claimed on HN that "if you have to ask how/where to solve your exploit (i.e. you have the respective contacts), you are very likely not able to".
This latter observation seems a lot more plausible to me than the claim often found on HN that some "lone individual" would be able to monetize on it if he found a way how to break ECDSA or RSA by selling it to some government.
dfedbeef · 3h ago
Yes. Start what's known as "a company".
close04 · 5h ago
If a government knows you have such information they’ll take it not buy it.
So your best bet would probably be to try to sell as many BTC as possible then give away the solution for free to your/a government.
echelon · 3m ago
> If a government knows you have such information they’ll take it not buy it.
They would probably kill you so you couldn't tell others.
If a government can break crypto, that's worth more than money. Especially if it can remain peerless and undetected.
cyberax · 3h ago
A method to efficiently factor large numbers will also break the ECDSA.
CamperBob2 · 2h ago
No, ECDSA relies on the hardness of the discrete logarithm problem. Nothing to do with factoring, at least not in the classical sense.
On a quantum computer, my understanding is that Shor's algorithm could potentially target both problems, though.
So a hypothetical classic algorithm that breaks the RSA is also highly likely to break the ECDSA.
capitainenemo · 5h ago
Well, this discussion is about prime number factorisation, and bitcoins use elliptic curve...
littlestymaar · 5h ago
True, we can never know what state actors know that we don't, and my cryptography professor at university taught us that NSA likely had 20 years of mathematical advance over the academic crypto community.
That being said, NFS is almost thirty years old so maybe the NSA doesn't have anything better still.
ginko · 6h ago
It recently occurred to me that now would be the best time ever for state actors to build out massive data centers without anyone noticing.
tripplyons · 5h ago
I could reasons for them to build datacenters for AI or collecting encrypted messages to decrypt later, but not for brute force attacks on encrypted messages.
tripplyons · 5h ago
I've seen pretty credible evidence that factoring large semiprime numbers is effectively a solved problem, even without considering quantum computing or gigawatt-scale computing. I'm not able to share specifics, but I would personally not trust RSA.
close04 · 5h ago
People who have seen this evidence don’t go around on the internet bragging they’ve seen this evidence.
EdNutting · 4h ago
I enjoyed the typo in "error corection" (sic).
NooneAtAll3 · 5h ago
> I think a more plausible amount of optimization would produce a circuit with 500x the cost of the factoring-15 circuit
I don't get this part
If author already produced "115x", how can optimizations make it worse?
tsimionescu · 4h ago
The point was that the amount of optimization work that went into making the circuit for factoring 21 only ~100x larger than the one for factoring 15 is not feasible for larger numbers. So, the general rule should be that you need ~500x more gates for a similar increase in the number to be factored, not just ~100x.
Strilanc · 2h ago
The more plausible amount of optimization is less optimization. Or, more accurately, the benefits of optimization at large sizes is expected to be less beneficial than it was for the N=21 circuit.
turtletontine · 4h ago
I think the idea is the minimal implementation will be unstable and unreliable. I don’t know the details, but there’s much work and thought on quantum error correcting qubits - where you hook up N qubits in a clever way to function as one very stable qubit. Terms such as “decoherence time” make appearances. You can imagine this quickly expands into an awful lot of qubits.
tromp · 4h ago
The 115x was obtained by doing a (less plausable) large amount of optimization...
avhon1 · 3h ago
The linked paper "Replication of Quantum Factorisation Records with an 8-bit Home Computer, an Abacus, and a Dog" is a good read!
Obligatory how? It's sort of funny but comes across as uninformed, over the top, and lacking substance.
api · 6h ago
It’s worth noting that the reason we are deploying PQ crypto is not that we are 100% convinced QC is coming soon. It may or may not depending on how development goes.
The goal of cryptography is to make something as close to theoretically unbreakable as possible. That means even theoretical vulnerabilities are taken seriously.
For ECC and RSA and related algorithms we have a theoretical and physically plausible pathway toward a practical machine that could break them. That means many cryptographers consider them theoretically broken even if such a machine does not exist and may not exist for a long time. The math works even if we can’t build it yet.
So it’s considered prudent to go ahead and upgrade now while no QC exists. That way if some major advance does arrive we are ready.
Nobody’s talking seriously about replacing SHA2, AES, ChaCha, etc because there is no physically plausible theoretically valid path to a machine that can break these in, say, less than many millions of years. AFAIK there is no proof that such a path does not exist but nobody has found one, hence they are considered unbroken.
Note that cryptography is not the only or even the most useful application of QC. Things like physical stimulation of quantum systems, protein folding, machine learning, etc. could be more useful. Like digital computers there’s probably a ton of uses we don’t know about because we need to tinker with the machine to figure them out.
leeoniya · 5h ago
> Things like physical stimulation of quantum systems, protein folding, machine learning, etc. could be more useful
is there still more to do in protein folding after AlphaFold?
The predictions don't tell us anything about why the answer is what it is. There is probably important (useful) fundamental scientific knowledge in being able to know that vs. just being able to predict the result.
api · 5h ago
There’s a difference between good AI predictions and theoretically perfect QC computations. The AI estimates while the QC will give you the answer, full stop. The latter could be relied upon more strongly. It could also generate infinite training data to make much better models.
QC might be directly applicable to AI training too. It may be possible to compute the optimal model over a data set in linear time. It could allow training that is faster and consumes a tiny fraction of the energy current brute force methods need.
I would expect this to become relevant later than crypto, though, because you need larger data sizes for things to get interesting.
tsimionescu · 4h ago
Is there any known quantum exponential speedup for gradient descent?
tialaramex · 5h ago
For the symmetric cryptography (so obviously AES and ChaCha, but also in effect the SHA-2 family) we can hand wave the quantum attacks as halving key length by enabling a sort of meet-in-the-middle attack (this attack is why it was 3DES not 2DES when they strengthened DES). There's a lot of hand waving involved. Your real Quantum Computer won't in fact be equivalent cost to the non-quantum computer, or as fast, or as small, the speed-ups aren't quite halving, and so on. But it's enough to say OK, what if AES-128 was as weak as a hypothetical AES-64, and that's fine because we have AES-256 anyway.
However, the main focus is on Key Exchange. Why? Well, Key Exchange is the clever bit where we don't say our secrets out loud. Using a KEX two parties Alice and Bob agree a secret but neither of them utters it. Break that and you can learn the secret, which was used to encrypt everything else - for any conversation, including conversations which you recorded any time in the past, such as today.
If future bad guys did have a Quantum Computer the Key Exchange lets them read existing conversations they've tapped but today can't read, whereas breaking say the signing algorithm wouldn't let them somehow go back in time and sign things now because that's not how time works. So that's why the focus on KEX. Once such a thing exists or clearly is soon to deliver it's important to solve a lot of other problems such as signing, but for KEX that's already too late.
taway789aaa6 · 7h ago
> Third, notice that the only remaining multiplication is a multiplication by 4. Because 15 is one less than a power of 2, multiplying by 2 modulo 15 can be implemented using a circular shift. A multiplication by 4 is just two multiplications by 2, so it can also be implemented by a circular shift. This is a very rare property for a modular multiplication to have, and here it reduces what should be an expensive operation into a pair of conditional swaps.
> Aside: multiplication by 16 mod 21 is the inverse of multiplying by 4 mod 21, and the circuits are reversible, so multiplying by 16 uses the same number of Toffolis as multiplying by 4.
I couldn't really find anything explaining the significance of this. The only info I found said that "4 mod 21 = 4" (but I don't know if it was AI slop or not).
Is "multiplying by 4 mod 21" something distinct to quantum computing?
shiandow · 7h ago
It is phrasing mathematicians sometimes use. In this sentence 'mod 4' does not indicate an operator but denotes what number system you are in.
For instance the following are equivalent:
2 = 6 mod 4
6 = 2 mod 4
This 'mod 4' can also appear in parentheses or in some other way, but it must appear at the end. Like I said it is not an operator rather it denotes that the entire preceding statement takes place in the appropriate quotient space.
So it is not (multiplying by (4 mod 21)) but ((multiplying by 4) mod 21)
Fractions are under any modulus are actually representable as whole numbers (provided they don’t share factors with the modulus).
For example under mod 21 a half can actually be represented by 11. Try it. Times any even number by 11 and you’ll see you halved it.
Take any number that’s a multiple of 4 and times it by 16 under mod 21. You now have that number divided by 4.
Etc.
Absolutely nothing to do with quantum computers.
oh_my_goodness · 7h ago
I mean 4 is equivalent to 4 mod 21. That part's not AI slop.
JohnKemeny · 7h ago
I think, in fact, for every prime number p at least 5, 4 mod p is (congruent to) 4.
oh_my_goodness · 7h ago
Even without the restriction to primes, that feels like a pretty good guess!
freehorse · 6h ago
Or for less than 5.
oh_my_goodness · 5h ago
lol good point.
alchemist1e9 · 8h ago
And these are the same quantum computers that will eventually break ecliptic curve cryptography? Now I’m very confused.
griffzhowl · 7h ago
If we can build a machine with enough coherent qubits, then it'll be able to break ECC.
As it turns out, that's a big if, but the bigness of the if is about hardware implementation. The theory behind it is just basic quantum mechanics
oh_my_goodness · 6h ago
Article: it takes 2405 entangling gates to factor the number 21.
wongarsu · 7h ago
In many applications you are concerned about data you encrypt today still being secure 20 years from now. Especially if your threat model includes a malicious actor holding on to data in hopes of decrypting it later.
From the article it sounds like we will still be safe for 20+ years. On the other hand 15 was just extraordinarily easy, progress after 21 will be much quicker. And we never know which breakthroughs might come in the next decades that speed up progress.
oh_my_goodness · 7h ago
"progress after 21 will be much quicker"
Can you provide a quick verification for that?
wongarsu · 7h ago
The article lists three reasons why 21 is so much harder than 15. Mostly that with 15 most of the required conditional multiplications are multiplications by 1 and the remaining multiplication can be done with cheap shifts because it's a multiplication by a power of 2 modulo 15 (which is one less than a power of two).
But 22 and 24 are in the same boat as 21 here. All three of them require computing only factors that are not one, all three are not one less than a factor of 2. You need slightly more multiplications (and thus more gates) as the numbers get larger, but that only grows linearly. Maybe the conditional multiplications required get slightly more expensive to implement, but I wouldn't expect a 100x cost blowup from that. Error correction is still an issue, potentially making a linear complexity increase quadratic, but qubit counts in quantum computers also increase at an exponential rate
oh_my_goodness · 6h ago
24 has 3 as a factor. 3 is one less than a power of 2.
freehorse · 5h ago
Well n=21 too but the solution for n=15 used that 15 is one less than a power of 2, not its divisors, because we are living in modulo n.
oh_my_goodness · 5h ago
Thanks. I don't understand quantum computing at all.
oh_my_goodness · 7h ago
23 and 29 are prime.
wongarsu · 6h ago
That's what I get for not enough coffee. Same holds for 22 and 24 though
bArray · 8h ago
I think the idea is that it doesn’t matter if it takes billions of gates to achieve, the point is that it can do it very fast. If we thought a table sized FPGA could do it, a state actor would most definitely build one.
lazide · 7h ago
theoretically
The practical problem is that ‘noise’ between gates seems to increase exponentially, so practically it may actually be impossible to construct anything with more than a handful of gates for the foreseeable (possibly indefinite?) future.
It’s essentially the crypto version of Fusion.
EthanHeilman · 7h ago
Quantum error correction addresses this problem and we now have tech demos showing that we can build scalable QCs with surface codes [0].
This, like all other purported advancements in quantum error correction, is a meme with zero practical impact.
lazide · 7h ago
Cool, so we should totally be able to factor 21 (or larger numbers)…. When?
EthanHeilman · 5h ago
You brought up gate noise, there has been quite a bit of progress on that problem.
> so we should totally be able to factor 21 (or larger numbers)…. When?
Just because we solve one problem doesn't imply all the problems in QC are also instantly solved. I guess it does if you assume noise is the only problem and once is it solved the engineering is trivial. That is not the case. Even assuming all foundational problems have been solved, figuring out how actually engineer and also mass produce large numbers of gates, will take a while.
As the article pointed out, going from 15 to 21 requires a 100x increase in gates.
As the article that you posted under says:
"Because of the large cost of quantum factoring numbers (that aren’t 15), factoring isn’t yet a good benchmark for tracking the progress of quantum computers. If you want to stay abreast of progress in quantum computing, you should be paying attention to the arrival quantum error correction (such as surface codes getting more reliable as their size is increased) and to architectures solving core scaling challenges (such as lost neutral atoms being continuously replaced)."
privatelypublic · 8h ago
Hasn't classical already severely crippled ECC because of some mathematical Assumptions that somebody came back in 2022 and Proved were wrong?
cwmma · 6h ago
I believe you are thinking of "Supersingular isogeny Diffie–Hellman key exchange" or SIKE which is a post quantum encryption algorithm that was spectacularly broken a couple years ago. The math involves elliptical curves but it's different from the elliptical curve cryptography used in your browser.
kevindamm · 8h ago
Which assumptions? ECDLP is still considered computationally hard, and ECC considered secure. There are invalid curve attacks and small subgroup attacks but that's a problem with key selection, not a fundamental problem with ECC.
Do you have a citation?
markusde · 8h ago
Could you link to any more information about this?
bitexploder · 7h ago
Not in general, no. It is still secure and used. There are of course attacks but those were not completely breaking
Mistletoe · 7h ago
This is the reality a million clickbait fearmongering articles won’t tell you. And pr machines for quantum computing companies won’t either.
z3phyr · 7h ago
"Is this what you can conjure Saruman?"
I have a strong belief that new mathematical tools and methods can be developed that can make it "easy" to break a lot of modern cryptography primitives without ever using a quantum computer.
santiagobasulto · 8h ago
The potential is there, we haven't made it yet. It's the same with AI, AGI and all that. Imagine if you'd read a response from GPT-2 back in 2019, you'd also be like "and these are the same models that will eventually give us AGI".
heyjamesknight · 8h ago
Not a great analogy, since there’s zero chance the kinds of model involved in GPT-2 will give us AGI.
ACCount37 · 7h ago
Zero? Aren't you a little bit overconfident on that?
Transformer LLMs already gave us the most general AI as of yet, by far - and they keep getting developed further, with a number of recent breakthroughs and milestones.
No comments yet
fmbb · 7h ago
Imagine if you'd read a response from GPT-5 in 2025, you'd also be like "and these are the same models that will eventually give us AGI".
raverbashing · 7h ago
My belief in achieving actual quantum computing is going down as noise in qbits goes up
Digital computers were much easier than that. Make it smaller, make a larger number of it, and you're set.
Quantum computers complexity goes up with ~ n^2 (or possibly ~ e^n) where n is the number of qbits
At the same time, things like d-wave might be the most 'quantum' we might get in the practical sense
analog31 · 6h ago
It turns out that error correction was easy on digital computers, and was essentially a solved problem early in their development. In fact, "noise immunity" is arguably the defining feature of a digital system. And error correction can happen at each gate, since there's no reason to propagate an indeterminate number.
The current best one- and two-gate errors are well below 0.01% and going down with every generation of chips. See: https://ianreppel.org/quantum.html
There are no theoretical reasons QEC can't exist. In fact it already does. Is it already good enough for universal fault tolerance? No. But then again no one said it would. We are slowly getting closer every year.
In his book, Dyakonov offers zero solid reasons other than "it's hard" and thus likely not possible. That's just an opinion.
analog31 · 2h ago
I took a QC course, and have done some reading, but am hardly an expert. But my impression has been: "This is analog computation." To reinforce the similarity, the error level of analog computers can be improved by running many of them in parallel.
tiahura · 6h ago
What? I thought quantum computing was going to be factoring billion digit prime numbers in 5 years?
sincerely · 4h ago
Sounds like a you problem
hulitu · 2h ago
> Why haven't quantum computers factored 21 yet?
They tried. But because they know exactly the question, they cannot give a precise answer. /s
m101 · 2h ago
Quantum mechanics is "true" insofar as it's useful for some purpose. Until then it's a theory and the jury is still out.
Randomness is something which I feel is a pretty weird phenomenon. I am definitely one of those 'God doesn't play with dice' types.
Randomness is also something that we call things when actually it's random from a subjective perspective. If we knew more about a system the randomness just falls away. E.g. if we knew the exact physical properties of a dice roll we could probably predict it better than random.
What if it's the case that quantum mechanics is similar. I.e. that what we think of as randomness isn't really randomness but only appears that way to the best of what we can observe. If this is the case, and if our algorithms rely on some sort of genuine randomness inherent in the universe, then doesn't that suggest there's a problem? Perhaps part of the errors we see in quantum mechanics arise from just something fundamental to the universe being different to our model.
I don't think this is that far fetched given the large holes that our current understanding of physics have as to predicting the universe. It just seems that in the realm of quantum mechanics this isn't the case, apparently because experiments have verified things. However, I think there really is something in the proof being in the pudding (provide a practical use case).
Most people don’t want to go down this hole. In the end, it means we might not have free will if there isn’t any randomness…
But if you are up for an existential crisis, just google “hidden variable theories”
AlienRobot · 2h ago
Turns out we only have "free as in free beer" will.
Sorry, I was destined to make this joke before I was even born.
dhampi · 1h ago
Yes, Schrodinger’s equation is entirely deterministic. There is no randomness inherent in quantum mechanics. The perceived randomness only arises when we have incomplete information. (It is another matter that quantum mechanics to some extent forbids us from having perfect information.)
I mean no disrespect, but I don’t think it’s a particularly useful activity to speculate on physics if you don’t know the basic equations.
Table 5 of [1] estimates 7 billion Toffoli gates to factor 2048 bit RSA integers.
> Is there some pathway that makes quantum computers useful this century?
The pathway to doing billions of gates is quantum error correction. [1] estimates distance 25 surface codes would be sufficient for those 7 billion gates (given the physical assumptions it lists). This amplifies the qubit count from 1400 logical qubits to a million physical noisy qubits.
Samuel Jacques had a pretty good talk at PQCrypto this year, and he speculates about timelines in it [2].
(I'm the author of this blog post and of [1].)
[1]: https://arxiv.org/pdf/2505.15917
[2]: https://www.youtube.com/watch?v=nJxENYdsB6c
That is a hard question to answer for two reasons. First, there is no bright line that delineates "cryptographically useful". And second, the exact design of a QC that could do such a calculation is not yet known. It's kind of like trying to estimate how many traditional gates would be needed to build a "semantically useful" neural network back in 1985.
But the answer is almost certainly in the millions.
[UPDATE] There is a third reason this is hard to predict: for quantum error correction, there is a tradeoff between the error rate in the raw qbit and the number of gates needed to build a reliable error-corrected virtual qbit. The lower the error rate in the raw qbit, the fewer gates are needed. And there is no way to know at this point what kind of raw error rates can be achieved.
> Is there some pathway that makes quantum computers useful this century?
This century has 75 years left in it, and that is an eternity in tech-time. 75 years ago the state of the art in classical computers was (I'll be generous here) the Univac [1]. Figuring out how much less powerful it was than a modern computer makes an interesting exercise, especially if you do it in terms of ops/watt. I haven't done the math, but it's many, many, many orders of magnitude. If the same progress can be achieved in quantum computing, then pre-quantum encryption is definitely toast by 2100. And it pretty much took only one breakthrough, the transistor, to achieve the improvement in classical computing that we enjoy today. We still don't have the equivalent of that for QC, but who knows when or if it will happen. Everything seems impossible until someone figures it out for the first time.
---
[1] https://en.wikipedia.org/wiki/UNIVAC_I#Technical_description
What made computing-at-scale possible wasn't the transistor, it was the precursor technologies that made transistor manufacturing possible - precise control of semiconductor doping, and precision optical lithography.
Without those the transistor would have remained a lab curiosity.
QC has no hint of any equivalent breakthrough tech waiting to kick start a revolution. There are plenty of maybe-perhaps technologies like Diamond Defects and Photonics, but packing density and connectivity are always going to be huge problems, in addition to noise and error rate issues.
Basically you need high densities to do anything truly useful, but error rates have to go down as packing densities go up - which is stretching optimism a little.
Silicon is a very forgiving technology in comparison. As long as your logic levels have a decent headroom over the noise floor, and you allow for switching transients (...the hard part) your circuit will be deterministic and you can keep packing more and more circuitry into smaller and smaller spaces. (Subject to lithography precision.)
Of course it's not that simple, but it is basically just extremely complex and sophisticated plumbing of electron flows.
Current takes on QC are the opposite. There's a lot more noise than signal, and adding more complexity makes the problem worse in non-linear ways.
> This century has 75 years left in it, and that is an eternity in tech-time.
As a comparison, we went from first heavier than air flight to man walking on the moon in only 66 years.
Yet it has been 53 years since we have been able to send a manned mission to the moon . No other program has or likely to come close in the next 13 years including the current US one. By 2038 the moon landings would be closer to Wright brothers than future us.
The curve of progress is only smooth and exponential when you squint hard .
It is a narrow few decades of exponential growth hardly can reasonably be expected to last for 100+ years .
It is for the same reason you cannot keep doubling grains on a chess board just because you did it 10-20 steps quickly.
Fusion power, quantum computing are all always two decades away for a reason despite the money being spent . AI has gone through 3-4 golden ages in living memory and yet too many keep believing this one would last.
Reality is when the conditions are right, I.e. all the ground work has been done for decades or centuries before there can be rapid innovation for a short(few decades at best) time
Related to your observation: A piece of the original Wright Flyer was landed on Mars just a bit over 117 years after the first flight.
And that was before Epoch (1969, unix time started in 1970). We went from calculator to AI in 55 years, which is, actually, extremely long. It took exactly the time to miniaturize CPUs enough that you would hold as many gates in a GPU as neurones in a human’s brain. The moment we could give enough transistors to a single program, AI appeared. It’s like it’s just an emergent behavior.
I think it is insanely fast.
Think about it: that planet has been here for billions of years. Modern humanity has been here for 200,000 years, give or take. It took 199700 years and change to get to a working steam engine. 266 years later men were walking on the moon and another 55 years and we had a good facsimile of what an AI looks like in practice. That's insane progress. The next 75 years are going to be very interesting, assuming we don't fuck it all up, the chances of which are right now probably 50/50 or so.
On the other hand, the Univac could do more useful work than current quantum computers.
You can do useful and valuable quantum chemistry calculations already with few 100s of qubits with that low error rates, while post-quantum algorithms are becoming more common everyday removing incentives to build crypto cracking quantum computers.
I think the quantum computing will advance fastest in directions that are not easy to use in cryptography.
In some special problems hybrid methods start giving gains in 100 qubits or below.
Gate count estimates for performing quantum chemistry on small quantum computers https://arxiv.org/pdf/1312.1695
A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits https://arxiv.org/pdf/2506.19337
As a layman the pathway seems to exist behind multiple massive materials science breakthroughs
Note that the magic of quantum error correction (exponential improvement in the error rate goes both ways): if you could get another 9 in qubit fidelity, you get a much larger improvement in qubit numbers. On the other hand, if you need to split your computation over several systems, things get much worse.
In addition, selling information to a government on how to break either system would be more valuable than the amount of bitcoin you would able to sell before exchanges stop accepting deposits or the price crashes.
Honest question because one can find such claims very often on forums like HN:
Does there really exist a "feasible" way how some "lone hacker" could sell such information to some government and become insanely rich?
I know that people who apparently have some deep knowledge about how exploit markets work claimed on HN that "if you have to ask how/where to solve your exploit (i.e. you have the respective contacts), you are very likely not able to".
This latter observation seems a lot more plausible to me than the claim often found on HN that some "lone individual" would be able to monetize on it if he found a way how to break ECDSA or RSA by selling it to some government.
So your best bet would probably be to try to sell as many BTC as possible then give away the solution for free to your/a government.
They would probably kill you so you couldn't tell others.
If a government can break crypto, that's worth more than money. Especially if it can remain peerless and undetected.
On a quantum computer, my understanding is that Shor's algorithm could potentially target both problems, though.
So a hypothetical classic algorithm that breaks the RSA is also highly likely to break the ECDSA.
That being said, NFS is almost thirty years old so maybe the NSA doesn't have anything better still.
I don't get this part
If author already produced "115x", how can optimizations make it worse?
https://eprint.iacr.org/2025/1237.pdf
The goal of cryptography is to make something as close to theoretically unbreakable as possible. That means even theoretical vulnerabilities are taken seriously.
For ECC and RSA and related algorithms we have a theoretical and physically plausible pathway toward a practical machine that could break them. That means many cryptographers consider them theoretically broken even if such a machine does not exist and may not exist for a long time. The math works even if we can’t build it yet.
So it’s considered prudent to go ahead and upgrade now while no QC exists. That way if some major advance does arrive we are ready.
Nobody’s talking seriously about replacing SHA2, AES, ChaCha, etc because there is no physically plausible theoretically valid path to a machine that can break these in, say, less than many millions of years. AFAIK there is no proof that such a path does not exist but nobody has found one, hence they are considered unbroken.
Note that cryptography is not the only or even the most useful application of QC. Things like physical stimulation of quantum systems, protein folding, machine learning, etc. could be more useful. Like digital computers there’s probably a ton of uses we don’t know about because we need to tinker with the machine to figure them out.
is there still more to do in protein folding after AlphaFold?
https://www.isomorphiclabs.com/articles/alphafold-3-predicts...
QC might be directly applicable to AI training too. It may be possible to compute the optimal model over a data set in linear time. It could allow training that is faster and consumes a tiny fraction of the energy current brute force methods need.
I would expect this to become relevant later than crypto, though, because you need larger data sizes for things to get interesting.
However, the main focus is on Key Exchange. Why? Well, Key Exchange is the clever bit where we don't say our secrets out loud. Using a KEX two parties Alice and Bob agree a secret but neither of them utters it. Break that and you can learn the secret, which was used to encrypt everything else - for any conversation, including conversations which you recorded any time in the past, such as today.
If future bad guys did have a Quantum Computer the Key Exchange lets them read existing conversations they've tapped but today can't read, whereas breaking say the signing algorithm wouldn't let them somehow go back in time and sign things now because that's not how time works. So that's why the focus on KEX. Once such a thing exists or clearly is soon to deliver it's important to solve a lot of other problems such as signing, but for KEX that's already too late.
> Aside: multiplication by 16 mod 21 is the inverse of multiplying by 4 mod 21, and the circuits are reversible, so multiplying by 16 uses the same number of Toffolis as multiplying by 4.
I couldn't really find anything explaining the significance of this. The only info I found said that "4 mod 21 = 4" (but I don't know if it was AI slop or not).
Is "multiplying by 4 mod 21" something distinct to quantum computing?
For instance the following are equivalent:
2 = 6 mod 4
6 = 2 mod 4
This 'mod 4' can also appear in parentheses or in some other way, but it must appear at the end. Like I said it is not an operator rather it denotes that the entire preceding statement takes place in the appropriate quotient space.
So it is not (multiplying by (4 mod 21)) but ((multiplying by 4) mod 21)
For example under mod 21 a half can actually be represented by 11. Try it. Times any even number by 11 and you’ll see you halved it.
Take any number that’s a multiple of 4 and times it by 16 under mod 21. You now have that number divided by 4.
Etc.
Absolutely nothing to do with quantum computers.
As it turns out, that's a big if, but the bigness of the if is about hardware implementation. The theory behind it is just basic quantum mechanics
From the article it sounds like we will still be safe for 20+ years. On the other hand 15 was just extraordinarily easy, progress after 21 will be much quicker. And we never know which breakthroughs might come in the next decades that speed up progress.
Can you provide a quick verification for that?
But 22 and 24 are in the same boat as 21 here. All three of them require computing only factors that are not one, all three are not one less than a factor of 2. You need slightly more multiplications (and thus more gates) as the numbers get larger, but that only grows linearly. Maybe the conditional multiplications required get slightly more expensive to implement, but I wouldn't expect a 100x cost blowup from that. Error correction is still an issue, potentially making a linear complexity increase quadratic, but qubit counts in quantum computers also increase at an exponential rate
The practical problem is that ‘noise’ between gates seems to increase exponentially, so practically it may actually be impossible to construct anything with more than a handful of gates for the foreseeable (possibly indefinite?) future.
It’s essentially the crypto version of Fusion.
[0] https://scottaaronson.blog/?p=8525
> so we should totally be able to factor 21 (or larger numbers)…. When?
Just because we solve one problem doesn't imply all the problems in QC are also instantly solved. I guess it does if you assume noise is the only problem and once is it solved the engineering is trivial. That is not the case. Even assuming all foundational problems have been solved, figuring out how actually engineer and also mass produce large numbers of gates, will take a while.
As the article pointed out, going from 15 to 21 requires a 100x increase in gates.
As the article that you posted under says:
"Because of the large cost of quantum factoring numbers (that aren’t 15), factoring isn’t yet a good benchmark for tracking the progress of quantum computers. If you want to stay abreast of progress in quantum computing, you should be paying attention to the arrival quantum error correction (such as surface codes getting more reliable as their size is increased) and to architectures solving core scaling challenges (such as lost neutral atoms being continuously replaced)."
Do you have a citation?
I have a strong belief that new mathematical tools and methods can be developed that can make it "easy" to break a lot of modern cryptography primitives without ever using a quantum computer.
Transformer LLMs already gave us the most general AI as of yet, by far - and they keep getting developed further, with a number of recent breakthroughs and milestones.
No comments yet
Digital computers were much easier than that. Make it smaller, make a larger number of it, and you're set.
Quantum computers complexity goes up with ~ n^2 (or possibly ~ e^n) where n is the number of qbits
At the same time, things like d-wave might be the most 'quantum' we might get in the practical sense
There are no theoretical reasons QEC can't exist. In fact it already does. Is it already good enough for universal fault tolerance? No. But then again no one said it would. We are slowly getting closer every year.
In his book, Dyakonov offers zero solid reasons other than "it's hard" and thus likely not possible. That's just an opinion.
They tried. But because they know exactly the question, they cannot give a precise answer. /s
Randomness is something which I feel is a pretty weird phenomenon. I am definitely one of those 'God doesn't play with dice' types.
Randomness is also something that we call things when actually it's random from a subjective perspective. If we knew more about a system the randomness just falls away. E.g. if we knew the exact physical properties of a dice roll we could probably predict it better than random.
What if it's the case that quantum mechanics is similar. I.e. that what we think of as randomness isn't really randomness but only appears that way to the best of what we can observe. If this is the case, and if our algorithms rely on some sort of genuine randomness inherent in the universe, then doesn't that suggest there's a problem? Perhaps part of the errors we see in quantum mechanics arise from just something fundamental to the universe being different to our model.
I don't think this is that far fetched given the large holes that our current understanding of physics have as to predicting the universe. It just seems that in the realm of quantum mechanics this isn't the case, apparently because experiments have verified things. However, I think there really is something in the proof being in the pudding (provide a practical use case).
But if you are up for an existential crisis, just google “hidden variable theories”
Sorry, I was destined to make this joke before I was even born.
I mean no disrespect, but I don’t think it’s a particularly useful activity to speculate on physics if you don’t know the basic equations.