Quantum fault-tolerance milestones dropping like atoms
Update: I’d been wavering—should I vote for the terrifying lunatic, ranting about trans criminal illegal aliens cooking cat meat, or for the nice woman constantly making faces as though the lunatic was completely cracking her up? But when the woman explicitly came out in favor of AI and quantum computing research … that really sealed the deal for me.
Between roughly 2001 and 2018, I’ve happy to have done some nice things in quantum computing theory, from the quantum lower bound for the collision problem to the invention of shadow tomography. I hope that’s not the end of it. QC research brought me about as much pleasure as anything in life did. So I hope my tired brain can be revved up a few more times, between now and whenever advances in AI or my failing health or the collapse of civilization makes the issue moot. If not, though, there are still many other quantum activities to fill my days: teaching (to which I’ve returned after two years), advising my students and postdocs, popular writing and podcasts and consulting, and of course, learning about the latest advances in quantum computing so I can share them with you, my loyal readers.
On that note, what a time it is in QC! Basically, one experimental milestone after another that people talked about since the 90s is finally being achieved, to the point where it’s become hard to keep up with it all. Briefly though:
A couple weeks ago, the Google group announced an experiment that achieved net gain from the use of Kitaev’s surface code, using 101 physical qubits to encode 1 logical qubit. The headline result here is that, in line with theory, they see the performance improve as they pass to larger codes with more physical qubits and higher distance. Their best demonstrated code has a distance of 7, which is enough to get “beyond break-even” (their logical qubit lasts more than twice as long as the underlying physical qubits), and is also enough that any future improvements to the hardware will get amplified a lot. With superconducting qubits, one is (alas) still limited by how many one can cram onto a single chip. On paper, though, they say that scaling the same setup to a distance-27 code with ~1500 physical qubits would get them down to an error rate of 10-6, good enough to be a building block in a future fault-tolerant QC. They also report correlated bursts of errors that come about once per hour, from a still-unknown source that appears not to be cosmic rays. I hope it’s not Gil Kalai in the next room.
Separately, just this morning, Microsoft and Quantinuum announced that they entangled 12 logical qubits on a 56-physical-qubit trapped-ion processor, building on earlier work that I blogged about in April. They did this by applying a depth-3 logical circuit with 12 logical CNOT gates, to prepare a cat state. They report an 0.2% error rate when they do this, which is 11x better than they would’ve gotten without using error-correction. (Craig Gidney, in the comments, says that these results still involve postselection.)
The Microsoft/Quantinuum group also did what they called a “chemistry simulation” involving 13 physical qubits. The latter involved “only” 2 logical qubits and 4 logical gates, but 3 of those gates were non-Clifford, which are the hard kind when one is doing error-correction using a transversal code. (CNOT, by contrast, is a Clifford gate.)
Apart from the fact that Google is using superconducting qubits while Microsoft/Quantinuum are using trapped ions, the two results are incomparable in terms of what they demonstrate. Google is just scaling up a single logical qubit, but showing (crucially) that their error rate decreases with increasing size and distance. Microsoft and Quantinuum are sticking with “small” logical qubits with insufficient distance, but they’re showing that they can apply logical circuits that entangle up to 12 of these qubits.
Microsoft also announced today a new collaboration with the startup company Atom Computing, headquartered near Quantinuum in Colorado, which is trying to build neutral-atom QCs (like QuEra in Boston). Over the past few years, Microsoft’s quantum group has decisively switched from a strategy of “topological qubits or bust” to a strategy of “anything that works,” although they assure me that they also remain committed to the topological approach.
Anyway, happy to hear in the comments from anyone who knows more details, or wants to correct me on any particular, or has questions which I or others can try our best to answer.
Let me end by sticking my neck out. If hardware progress continues at the rate we’ve seen for the past year or two, then I find it hard to understand why we won’t have useful fault-tolerant QCs within the next decade. (And now to retreat my neck a bit: the “if” clause in that sentence is important and non-removable!)
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Comment #1 September 10th, 2024 at 1:19 pm
Thanks for the nice post Scott. If you’ll permit me to indulge, I’d like to compare this to the predictions from the 2020 forecasting paper by Jamie Sevilla and me: https://arxiv.org/abs/2009.05045
I understand the Google results to be that they have ~10^-3 physical two-qubit error rates and they they *would* have ~10^-6 logical error rates *if* they had ~1500 of physical qubits, but they actually have 101 in the present device.
For forecasting purposes, Jamie and I defined a figure of merit, the “generalized logical qubit” (GLQ) count. See Eq. (1) and Fig. 1. It essentially equals the surface-code logical qubit count in the limit of low errors and many qubits (assuming we demand 10^-18 logical error rate), but is smoothly defined with fractional values when error rates are larger and/or physical qubit counts are smaller. Our naive (log linear regression) forecast from data at the time was that 1 GLQ would be achieved 2026-2033 and 4,100 GLQs (the rough number necessary to be cryptographically dangerous) would be achieved in 2029-2060 (both 90% confidence intervals — not Bayesian credences!). Our forecasts for 2024 were 0.02-0.3 GLQs.
I’m pleased to see that the above Google numbers correspond to a GLQ count of about 0.03, which is consistent with our model (though this is perhaps not impressive since it’s only been 4 years and our confidence intervals were wide). At this rate, we predict only about 3 GLQ in a decade’s time (2034), where, as mentioned, this would mean logical qubits with a 10^-18 error rate.
If you relax the logical error rate you demand to 10^-10 (the number discussed in Google’s paper and corresponding to smaller computations), I think you’re still only looking at like a dozen or two logical qubits by 2034, which is still classically simulable. So I think 1 decade still seems too soon to have something useful.
What sort of thresholds (for logical qubit count and logical error rate) are you thinking when you make your tentative one-decade prediction for something useful?
Comment #2 September 10th, 2024 at 2:00 pm
[…] and other NISQ experiments that I mentioned at the end of this post. There is also a new cautiously optimistic post over SO about these […]
Comment #3 September 10th, 2024 at 2:35 pm
Hello, I’m interested in the latest status of Nitrogen Vacancy Centers, since they could work closer to room temperature. Do you see any promising progress in these or other types of closer to room temperature quantum computers lately, so types other than trapped ion and superconducting QC? Thanks!
Comment #4 September 10th, 2024 at 2:46 pm
[…] Aaronson has a nice post discussing recent experimental progress in quantum computing from Google, Microsoft, and […]
Comment #5 September 10th, 2024 at 3:00 pm
The prediction that multiple logical qubit technologies would be blatantly better than their physical qubits within five years is very much on track. Seeming almost pessimistic now, actually.
Beware that the quantinuum numbers are again mixing error detection and error correction. In table III and figure 13 of https://arxiv.org/pdf/2409.04628 you see discard rates ranging from 10% to 50%. Discarding is enormously helpful, but makes the results non-representative of what to expect in the future because discarding has exponential cost scaling vs rounds. What they report still strikes me as impressive numbers; just kinda annoyed at how they report them.
On the google end, to be 100% logical-better-than-physical, there’s still the need to pay down the multi-round overhead of lattice surgery. A 2x better lifetime means logical storage is better, but logical operations are probably not yet better. With a lambda of 2, that probably happens at distance 11 or 13? Hard to say until it’s actually tried experimentally.
A week ago I did a complementary-gap-decoding analysis of the newly released google data ( https://zenodo.org/records/13273331 ), to get a sense of how much postselection would help at small round counts for various discard rates ( https://x.com/CraigGidney/status/1830817935264489695 ). At a 20% discard, a 10-round experiment has 10x lower error rate. There weren’t enough shots in the data to determine the single-round improvement at 20% discard; eyeballing the curves to extrapolate I’d guess it’s at least 100x. This is sort of typical I think; the smaller the experiment the more a fixed discard budget will help. This is interesting, and relevant to things like magic state injection, but not really applicable to trying to make 1000 logical operations better than 1000 physical operations.
Comment #6 September 10th, 2024 at 3:19 pm
With the Google result, are they able to run these fault-tolerant qubits through logical gates with each other? When you say:
With superconducting qubits, one is (alas) still limited by how many one can cram onto a single chip.
does that mean they can’t have two separate chips, each with a fault-tolerant logical qubit, interact with each other?
Comment #7 September 10th, 2024 at 4:13 pm
Craig Gidney #5: What are the error rates without error detection (just error correction)?
Comment #8 September 10th, 2024 at 4:47 pm
Maurice #7: The left hand side of the figure I posted is the no-discard numbers. The google paper reports a much wider variety of no-discard numbers.
Comment #9 September 10th, 2024 at 5:50 pm
Jess Riedel #1:
What sort of thresholds (for logical qubit count and logical error rate) are you thinking when you make your tentative one-decade prediction for something useful?
For starters, maybe like 100 logical qubits and a 10-6 logical error rate? That should already be enough to do useful simulations of the Fermi-Hubbard model, no?
Comment #10 September 10th, 2024 at 5:51 pm
Robert Ruxandrescu #3: I haven’t heard much about NV centers for the past few years, but anyone who’s followed the subject is welcome to chime in!
Comment #11 September 10th, 2024 at 5:53 pm
Craig Gidney #5: Thanks so much for those caveats! Will try to work something about them into the post (though some people complained it’s already too technical for them).
Comment #12 September 10th, 2024 at 5:57 pm
Max #6: No, unless I’m mistaken, only the Microsoft/Quantinuum team and not the Google one is currently reporting fault-tolerant gates. Of course everyone eventually plans to do fault-tolerant gates. Likewise, eventually the plan with superconducting is to have multiple chips interact with each other. But I don’t think anyone has successfully demonstrated that yet, and it would surely induce lots of new noise.
Comment #13 September 10th, 2024 at 6:53 pm
Any speculation about the cause of the correlated errors, if not cosmic rays or Gil Kalai?
Comment #14 September 10th, 2024 at 7:18 pm
Jair #13: I’m not going to know any more about it than the Google folks do!
Comment #15 September 10th, 2024 at 7:22 pm
Something interesting to note is that, in the previous Microsoft/Quantinuum paper, they used a smaller amount of postselection (0.5% to 5% discard). In this paper they ran a larger circuit and used more postselection (10% to 50% discard). This is perhaps a microcosm of how postselection costs scale up as circuit sizes scale up.
If the next paper continued this trend then it would run an even larger circuit, and get impressive numbers, but with 90% to 99% postselection. The trend would likely have to end there, because the retry costs really start getting out of control and ion traps are pretty shot rate limited already.
Comment #16 September 10th, 2024 at 9:32 pm
Does it make sense to build a quantum computer in low gravity environments – like on the ISS – companies like Google have the financial wherewithal and collaborations with NASA etc to do this. The main motivation for this question is ” correlated bursts of errors that come about once per hour, from a still-unknown source that appears not to be cosmic rays”. If its not cosmic rays, and other known factors, can gravity play a role at such sensitive scales ?
Comment #17 September 10th, 2024 at 11:02 pm
Taking the Devil’s Advocate role, I proffer my usual $1 bet that there will NOT be a useful QC within a decade.
I have been doing pretty good betting against both controlled fusion and QC for the last six decades or so.
For extra fun, I will bet $2 that no human being will land on the surface of Mars and return to Earth alive in the next 100 years.
Comment #18 September 10th, 2024 at 11:30 pm
Craig, we tried to be clear about the role of postselection with a distance-four code—it is on page 1 of the paper—but I am happy to take suggestions (my.name@gmail). Let me remark that even in the worst of our experiments (5 rounds of error correction on 8 logical qubits), the postrejection rate is 30%, not 50%.
Clearly, neither distance-four codes nor distance-seven codes will be enough for thousands of logical qubits. We’re working with what we have now, and limited postselection is a valuable tool. It might be even more useful for fast superconducting qubits, so I’m glad you’re investigating it.
Comment #19 September 11th, 2024 at 7:35 am
Scott #9:
Oh yea, I agree 100 logical qubits and a 10-6 logical error rate is achievable (and probably more likely than not) by 2034. As a (very) non-expert, it’s just surprising to me that this would tell us anything particularly interesting. Thanks.
If anyone has a reading recommendation that makes an earnest (not sales-y) case for the interestingness of what can be learned on these early devices, I’d be grateful.
We should of course expect a smooth transition between (1) squeaking out quantum advantage on completely useless problems and (2) really powerful quantum computers doing really useful things. Practical usefulness is a bit subjective, and scientific interestingness is really subjective, so we’ll have several years of people debating whether the threshold has been crossed. It’ll be worse than it has been for quantum advantage.
Comment #20 September 11th, 2024 at 8:50 am
“I’d been wavering—should I vote for the terrifying lunatic, ranting about trans criminal illegal aliens cooking cat meat, or for the nice woman constantly making faces as though the lunatic was completely cracking her up? But when the woman explicitly came out in favor of AI and quantum computing research … that really sealed the deal for me.”
LOL …{ claps }
Comment #21 September 11th, 2024 at 9:38 am
What’s the meaning of “error rate” in this context?
Is it the probability that the logical qubit will be in the wrong state whenever it’s being manipulated once? Then for a full computation a logical qubit would be manipulated many many times and the chance of error increases?
Wouldn’t that also depend on how long the qubit is maintained (i.e. the time it takes do perform an entire computation from initial input preparation to final output measurement, even if a particular qubit isn’t manipulated much)?
Comment #22 September 11th, 2024 at 10:02 am
“Any speculation about the cause of the correlated errors, if not cosmic rays or Gil Kalai?”
It’s our universe simulation doing garbage collection once every hour.
Comment #23 September 11th, 2024 at 11:30 am
Can I interrupt the discussion to ask a stupid question?
Does there currently exist a quantum algorithm for numerically solving the Schrodinger equation that doesn’t take exponentially more time when you increase the number of electrons in the simulation (other than “literally build the system you’re trying to simulate and measure it”)?
I’m asking because I read a Substack article (https://titotal.substack.com/p/bandgaps-brains-and-bioweapons-the) which, among other things, discusses the difficulties in trying to use the Schrodinger equation to predict band gaps in arbitrary materials.
Comment #24 September 11th, 2024 at 2:11 pm
Ben Reichardt #18:
I agree in the content of the paper you’re very clear about the postselection, but that’s not true in the abstract or in the blog post. Error detection is qualitatively different from error correction, both in its performance and in its implications for large scale system design, so it’s a key distinction to call out in any summary.
On rereading I see the blog post actually does say “error detection code” at one point in passing. But it makes no mention of how much detection. This stands out as strange since otherwise the blog post is including precise numbers on things like logical error rates.
For others: we clarified via email that the 30% vs 50% thing was a confusion over postselection vs preselection. I was basing 50% on the “acceptance rate” column of table III, which merges the two. There are reasons you’d merge them or not merge them, depending on the exact analysis you were doing.
Comment #25 September 11th, 2024 at 5:05 pm
Craig Gidney #24, Ben Reichardt #18: You mention error detection code, but isn’t the code distance-4? Do we need to post-select? What are the improvements without post-selection?
Comment #26 September 12th, 2024 at 3:34 am
Let’s hype up the possibility that the mysterious errors come from fundamental objective quantum collapse!
Comment #27 September 12th, 2024 at 8:46 am
> They also report correlated bursts of errors that come about once per hour, from a still-unknown source that appears not to be cosmic rays. I hope it’s not Gil Kalai in the next room.
Someone is looking at what humans are doing on the Earth once per hour.
Comment #28 September 12th, 2024 at 1:48 pm
Semi-joking meta-level question for Scott: Why are you so much better at summarizing quantum computer papers than the paper authors themselves are? I find that for most of the papers that you discuss in this blog, your one-paragraph summary would have made for a better abstract than the paper’s actual abstract. (And your description is often just as short.)
Comment #29 September 12th, 2024 at 3:43 pm
Ted #28: I have enormous unfair advantages, for example that I just need to write whatever interests me about a given paper, rather than making the boldest claims for it that can survive nitpicking by adversarial experts.
That said, yes, often when a student is stuck on how to write an abstract or introduction, I ask them to explain to me what they did and why it’s important, and then I say “yeah, so now just write what you told me.” 😀
Comment #30 September 12th, 2024 at 4:11 pm
Is it worth highlighting that Google does not do real-time decoding in that experiment, even though they call one of their decoders a ‘real-time decoder’? For experts this is probably implied in the term ‘quantum memory’, but for non-experts it could be confusing. Certainly for me (a weird mix of expert and non expert) a real-time decoder means real-time feedback (which is not needed for idling or Clifford gates, I agree, but still..).
From what I understood by browsing the paper, they call it that to emphasize how its performance passes the requirement for a (future) experiment involving active error correction and logical gates.
Comment #31 September 12th, 2024 at 7:48 pm
H #30: Just to clarify, the additional piece you’d like to see is taking the real-time decoded value and applying a conditional gate? I guess any such gate is trivial for a Clifford circuit, but just to show it (like not only obtaining the value in real-time but acting on it)? I guess for a memory circuit there’s nothing to do, but you could do “something” just to show you could. Like just send some dummy operation back to the device.
I suppose there won’t be non-trivial conditional logic until non-Clifford gates come around. Semantically, I would call the decoding real-time (since you get the value in real-time), but they haven’t shown conditional feedback. I do think that real-time decoding is the hard part, but I don’t know how much extra complexity doing something with the value introduces.
Comment #32 September 12th, 2024 at 10:57 pm
H#30 >(Is it worth highlighting that Google does not do real-time decoding in that experiment, even though they call one of their decoders a ‘real-time decoder’?)
You seem to be defining “real time decoding” to mean a full real time system. I would call that “real time control” or “real time feedback”. Decoding is just the “figure out the measurement result” part of real time control.
A “real time decoder” is a decoder that operates in a streaming fashion, while keeping keep pace with the quantum computer. In particular, it means the decoder should use an amount of memory, and have a delay-from-shot-ends-to-answer-available, that’s independent of how long the shot has been running.
I don’t think the paper is ambiguous on this point, but if there are specific sentences that feel that way to you then point them out and I’ll make sure they get consideration.
Comment #33 September 13th, 2024 at 10:02 am
Craig: Agreed, I concur. When I read ‘real time decoder’ in the abstract I thought that meant real time control, and became disappointed later when I realized what it really meant, hence my comment. I also agree that the authors are not ambiguous about this. Thanks for clarifying!
Comment #34 September 13th, 2024 at 10:20 am
Craig: Also, congratulations on this great milestone! (I realized just now that you’re one of the authors!)
Comment #35 September 14th, 2024 at 12:42 am
“They also report correlated bursts of errors that come about once per hour, from a still-unknown source that appears not to be cosmic rays.”
Reminds me of the radio astronomers who kept receiving mysterious signals every day at around lunchtime. After a long search, they finally traced the signal to the microwave oven in the lab’s kitchen. As soon as it was isolated, the mysterious signals stopped.
Comment #36 September 15th, 2024 at 2:42 am
This is off-topic, but what do you think of the new GPT models (starting at o1), published yesterday (for France) ?
Comment #37 September 15th, 2024 at 12:08 pm
f3et #36: o1 is pretty cool, isn’t it? 🙂 I played around with it 6 months ago, when it was still called “Strawberry”—but, just like with GPT-4 back in 2022, I wasn’t allowed to talk it publicly. Thankfully, it’s not yet at the point where it can do my job for me, but it probably is at the point where I’ll sometimes try using it to prove lemmas when I’m writing a research paper.
Comment #38 September 16th, 2024 at 10:53 am
Scott #9:
> For starters, maybe like 100 logical qubits and a 10-6 logical error rate? That should already be enough to do useful simulations of the Fermi-Hubbard model, no?
Not according to the AWS survey (https://arxiv.org/abs/2310.03011), which itself admits to being optimistic in the caveats subsection.
Comment #39 September 23rd, 2024 at 8:18 am
[…] just last week, a collaboration between Microsoft and Quantinuum announced that, in the trapped-ion architecture, they applied pretty substantial circuits to […]
Comment #40 November 26th, 2024 at 6:07 pm
[…] decreases additional as extra bodily qubits are added to the logical qubit. Scott Aaronson’s dialogue is price […]
Comment #41 December 10th, 2024 at 10:10 am
[…] already blogged about this!!! Specifically, I blogged about Google’s fault-tolerance milestone when its preprint appeared […]