NISQ and quantum supremacy did not fail
A week ago, a philosopher named Amit Hagar put out a preprint entitled The NISQ Trap: Eight Years of Demonstrations the Hardware was Built to Lose. Here’s the abstract:
With a single clear exception, every NISQ-era flagship demonstration of ‘quantum advantage’ has, within eighteen months of its announcement, been classically reproduced, shown to rest on classically tractable structure, or closed by a simulability theorem. Six theoretical results from 2024 through April 2026 explain the pattern: the regions of circuit-space NISQ hardware can run with sufficient fidelity coincide with the regions classical algorithms compress efficiently, because the features that admit one (low effective depth, strong algebraic structure, geometric locality) are the features that admit the other. This reading dates the NISQ programme from its 2018 articulation as an interim retreat from the unmet conditions of the 1996 threshold theorems, characterises the eight years that followed as a closed loop in which the demonstrations the hardware could run were drawn from regions classical methods could already reach, and locates the exit from the loop where the threshold theorems originally located it: in fault tolerance. The empirical pattern could in principle break with a demonstration that escapes the current simulability results. After eight years and more than thirty advantage-class announcements, the burden of producing such a demonstration falls to the defenders of NISQ.
You can also read some debates about the paper on SciRate here. I think it’s fair to say that the paper is purely polemical, without new ideas, and Pangram agrees with my suspicion (and that of a SciRate commenter) that significant portions of it are AI-generated.
Nevertheless, the basic thesis—that quantum supremacy in the NISQ (Noisy Intermediate Scale Quantum computing) era has been a failure, or even an example of pathological science—seems surprisingly widely shared, along with the opposite thesis that quantum computing already gives oodles of useful advantages for optimization and finance.
So it seems worth stating for the record that I have an extremely different view. I would say:
- Sampling-based quantum supremacy experiments, including those based on Random Circuit Sampling and BosonSampling, passed the point about two years ago where, absent a breakthrough in classical algorithms, they quite clearly are beating what can easily be simulated on any existing classical computer. Hagar seems to claim that these experiments have been killed by the October 2025 paper Classical simulation of noisy random circuits from exponential decay of correlation, but he ignores that the algorithm from that paper still needs time that’s exponential in the circuit depth (see Theorem 2).
- Indeed, simulating deep ~100-qubit random circuits, like those that Google and Quantinuum have now demonstrated experimentally, still seems pretty hopeless with any current classical method. This is particularly true for Quantinuum’s experiments, which had high enough gate fidelity to maintain a Linear Cross-Entropy score of order 1 (i.e., they’re no longer all that “noisy”). The central drawback of these experiments is no longer lack of confidence about quantum advantage; rather, it’s just that we only get samples as output, and directly verifying the quality of the samples seems just as intractable for a classical computer as spoofing the samples.
- As of this past year, however, we have some strong candidates for verifiable quantum advantage. One is the Google OTOC experiment, as even Hagar himself acknowledges (that’s his “single clear exception”). A second is the simulations of the 2D Fermi-Hubbard model on Quantinuum and Google machines, like this one. The 1D Fermi-Hubbard model can be classically simulated pretty easily (see here for example), but the 2D one still presents challenges, meaning that in some regimes, the best available estimates of certain observables apparently now come from quantum computers. I wish I could write about other examples that will be public shortly.
- Yes, the “real” goal remains, as it’s been since the 1990s, to build a scalable fault-tolerant quantum computer—and I’m glad that Hagar (unlike, say, Gil Kalai) never suggests that we’ve learned anything to rule that goal out. In the meantime, an intermediate goal would be to use NISQ devices to do physics and chemistry simulations that are commercially useful, or that help solve important scientific problems. The point of quantum supremacy experiments, you might say, is that by demonstrating the reality of quantum speedup about as clearly as it can be demonstrated with current hardware, they let us cleanly turn our attention to those more ambitious goals.
Anyway, my son and I need to catch a plane to Utah now, for the next iteration of the wonderful Epsilon Camp, where I’ll again be teaching theoretical computer science to 11- and 12-year-olds. But feel free to discuss in the comments! Nothing about world affairs in this thread please, just quantum supremacy.
Update (July 19): Not unrelated to the subject of this post, here’s a podcast I did with Gill Eapen of “Scientific Sense” about the current situation in quantum computing including recent experimental victories.
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Comment #1 July 18th, 2026 at 10:33 pm
Motivated in part by John Wheeler’s assertion that the continuum nature of Hilbert Space conceals the ‘it-from-bit’ information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics – RaQM) is proposed based on a specific discretisation of complex Hilbert Space. The Schrödinger equation is not modified in RaQM, even during measurement. However, the bases in which the quantum state is defined must satisfy certain rational-number constraints. These constraints lead to the notion of finite qubit information capacity Nmax: for any N > Nmax qubit state, there is insufficient information in the N qubits (linearly growing in N) to allocate even one bit to each of all 2^(N+1)−2 continuum degrees of freedom (exponentially growing in N) associated with quantum mechanics/theory (QM, where Nmax = inf). It is proposed that the discretisation of Hilbert Space in RaQM is due to gravity, hence QM is the (singular) continuum limit of RaQM at G = 0. On this basis, it is estimated that Nmax lies between about 200 and 400 for current qubit technologies, and will never exceed 1,000. Whilst QM and RaQM are experimentally indistinguishable for small numbers of qubits, RaQM predicts that the exponential advantage of quantum algorithms which, like Shor’s, require bases with maximal N-qubit superposition/entanglement, will have saturated at 1,000 perfect qubits. Hence, insofar as a classical computer will never factor a 2048-bit RSA integer, RaQM predicts that a quantum computer won’t either. This predicted breakdown of QM could be testable in less than 5 years.
https://arxiv.org/abs/2510.02877
Comment #2 July 19th, 2026 at 1:39 am
What’s a commercially useful use case in Chemistry. I am curious. How close are we to anything commerixlaly useful.
Compared to the funds put into quantum computing, the results so far seem a collosal waste.
Comment #3 July 19th, 2026 at 1:58 am
Ethereal Bliss #1: I’m glad that “RaQM” makes such a clear falsifiable prediction! I hope its proponents don’t try to move the goalposts if indeed it gets falsified. 😀
Comment #4 July 19th, 2026 at 2:05 am
Rahul #2: One example of a chemistry use case that people thought about a lot a decade ago, was better understanding the Haber-Bosch process that makes most of the world’s fertilizer, and possibly figuring out how to run the reaction in a more energy-efficient way. There are lots of other examples — since we’re nearing the World Cup final, let’s say many shots on goal, only a few of which would need to succeed to yield tons of value.
You’re right that, if you just look at the commercial value right now versus money spent to date, quantum computing looks like a colossal waste — as did classical computing before it scaled, as did nuclear power and heavier-than-air flight and every other nontrivial new technology. It’s all about whether you believe the science or engineering case or you don’t. People who believe such things when others don’t, and invest on that basis and turn out to be right, often get rich. Of course, even assuming that QC does work like the theory says it will, there remain lots of questions about its range of applications, as any reader of this blog knows.
Comment #5 July 19th, 2026 at 6:36 am
Scott, thanks for engaging with the paper seriously. Four numbered points is more than most preprints get. I also replied on Scirate since this is where you sent your readers.
On the AI question: the title-page acknowledgment of v3 (announced July 14) states that the paper was drafted with AI assistance and substantially edited by the author, with all claims and references checked by hand; the one substantive error found on SciRate was corrected in v2 within hours. The interesting question was never who typed it.
On your point 1: Theorem 2 of arXiv:2510.06328 is indeed exponential in depth, but it is the intermediate result. The paper’s Main Theorem (Theorem 3) applies Theorem 2 only at the effective depth, yielding quasi-polynomial runtime independent of the physical depth. The closure is conditional on exponential CMI decay, an assumption with numerical support across unital and non-unital noise, and asymptotic rather than instance-level, which is why my paper says the samples remain unreplicated end-to-end. A conditional closure, answering the threshold theorems’ conditional opening. I like the symmetry here.
On your point 2: “verifying the quality of the samples seems just as intractable as spoofing the samples” is the verification bind, my paper’s central claim, and I’m glad we agree it is now the central drawback. v3 also points to the recent PRX on the Vast World of Quantum Advantage which makes a similar point.
On your point 4: your 2004 STOC paper challenged quantum-computing skeptics to say where quantum mechanics itself gives way, arguing that skepticism owes a Sure/Shor separator. My Philosophy of Science paper (76, 2009, 506–535) was an answer to that challenge: a skepticism that concedes quantum mechanics everywhere, doubts the noise assumptions instead, and rules nothing out about fault tolerance. I called it optimal skepticism, and The Complexity of Noise (2010) developed it also for the passive approach to error correction. Your point 4, seventeen years on, reads as agreement that this position is coherent, and I’ll take it. The exit is where the threshold theorems put it, and I say so explicitly, so we seem to disagree about the instances on the table, not about where the field must go.
Amit Hagar, philosopher
Comment #6 July 19th, 2026 at 7:15 am
The difficulty for me is that the speed separation is *not* between ‘classical’ and ‘quantum’ computing but between different hardware implementations of statistically equivalent input-output sets for elaborate algorithms. Classical computing always included analog computing, but it now also includes Probabilistic Analog Computing, using different hardware noise sources.
In particular, we should distinguish between noise sources that are generated algorithmically, thermally, and by a Lorentz invariant analog of thermal noise, with the latter being commonly called ‘quantum noise’ (or, in SED, the “Zero-Point Field”, ZPF) with it’s amplitude determined by Planck’s constant.
With the introduction of noise, it becomes useful to consider characteristic functions as Fourier transforms of probability distributions, which introduces HUP, contextuality, Generalized Probability Theory, and Hilbert spaces and operator methods into classical modeling of Probabilistic Analog Computing.
Hilbert space modeling for Probabilistic Analog Computing that uses ‘quantum noise’ as a noise source can be an essentially classical model for any experiment or algorithm that can be modeled by the Hilbert space methods of quantum theory. An essential starting point is IMO Bernard Koopman’s introduction of a Hilbert space formalism for classical mechanics in PNAS 1931.
Given that we can construct a steel-manned classical physics that is as powerful as quantum physics, the game becomes to introduce faster hardware accelerators for a given algorithm, not whether an algorithm or its physical implementation is called classical or quantum. For an computationally inclined experimentalist this is no change at all, but for theory it can make sense of the relationship between classical and quantum physics, make sense of the many successful attempts to reproduce quantum algorithms in classical form, and enable new intuitions.
Perhaps try my AnnPhys 2020, “An algebraic approach to Koopman classical mechanics” for a slightly raw beginning on this or my YouTube channel for how that has developed since.
Comment #7 July 19th, 2026 at 8:50 am
Scott #4
> You’re right that, if you just look at the commercial value right now versus money spent to date, quantum computing looks like a colossal waste — as did classical computing before it scaled, as did nuclear power and heavier-than-air flight and every other nontrivial new technology.
In each of these cases, the potential technology had an obvious qualitative advantage over the existing technologies. Quantum computing also has an obvious qualitative advantage over classical computing, namely the ability to efficiently simulate unitary evolution, but – as I never tire of pointing out – that ability does not in itself translate to commercial value in any known case, since the physically interesting problems (e.g. the Haber-Bosch process) aren’t “time-evolve an arbitrary initial state according to some Hamiltonian” but “find the ground state of some Hamiltonian”, for which there is no known efficient quantum algorithm absent extremely strong additional assumptions, most commonly being able to construct an input state which has a substantial overlap with the target state.
Comment #8 July 19th, 2026 at 10:31 am
Amit Hagar #5: Thank you for engaging here! Hope I represented your views fairly.
Yes, arxiv:2510.06328 gives a result that’s independent of depth, but that’s because when the depth becomes too large, the state converges to nearly the maximally mixed state, correct? And do you agree that Quantinuum’s and even Google’s experiments are not near the regime where that happens, as demonstrated by their ability to extract an LXEB signal?
Provided we agree on these things, the real situation is subtle: yes, NISQ QC ultimately becomes efficiently classically simulable, because to get a true scaling advantage you need fault-tolerance—something we’ve understood since the 1990s. Nevertheless, existing Random Circuit Sampling experiments with ~100 qubits give an extremely clear practical advantage, and not only that, but crucially, that practical advantage comes directly from the exponentiality of the Hilbert space (and the exponential number of terms in the Feynman path integral) — ie, exactly what we expect to be the ultimate source of scaling advantages, once fault-tolerance comes online. It therefore, I would say, provides clear empirical evidence for the reality of those scaling advantages, despite not scaling itself beyond some point without fault-tolerance.
Anyway, it sounds like we agree both about what eventually needs to be demonstrated (scalable fault-tolerance to blast through any candidate Sure/Shor separator), and about the viability of the program for getting there. I regard the remaining disagreements, about how impressed to be by current NISQ experiments, as less important by comparison.
Comment #9 July 19th, 2026 at 12:18 pm
Scott #8: Represented mostly fairly, with one label to decline below, but first your question.
Not quite mixedness. The mechanism in 2510.06328 is decay of conditional mutual information, not convergence to the maximally mixed state; that paper’s motivation is precisely the regimes where anti-concentration and mixedness fail (non-unital noise, T1 decay), where deep circuits converge to a nontrivial but still patchable distribution. Effective shallowness is memory loss, and it is compatible with a nonzero XEB signal. Whether the current experiments stay inside the algorithm’s feasible-constants window is an open question. I would only note that at advantage scale the LXEB signal is itself certified by extrapolation and by assumed error models rather than by direct verification, so placing the experiments outside the simulable regime relies on the same certificate you question in your point 2. That circularity is the subject of the paper. The size of the Hilbert space can wait.
One label to decline: you place me next to Gil Kalai, which is flattering, but I’m not a skeptic, and not a believer either. My view is (and has always been) that whether the damn thing can be built is an empirical question. The paper’s method is, accordingly, empirical and I carefully audit every claim against the record. I also welcome any demonstration that breaks the pattern, and concede within hours when I’m wrong, as the v2 correction shows. So far the record shows the pattern, and that is all the paper says. When the record stops showing it, I’ll say so with the same speed.
On viability, accordingly, my position rules nothing out; it asks only that the 1996 conditions, i.i.d. noise, later relaxed to fast decaying correlations, be checked rather than assumed. It’s the same if, just thirty years later.
Thanks for the exchange. It improved the record on both sides.
AH, philosopher, among other things
Comment #10 July 19th, 2026 at 1:09 pm
For completeness: there also exist several proposals for certification of boson sampling, including work by Ulysse Chabaud and by the group of Jens Eisert, and mine. We recently implemented one of these protocols in an experiment (https://arxiv.org/pdf/2602.12269). It’s way too small for quantum advantage (only three photons) but it’s a start.
Comment #11 July 19th, 2026 at 2:18 pm
Scott
Agree about Haber Bosch being a great target problem. However most of the work to create a better catalyst for ammonia synthesis uses combinatorial experiments or Density Functional Theory / Machine Learning. Is there really much serious effort that uses Quantum Computing for this.
I also agree about your other point. The question for a policymaker, VC or a funding agency is when is the right time to give up. Quantum computing from an applied commercial perspective seems pretty stagnant for the last decade. Outside of the quantum supremacy race I have not seen any practical applications emerge.
Yes but maybe a fantastic use case is just around the corner. Who knows. Fusion and flying cars are in that genre too.
Comment #12 July 19th, 2026 at 3:08 pm
Rahul #11
> Agree about Haber Bosch being a great target problem. However most of the work to create a better catalyst for ammonia synthesis uses combinatorial experiments or Density Functional Theory / Machine Learning. Is there really much serious effort that uses Quantum Computing for this.
The idea is that a quantum computer will eventually allow us to find better catalysts because it’ll allow us to obtain a potential catalyst’s exact energy landscape, rather than a DFT/ML-based approximation. The problems with this idea are (a) as alluded to in my previous comment, there’s no guarantee that even a completely error-free quantum computer will allow us to find exact energies, and (b) for a QC to be useful in this context (and many similar others), it’s not enough to obtain the exact energies, they need to be sufficiently different from our best available classical approximations such that they’ll shift the relative ranking of potential catalysts, e.g. DFT says catalyst A is better than B, but QC says the opposite. That’s a harsher requirement than it might sound, because it’s inherently in tension with the previous one (insofar as there’s reason for optimism regarding QC obtaining exact ground states, it’s exactly because we believe we have very good classical approximations we can use as the input for a quantum phase estimation algorithm), and because these things are ultimately tested in experiment anyway, so for QC to make a real difference it’s not enough for catalyst B to be better than A, DFT has to have said that B sucks so much it’s not worth testing.
Comment #13 July 19th, 2026 at 9:30 pm
Rahul #11: From the perspective of someone in the field, saying “Quantum computing from an applied commercial perspective seems pretty stagnant for the last decade” is sort of like someone saying in 1906 that the field of heavier-than-air flight has been “commercially stagnant for the last decade.” I.e., it’s true in the narrow sense that commercial usefulness simply isn’t there yet at all, but it’s also comically uncurious about the actual historic thing that did happen in the decade in question. Namely, that the technology itself went from basically not working to basically working.
No wonder that, while I argue in my comment section with people who think QC is “stagnant,” out in the real world one QC startup after another is right now doing multi-billion-dollar IPOs (including, yes, the ones that are intellectually dishonest and therefore don’t “deserve” it, but the basically honest ones as well). Evidently investors think about the future differently from blog commenters!
Comment #14 July 19th, 2026 at 9:40 pm
Amit Hagar #9: As a general matter, I reject the “naïve empiricism” that says that we can’t know anything about X until a direct experiment is done, when we have well-tested, hard-to-modify underlying theories that strongly predict a particular answer.
E.g., hopefully everyone now understands that the WHO were idiots when they declared that “there’s no evidence for person-to-person transmission of COVID” back in January 2020. They should’ve said: based on what we do understand about this disease, it would be absolutely shocking if it didn’t spread person-to-person, even if we don’t have a confirmed case quite yet.
Likewise with quantum computing: my position is that, based on what we understand about the laws of physics, it would be shocking and revolutionary if scalable QC turned out not to be possible. Of course we can’t be 100% certain until we actually see it work, but it’s misleading to treat it as some 50/50 thing where no one has any idea.
Comment #15 July 19th, 2026 at 9:56 pm
Vladimir #7, #12: I’m of course a theoretical computer scientist, not a chemist. But I talk to people who do know chemistry extremely well, who’ve given me many reasons to trust their intellectual honesty, and who are somewhere between cautiously excited and very excited about the potential to learn new things about chemistry from QCs. This seems to be, firstly, because they do care about dynamical questions (like reaction rates), and secondly, because even for ground state questions, they think you’ll often get a super-Grover advantage by guessing a “guiding state” using some ansatz and then improving it.
And then I also talk to Vladimir in my comment section, who confidently declares that all of that is nonsense and QCs will never help for chemistry at all.
How do you suggest I move forward given this epistemic situation? E.g., just brainstorming, but might you be interested in a public debate, to be hosted on this blog, between you and one of my QC-for-chemistry colleagues?
Comment #16 July 19th, 2026 at 11:53 pm
Scott #9: we agree on rejecting naïve empiricism, and I am not naïve, nor do I assign 50/50. I just refuse to bet. But the analogy misplaces the disagreement. “Based on the laws of physics it would be shocking if scalable QC were impossible” treats the threshold theorem’s noise conditions as if they followed from quantum mechanics. They don’t. The theorem is a conditional: if noise is i.i.d., later relaxed to fast-decaying correlations, then arbitrary computation.
That “if” is not a theorem of QM; it is a physical assumption about noise at scale. How do I know it’s an assumption? Because it sits in the hypothesis, not the conclusion: if i.i.d.-ness fell out of quantum mechanics, fault tolerance would be a corollary, not a landmark.
So doubting the noise condition is not doubting QM, it is naming an empirical premise QM does not supply. Your COVID case is the disanalogy: “it would be shocking if it didn’t spread” rested on a well-modeled mechanism. “Noise at scale is i.i.d.” is not a mechanism physics predicts; it is a hope about hardware.
And at scale the independence is being assumed rather than measured, while the evidence that exists already runs the other way. Here is just one example: Oda et al. (PRX Quantum 7, 020327, 2026) find that non-Markovian, time-correlated noise contributes substantially to transmon multi-qubit dynamics, improving prediction 7× over the independent-noise hardware models, and they note it is unclear whether the memoryless modeling remains viable as system size grows. The independent noise the threshold theorems require is the exception being corrected for, not the rule being confirmed.
That hope, the noise premise, not quantum mechanics, is what my paper questions and what I have been questioning since 2009. Everything downstream of it, including how impressed to be by 100-qubit RCS, follows from whether it holds.
AH
Comment #17 July 20th, 2026 at 1:05 am
It seems relevant that:
1. In the paper and possibly in this discussion, Amit Hagar used an LLM to produce output. (I’ve interacted with LLMs and taught students in the last year or two. I suspect the comments here were at least partly written by an LLM, though I could be mistaken.)
2. LLMs are capable of superhuman output speed.
And so, in this conversation and on Scirate, Amit Hagar informs us that “The interesting question was never who typed it.” And he claims that he concedes errors within hours.
I don’t think it’s true that it’s not interesting who typed it. Arguing with an LLM, we are faced with an asymmetry in the amount of text per human effort. Is it a good use of our energy? Is it a good thing for our society if academics try to pass LLM output as their own intellectual output?
The interesting question was never how long it takes someone to make or to concede some point or another. The interesting question was: what did we learn?
I feel the norms are more important than the content in this instance. It is interesting to note that recently, mathematicians have often disclosed LLM prompts and/or full conversations when using significant AI assistance. Would the philosophers?
Best wishes to all.
(Written by a human, read by AI, revised by human to soften the tone.)
Comment #18 July 20th, 2026 at 1:45 am
Amit Hagar #16: For scalable quantum speedups not to be possible, it’s not enough for the assumptions of some particular fault-tolerance theorem to fail, or even for any particular approach to error-correction to be a dead end. Instead, there needs to be an efficient classical simulation for any realistic quantum system. If we take that implication seriously, while still believing in QM itself, we find that the burden of proof shifts decisively to the QC skeptic’s court. How does the simulation work? How is the exponentiality of Hilbert space reliably “screened off” or “censored”? Is there some “global conspiracy” of errors to ensure this, as Gil Kalai has sometimes speculated? That’s why I stand by my statement that it will be shocking and revolutionary if QC turns out to be impossible, much like if person-to-person COVID transmission had turned out impossible in January 2020.
Comment #19 July 20th, 2026 at 2:16 am
Scott 16: I thought we were talking about the feasibility of FTQC, not speed up. Speed up is another issue entirely, because the set of possible speed ups currently is rather thin in terms of the families of algorithms that promise it. My point is only about FTQC. The possibility of realizing a large scale FTQC depends on the noise behaving. So far it has been assumed across the board that it does. And then it is extrapolated to the scale that matters without checking. And it is assumed all over the hardware spectrum, especially in the decoders, which are every now and then bolted with additional crutches once misbehaved noise is encountered. If you want a discussion of burden of proof, let’s have it. Here is an experiment that can be run today, on current hardware, even with one qubit. Just run the machine for a long time, do not dynamic decouple it to twirl the noise, and record it. If the noise behaves, you should see an exponential decay of correlations. If it doesn’t you might see a power law decay. Willow’s unexplained bursts at repetition code 29 are first hint that the correlations do not decay nicely. And BTW, it’s not Hilbert space censorship, it’s just plain old thermodynamics of open quantum systems that dictates that the correlations decay as a power law.
Comment #20 July 20th, 2026 at 9:46 am
Scott #18: “there needs to be an efficient classical simulation for any realistic quantum system. … How does the simulation work?” Copenhagen says ‘give a classical description of experiments’, but its version of “classical” is straw-manned so it does not allow multiple experiments/state preparations to be encoded into a single formal structure. Contextuality is classically understandable and can be accommodated in the mathematics of Generalized Probability Theory, but traditional straw-manned classical modeling does not allow it. Other interpretations of QM straw-man classical physics in the same way.
If we steel-man classical physics, however, by using the full power of the Poisson bracket and Koopman’s Hilbert space formalism for classical mechanics, we can classically describe anything that can be described by quantum physics. *Isomorphisms* between those steel-manned classical and quantum models can be exhibited because they are both just Hilbert space formalisms, however I won’t rehearse here at length the formal and practical differences that lead to different tools and intuitions.
We have already found ways to use suitably curated noise as a resource to build analog hardware that usefully accelerates the execution of some algorithms. This is only an elaboration of replacing a single system clock by asynchronous system clocks in multiple CPUs, GPUs, et cetera (asynchronous ~ noisy analog timing; to that we add noisy analog signal levels), which has evolved as a way to speed up algorithms that can be executed asynchronously in parallel threads until the algorithm requires synchronization.
Amit & Gil Kalai suggest that correlations in the noise are somehow in principle insuperable, but ingenuity has found ways to have just enough control (and it will find more ways). I think we can understand the conceptual landscape better than we do by calling the resulting hardware ‘quantum’ or ‘classical’: in particular, understanding that ‘quantum noise’ differs from other noise in the mathematics of QFT and of an algebraic classical equivalent of QFT only by being Lorentz invariant clarifies the issues.
Comment #21 July 20th, 2026 at 11:18 am
Scott #18:
“Realistic quantum system” may be the sticking point. What if all quantum systems for which there are provably no efficient classical simulations cannot, for boring practical reasons that do not follow from QM, be actually constructed on real equipment? Is that statement already known to be false?
Rahul #11:
These problems are more interdependent than they look. Flying cars will follow from (portable, aneutronic) fusion, and speaking as someone who works on it, if the QC field gives us a 10^7 speedup in a PDE solver with no decrease in throughput or latency, I’ll give you a fusion reactor in 90 days. (Many other people will, too – not just me. This is a well-known barrier to adaptive control of a nonlinear system of ~270 million second-order PDEs.)
Consequently – I’d contend that “the question for a policymaker” or funder is absolutely *not* when to give up! New math will be useful, somewhere. I think one of the cheapest things vis-a-vis real-world impact that the federal government could fund would be a “National Endowment for Mathematics” that would pay newly-minted math and theoretical CS Ph.Ds a small stipend to write the papers that they hope will get them a professorship somewhere, without having to work at McDonald’s while doing it. Just pure theory – no expensive equipment and no institutional overhead. Presumably, if they got a Ph.D, they know what they’re doing, and funding these people to the same level as, say, paintings of Jesus in elephant poop would not break the federal treasury.
Policymakers and funders absolutely should not be in the business of trying to predict the technological future, or trying to figure out what will be popular or the “hot” field that they don’t want to miss. They should find people who are familiar with the problems that they want to solve, ask them what the obstacles are to their work, collate the responses, and fund many possible divergent and unrelated approaches to the common problems. They should also approach the task from the other direction, funding basic research on the entirely theoretical gaps in our understanding of the systems being studied, which is where almost all new capabilities come from.
The worst possible approach is for a nontechnical policymaker (or, for that matter, a computer programmer who got rich and decided he knows everything about other fields of study) to look at a problem, decide what the solution is, and fund only work on that solution. Putting researchers in an impossible position by declaring, as an infallible doctrine, that the funding source’s preferred solution will solve the problem and he will fire you if it doesn’t, well, that’s where both failed startups and failed government programs come from.
Train of thought #17:
I recently had the displeasure of exchanging emails with a “businessman” type who decided to generate all of his replies by putting my communications to him into an LLM. I attempted to explain to him that this was a serious breach of not only trust but potentially the federal regulations that we were operating under (export controls, basically, since the LLM operator almost certainly has non-US persons working on it), that “his” response contained suggestions to violate at least two federal statutes and that if I had done as he suggested, he would have been guilty of conspiracy and could have gone to prison, and finally and most importantly, that the purpose of my communicating with him was to convey ideas to him, not to an LLM, so that he could understand something which I felt it was important for him to understand, not so that we could do the 21st century equivalent of two answering machines talking to each other. The purpose of human communication, in other words, is for the other person to understand you – even when understanding you involves taking five minutes to sit still and think instead of “hustle” and “grit” – not for the other person to generate text in response as efficiently as possible without any of your ideas ever passing through his brain. That is an act of contempt.
He responded that *I* was wasting *his* time.
We are in la-la-land.
Comment #22 July 20th, 2026 at 11:43 am
Scott #15
I’m not a computational chemist either, but I am (or was) a computational condensed matter physicist, which I feel is a sufficiently close field for me to express a reasonably informed opinion. To be clear, my opinion isn’t “we’ll never learn new things about condensed matter and/or chemistry from QCs”. A large, fault-tolerant QC would be a qualitatively different tool from anything we’ve previously had, a new angle of attack; it’d be exceedingly odd if it came up with no new results. In this sense, I too am excited to see what QCs could help us discover about strongly-correlated electron systems. What I’m pushing back against is the claim that known quantum algorithms already give us good reason to think that major commercial applications for QC are just around the fault-tolerance corner.
> firstly, because they do care about dynamical questions (like reaction rates)
As I’ve previously pointed out (https://scottaaronson.blog/?p=7624#comment-1959122 [sheesh, November 2023, I really have been harping about this for a long time]), caring about dynamical questions doesn’t eliminate the problem of finding an interesting initial state to evolve. It will of course be scientifically interesting to e.g. prepare the best possible classical ground state candidates of a couple of molecules on a QC, find their “real”, i.e. fully quantum-mechanical, reaction rate, and see whether, how, and under which circumstances it differs significantly from our present semi-classical approximations. However, this sort of thing is also unlikely to have commercial implications, due to a direct analogue to argument (b) in my previous comment.
> secondly, because even for ground state questions, they think you’ll often get a super-Grover advantage by guessing a “guiding state” using some ansatz and then improving it
If all your QC-for-chemistry colleagues are assuring you is reasonable to expect is doing better than Grover, I have no disagreement with them, since “super-Grover” includes “exponential and intractable in practice”.
> How do you suggest I move forward given this epistemic situation? E.g., just brainstorming, but might you be interested in a public debate, to be hosted on this blog, between you and one of my QC-for-chemistry colleagues?
I don’t think evaluating the claims I’ve made here requires expertise in chemistry (presumably you see at least some merit in them yourself, otherwise you wouldn’t offer to subject a colleague to my badgering). I would welcome serious engagement with my arguments from one of your colleagues, or from anyone else.
Comment #23 July 20th, 2026 at 12:13 pm
In the end a working QC boils down to maintaining quantum entanglement between millions of objects, which will never be what we call a “scalable process”. The open question is whether we can push it far enough to achieve non trivial computation.
It’s not a matter of QM theory but a matter of engineering feasibility.
Comment #24 July 20th, 2026 at 3:10 pm
Hello Prof. Hagar,
I admit, I’m utterly ignorant, but your proposal to measure C(t) “even with one qubit” (as per comment #19 — better a few more, I’d say) touches on an epistemological Popperian point about the noise assumptions underlying the field that seem haven’t yet been systematically tested at full scale; that’s a methodological gap worth closing, if not before, at least in parallel with any novel progress. Scientific transparency is not merely an ethical value — it is strategically rational in the long term.
Best,
Matteo Vitturi
Comment #25 July 20th, 2026 at 3:44 pm
Amit Hagar #19: For near-term purposes, there’s not a huge loss in restricting discussion to the feasibility of quantum fault-tolerance, since that is our primary technological path right now to demonstrating the reality of exponential quantum speedups.
For me, though, the real game always has been to learn the truth or falsehood of the Extended Church-Turing Thesis: that is, can all of nature be simulated on a standard Turing machine with polynomial overhead, or is quantum mechanics a counterexample to this? And from that standpoint, it seems obvious to me that the burden of proof lies with those who think the Extended Church-Turing Thesis still holds in a quantum-mechanical universe. Why does it hold? What astonishing new principle causes it to hold, despite the exponentially many canceling terms that generically arise in a path integral?
I get enraged when (some) QC skeptics seem not even to notice these profound questions, and content themselves to poke holes in this or that specific quantum fault-tolerance proposal and then call it a day. That seems to me to reflect a staggering incuriosity about the way the world actually is.
Comment #26 July 20th, 2026 at 5:31 pm
Dr Scott #25
it’s equally “exhausting” to have QC evangelists twisting themselves in all kinds of knots in order to declare (premature) victory ASAP, year after year after year, by taking all kinds of convoluted extrapolations from the current state of hardware prototypes to full fledged QC of the sort that could break encryption.
The equivalent of claiming that the milky way was now ours to explore on the day the Wright brothers took their first flight… hey, it’s just a matter of strapping a rocket, make things a bit sturdier to resist max dynamic pressure, reaching escape velocity, …
Maybe the burden is actually on you to chill until the hardware actually catches up (or not) with the actual advertised goals.
Using “investors” hype as a proof that things are happening is baffling to say the least… what’s your projected ROI and how soon? 😛
Comment #27 July 20th, 2026 at 5:58 pm
Thoughts on Fable’s disproof of the Jacobian conjecture? Seems hard now for those saying the models are just sweeping up low hanging fruit that haven’t had a lot of mathematical effort put into them.
Comment #28 July 20th, 2026 at 7:57 pm
AI Math Proof.
a fairly elementry counterexample to the 3 dimensional Jacobian Conjecture (Smale’s list #16) is all over the internet today. seventh degree polynomials, easy to check by hand!
Comment #29 July 20th, 2026 at 9:02 pm
Scott, I think you may have accidentally linked to the wrong paper in the phrase “like this one” in your paragraph #3. The text is discussing “simulations of the 2D Fermi-Hubbard model on Quantinuum and Google machines”, but the linked paper discusses simulations of the 1D Fermi-Hubbard model on IBM machines.
Comment #30 July 21st, 2026 at 2:05 am
AI Math Proofs — conjectures.
I think the counter example in the Jacobian conjecture is much deeper (hundreds of mathematicians have worked on it, in some cases for many years) than the recent cases of Erdos conjectures, which leads me to making a couple Raoul Conjectures.
RC1: AI math will prove vastly better at producing counterexamples than proofs of conjectures.
RC2: The Jacobian conjecture is obviously true for n = 1, and has now been disproven for n >=3, which leaves the critical case of n = 2. The n = 2 case is probably getting a huge amount of attention (starting Monday morning), much of it using AI. I conjucture the n = 2 case will be solved, one way or the other, within 32 days.
Comment #31 July 21st, 2026 at 6:35 pm
Hi everybody,
It is a pleasure to hear about Amit Hagar’s new and interesting paper on quantum supremacy. (Already in 2009, Amit wrote about quantum fault tolerance from the perspective of the philosophy of physics.) Let me mention that Amit was a PhD student of my friend Itamar Pitowsky, whom I first met during our school days at the Hebrew University. We later became colleagues when we both joined the faculty there. Itamar and I had many interesting discussions about quantum computation. Pitowsky wrote one of the earliest papers on the Physical (efficient) Church–Turing Thesis.
A) My agreements and differences with Amit Hagar’s views
I largely agree with Amit’s conclusion that the “quantum supremacy” program served mainly as an intermediate goal on the way to—or perhaps instead of—the main road toward scalable quantum computing, namely quantum error correction and quantum fault tolerance. This diversion also enabled the community to keep setting essentially the same goals for experimental quantum error correction—the goals set today for the next three to five years are similar to those set back in 2013.
I also tend to agree with Amit’s conclusion that the quantum supremacy claims are either false or inconclusive. My own view is based on a rather extensive study of several experimental claims and rests on considerations different from those emphasized by Amit. In addition, work by Guy Kindler and me from 2014 gives strong reasons to regard NISQ computers as classical computational devices from the perspective of computational complexity. This viewpoint has since been reinforced by work of Gao and Duan, Aharonov, Gao, Landau, Liu, and Vazirani, among others. (Our work, as well as several of the later papers, relied on Fourier-analytic methods.)
I should also mention that a number of researchers, both optimistic and skeptical about scalable quantum computing, regarded the “quantum supremacy” direction for NISQ devices as something of a distraction—or even a somewhat silly direction.
B) A suggestion to split the burden of proof
For more than two decades, Scott has argued that the burden of proof lies on the shoulders of the skeptics. I suggest that we split the burden of proof as follows:
The burden of showing that the engineering obstacles to high-quality quantum error correction and quantum fault tolerance are not far beyond reach lies with the proponents of quantum computing. They still have a long way to go before providing convincing evidence that these goals are feasible and can be achieved in the foreseeable future.
The burden of showing that these engineering obstacles reflect inherent physical limitations, rather than merely technological ones, lies with the skeptics.
C) Scott’s request for classical algorithms for realistic quantum processes
I believe that identifying physically plausible noise models that rule out quantum fault tolerance, and obtaining experimental support for these noise models, could go a long way toward demonstrating that scalable quantum computation is impossible.
Scott makes an additional demand: to explain how realistic quantum evolutions can be simulated efficiently on classical computers. This is an important point that Scott has emphasized for more than two decades. I certainly have not ignored it and have discussed it in various places over the years. It would certainly be useful to devote another round of discussion to this issue. (I am all for it.)
Comment #32 July 21st, 2026 at 9:54 pm
Gil #31, thank you for the kind words and for remembering Itamar, the oracle from Givat Ram, a real mentsch and a giant in all things quantum. One minor correction for the record: I was his MA student in 1998, not PhD. And my work, including the 2009 paper you cite, has benefited from many conversations with him. The way you split the burden of proof, I think, is the right formalization of what I’ve been calling checking the noise conditions rather than assuming them.
Comment #33 July 21st, 2026 at 11:42 pm
Stewart Peterson #21: Do you have some reason to believe that even scalable quantum computing would bring a speedup to simulating those partial differential equations for controlling fusion in real time? Because I think that’s a case where even the quadratic speedup from Grover’s algorithm doesn’t apply.
Comment #34 July 22nd, 2026 at 10:39 am
Scott #4: About the Haber-Bosch process:
The planetary boundaries report indicates that fertiliser disruption of the N & P cycles looks extremely serious, perhaps even on the scale of climate change.
https://www.stockholmresilience.org/research/planetary-boundaries.html
Jevons suggests that the Haber-Bosch process becoming even more efficient could be disastrous, certainly for existing ocean life, but quantum computers might not improve efficiency there anyways.
Comment #35 July 22nd, 2026 at 3:39 pm
At this point, I’ve little hope that quantum computers wind up being impossible. Now our world would be a much better place if quantum computers were impossible, because elliptic curve cryptographic is really wonderful for privacy, and the post-quantum stuff lacks many features.
I’m wishfully thinking quantum computers might cost enough to bankrupt any nation that tries to build one, say $10 trillion for say a 2000 logical qubit machine, or whatever is required to break Ed25519, inflation adjusted to whenever they finally get built.
I’m not so hopeful even there though, probably quantum computers would cost only a measly $1 trillion for a 2000 logical qubit machine each, so only 30 x more than the Manhattan project, and cheap enough that the US and China do build them. At least they’ll stay out of the price range for startups, google, etc.
If we’re very lucky they’ll never benefit from Moore’s law either, not even the flavor from which atomic bombs benefited, or maybe they are extremely slow and they never get cheaper but they do get faster after investing more & more trillions.
Comment #36 July 23rd, 2026 at 2:39 pm
Hi Scott, Hagar, everybody,
Scott has argued that, to show that quantum computational advantage is impossible, it is not enough to demonstrate that realistic models of noise do not permit quantum fault tolerance. One must also explain how realistic quantum evolutions can be simulated efficiently on classical computers.
Let me draw an analogy.
Is the complexity class NP—and the P versus NP problem—actually relevant to the way mathematicians prove theorems and to what one might call the “creativity gap”?
This question has been the subject of an ongoing discussion between my good friend Avi Wigderson and me for more than two decades. Avi has consistently advocated a strong affirmative answer, arguing in papers and lectures that the kinds of statements mathematicians seek to prove are naturally modeled by NP problems (and sometimes by NP-complete problems), and that the P ≠ NP problem captures an essential feature of mathematical proofs: they may be hard to discover but easy to verify.
I tend toward a more skeptical view. In my opinion, human mathematical activity is constrained by feasible computational processes, and P ≠ NP is, at best, a metaphor for the gap between verification and discovery. There is indeed a gap between proving and verifying, but human proofs—like other human activities—are themselves generated by efficient computational processes.
The remarkable progress in formal proof verification a few years ago provided some support for Avi’s position by emphasizing the distinction between finding proofs and checking them. On the other hand, the recent progress of AI in mathematics may be viewed as lending strong support to my position, suggesting that aspects of mathematical creativity may be far more algorithmic than we had imagined.
The point is that even if my position suggests that human mathematical ability can ultimately be described by efficient algorithms, it does not tell us what those algorithms are. By analogy, even if the skeptical position suggests that realistic, robust quantum evolutions admit efficient classical algorithms, it does not necessarily tell us what those algorithms are.
It is conceivable that AI tools will eventually help uncover efficient classical descriptions of realistic quantum evolutions, just as they may illuminate the algorithmic aspects of mathematical creativity. Ironically, progress on these two analogous questions may ultimately come from the same algorithmic tools.
One important difference between the question of whether human creativity can produce proofs of NP-complete statements and the question of whether quantum computational advantage is possible is that the latter is not merely a romantic philosophical belief—it also serves as the basis for multi-billion-dollar scientific and technological investments.
Comment #37 July 23rd, 2026 at 7:44 pm
jonas #33:
In the algorithmic sense, no, not at all. (In the hardware sense, maybe. See below.) I deeply want it to be the case, and I also understand that the universe does not arrange itself around what I deeply want. Nobody in the field is working on active control, and that’s why. The consensus of fusion researchers agrees with you.
That said, I’m not aware of any results that indicate that a quantum PDE solver is not worth working on, and until there is such a result, I think work on one should continue and I’ll keep paying attention to major developments in QC.
I also want QC research to continue because, even if a successful QC is no faster per cycle than a classical computer, it is entirely possible that the engineering necessary to make a QC run at all could make each cycle 10^7 faster. Let’s say, for example, that a successful QC, for some non-quantum boring engineering reason, needs a photonic coprocessor – and that coprocessor is the 10^7 speedup. I don’t need the QC in that case, but I sure need the research that went into making a QC viable.
Also, and please do correct me if I’m wrong, but as I understand it, the inverse of my original question could also be true. It’s also possible that the hypothetical successful QC itself runs 10^7 faster than today’s best classical computers, because the QC can only run on hardware that happens to run 10^7 faster anyway – i.e., that there’s no quantum algorithmic advantage, but you need the QC hardware, running simulations of classical algorithms no faster than an equivalent classical computer, because there’s no practical way to build an equivalent classical computer.
Comment #38 July 24th, 2026 at 9:04 am
Gil Kalai #36
also what’s often ignored is that, for any particular problem, there’s a massive variety of instances, some easier to solve, some harder to solve, all with their own solving strategies.
Comment #39 July 24th, 2026 at 12:38 pm
[…] entitled The NISQ Trap: Eight Years of Demonstrations the Hardware was Built to Lose. (There is a post about it and an interesting discussion on Shtetl-Optimized.) This joins an earlier paper of Amit’s […]
Comment #40 July 25th, 2026 at 2:46 am
Scott, it was open-minded of you to discuss Amit’s paper here on your blog, bravo. Still, I have the impression that you, and the quantum computing community in general, look on Amit and Gil and some other “sceptics” as “troublemakers that have to be proven wrong”. To me it seems the community itself would profit if it followed their lead and actively identified and addressed problems which seem to be a “red brick wall” in the development of a large quantum computer. I borrowed this term from the “International Technology Roadmap for Semiconductors” (ITRS reports 1999–2016) for the development of classical computer chips. I quote from the ITRS 2009 (https://www.semiconductors.org/wp-content/uploads/2018/09/1_Executive-Summary.pdf): “The ‘red’ is officially on the Roadmap to clearly warn where progress might end if tangible breakthroughs are not achieved in the future. … There can be a tendency to view any number in the Roadmap as ‘on the road to sure implementation’ regardless of its color. To do so would be a serious mistake.”” Does the quantum computer community really think there are no red brick walls in their roadmaps, when there were red brick walls in all 17 ITRS reports?
Comment #41 July 25th, 2026 at 8:55 am
InquireR #40: To the extent that Gil Kalai identified a “red brick wall,” he turned out to be wrong! He said that at the scale of 50-100 qubits, we’d see correlations in the errors of a kind that would prevent quantum fault-tolerance from working. But the requisite experiments have now been done, and there are no such correlations. Instead, the total circuit fidelity just scales like the gate fidelity to the power of the number of gates, as in the simplest models of noise. To maintain his position, Gil has been forced to the ludicrous extreme of claiming that all the experiments by different labs that show this must somehow be invalid.
As for Amit Hagar, he doesn’t even claim to have identified any “red brick wall”! He explicitly says that scalable fault-tolerant QC is perfectly possible for all he knows.
So I don’t understand what I’m supposed to be paying attention to here that I’m not already.
Comment #42 July 25th, 2026 at 9:45 am
Scott,
It seems to me that a ‘red brick wall’ as used by the ITRS report isn’t a ‘prediction,’ it’s simply an achievement that is necessary for future progress but which is not certain to be achieved. In that respect, ‘at the scale of 50-100 qubits, we’d see correlations in the errors of a kind that would prevent quantum fault-tolerance from working’ absolutely qualifies! If that was not achievable, that would be a serious roadblock to the development of QCs.
Overcoming a ‘red brick wall’ isn’t a sign that the wall was ‘wrong,’ it simply means the necessary step was achieved.
Comment #43 July 25th, 2026 at 1:10 pm
Going back to 2018, I think most people, me included, understood the “NISQ era” hope as “the existence of somewhat-noisy 50-qubit machines opens up an avenue for algorithmic experimentation, mainly via exploration of heurestic quantum algorithms, optimistically we’ll have a better-than-classical performance on some concrete problem”. This is also my reading of Preskill’s 2018 “Quantum Computing in NISQ era and beyond” paper. With this meaning in mind, I do think that “NISQ era” has been a failure, or at least a disappointment, with main outputs being
(1) hundreds or thousands of various QAOA and VQE papers which didn’t yield much of interest
(2) the quantum supremacy experiments, while successful, also feel unsatisfactory due to the sampling-based nature and also the fact that they were built to suit the quantum machine at hand
Comment #44 July 25th, 2026 at 4:47 pm
Scott P. #42: OK, but in that case it shouldn’t be called a “brick wall”! It should be called a styrofoam wall or something.
Comment #45 July 25th, 2026 at 4:51 pm
djmati #43: Your information is somewhat outdated. We now have 50-100 qubit NISQ simulations of OTOCs, the Fermi-Hubbard model, and more, which actually provide new information of potential interest for condensed matter physics.
Also, the NISQ era isn’t over yet! And the next couple years should be pretty exciting ones, now that there’s finally hardware that actually works.
Comment #46 July 25th, 2026 at 8:15 pm
Scott #45
> We now have 50-100 qubit NISQ simulations of OTOCs, the Fermi-Hubbard model, and more, which actually provide new information of interest for condensed matter physics.
Ah, but do they provide information of interest to condensed-matter physicists? Do you know of a paper primarily by condensed matter physicists that treats a result from a QC experiment as providing new insight into the Fermi–Hubbard model?
Comment #47 July 26th, 2026 at 1:31 am
Greetings from Philadelphia, where I am taking part in ICM 2026. It is both exciting and hectic here. Let me make just a few remarks about Scott’s comment #41.
1) “To the extent that Gil Kalai identified a ‘red brick wall,’ he turned out to be wrong! He said that at the scale of 50–100 qubits, we’d see correlations in the errors of a kind that would prevent quantum fault tolerance from working.”
In 2006 I proposed a conjecture asserting that entangled physical qubits are subject to correlated errors, and I discussed it in several subsequent papers. As far as I can see, this conjecture, if correct, poses a serious obstacle to quantum fault tolerance. I recently returned to this conjecture in my paper The Fully Depolarizing Noise Conjecture for Entangled Physical States: A Twenty-Year Perspective. (It is still a draft, and comments are most welcome.) Current NISQ devices already provide opportunities to test the conjecture experimentally in the near future.
Scott’s claim that current NISQ experiments (assuming their reported results are correct) have already refuted my conjecture is itself incorrect. This brings me to the next point.
2)“But the requisite experiments have now been done, and there are no such correlations. Instead, the total circuit fidelity just scales like the gate fidelity to the power of the number of gates, as in the simplest models of noise.”
The assertion that the total circuit fidelity scales like the product of the gate fidelities does not contradict my conjecture. Fidelity measures estimate the probability that a circuit is executed without any error. They are not sensitive to the correlated structure among the error events that do occur.
3) “To maintain his position, Gil has been forced to the ludicrous extreme of claiming that all the experiments by different labs that show this must somehow be invalid.”
I have certainly not studied every experiment. I studied the 2019 Google experiment carefully and have looked at several others. There are good reasons to question the claimed agreement between the product of the gate fidelities and the measured circuit fidelity.
One reason is that, even today, more than six years after the publication of Google’s paper, the individual gate fidelities have still not been disclosed. Consequently, the calculations reported in the paper cannot be independently verified, either from data released by Google or by reconstructing the missing data from the figures in the paper. I also have concerns about several other aspects of the Google experiment.
4) One issue that I find particularly puzzling concerns Scott’s position on point (2). For years, Scott has argued that the observed scaling of circuit fidelity with the product of the gate fidelities refutes my correlated-error conjecture. For years, I have explained why this observation—even if taken at face value—does not contradict the conjecture. This is a simple mathematical point, and I genuinely do not understand the source of our disagreement.
Comment #48 July 26th, 2026 at 9:44 am
Scott #41 In the vein of Scott P. #42: to identify “red brick walls” is a constructive enterprise, even if those of Gil were all already overcome, you and in particular the experts on QC hardware should follow his quest to identify the ones still open. Having said that, I feel, in agreement with Amit, that it is an open question whether e.g. the Google group “saw no correlations in the errors of a kind that would prevent quantum fault-tolerance from working”, down to the required error rate for useful QC. As a physics experiment testing a 100-qubit architecture their agreement of the predicted error suppression factor Λ from simulation with the experimental value to within 14% was an impressive achievement. Interpreted as a first test chip for a useful QC, such a highly significant deviation (the error on experimental Λ is about 1%) seems at least a red flag, because it means that there is a major noise source which is not understood. In the worst case, the nature of this noise might confirm Gil’s basic idea for larger d. So I agree with Craig who wrote (https://scottaaronson.blog/?p=9425#comment-2021518): “I intend to declare victory over Kalai and other skeptics somewhere around 1e-12 error per logical Clifford”. The red brick wall here: for the industrial development of a large QC chip, in practice the agreement between simulation and experiment has to improve by about an order of magnitude.
Scott #44 Yeah you have a point, a better term would have been “red walls”, they could be made out of styrofoam, bricks or be a hard-stop frontier a la Gil, making useful QC as impossible as, say, interstellar travel.
Comment #49 July 26th, 2026 at 12:30 pm
The field is really in an unfortunate position.
The current state of the art pretty much requires two phds to interpret it (and even so, experts seem to disagree): systems that basically are nothing more than an organized macro quantum object, which samples its own state, randomly. And the result can’t really be verified easily because by definition quantum systems are not classical systems.
Experts hope to make that useful in the same way Monte-Carlo simulations are useful.
But the era of true quantum computation will only start once Shor’s algorithm is implemented and the number 15 is consistently factored, an unambiguously verifiable achievement that anyone could understand.
But since prime factorization is the corner stone of cryptography, this milestone will probably be kept secret for as long as possible because whatever state entity does it would want to keep that edge as long as possible…
Comment #50 July 26th, 2026 at 12:50 pm
To keep with Scott’s favorite analogy, it’s as if the Wright brothers hadn’t yet achieved full powered flight, but their prototype would be able to roll along for a while and then leap up in the air for about 5 seconds. Then experts and investors would be endlessly arguing whether this achievement already demonstrate the superiority of powered flight over cars because cars just can’t leap over a fence like this prototype can, at least when everything is timed just right, with the right amount of wind, and the right spacing of fences…
Comment #51 July 26th, 2026 at 1:26 pm
Shtetl-Randomized #50: The Wright brothers’ first flight lasted only 12 seconds, not much more than the 5 seconds in your hypothetical. What mattered was that they’d mostly solved the technical problem of how to keep an aircraft stable (via dynamic three-axis control), much like people are now finally solving the technical problems of how to keep qubits stable.
For whatever it’s worth, hopefully we’d agree that, with hindsight, virtually the entire world erred in the early 1900s by paying too little attention to what was happening with rudimentary experiments on powered flight, rather than too much attention.
Comment #52 July 26th, 2026 at 4:20 pm
Scott #51
> For whatever it’s worth, hopefully we’d agree that, with hindsight, virtually the entire world erred in the early 1900s by paying too little attention to what was happening with rudimentary experiments on powered flight
Did it? The Wright brothers had been negotiating with the US, UK, France, and Germany, starting from 1905, finally signing a contract with the US Army in Feb 1908, before powered flight had even been publicly demonstrated in the US. Airplanes were used in WW1 by all major participants, and their use was publicized and romanticized extensively, yet the first commercial airline operating at a profit without any sort of subsidy was inaugurated all the way in 1936 (see https://en.wikipedia.org/wiki/Douglas_DC-3). Do you have strong reason to believe that the technology didn’t really need this time to mature?
Comment #53 July 26th, 2026 at 7:32 pm
Scott #51
hehe, it’s interesting that the Wrights were apparently very secretive about their efforts
https://perfectmanifesto.com/wp-content/uploads/2022/06/wright-brothers-new-york-times.jpg
Comment #54 July 26th, 2026 at 7:49 pm
The improvement happened mostly in the first two or three decades:
1906 – the Wrights fly at 38 mph
1935 – Howard Hughes breaks the speed record for a single seat propeller plane at 352 mph (900% improvement)
2017 – the new world record is at 531 mph (50% improvement over 82 years)
Comment #55 July 26th, 2026 at 8:36 pm
Vladimir #52: Yes, if someone in the early 1900s only cared about the next few years, they might well have been paying too much attention to experiments on powered flight. If, on the other hand, they cared about the next few generations, they were almost certainly paying too little attention. And this is a pattern that one sees repeated throughout history.
Comment #56 July 26th, 2026 at 8:40 pm
Shtetl-Randomized #54: Yes, essentially all technologies asymptote at some point, when they run up against physical and economic limits. Since quantum computing is only just now starting to work, it seems due for rapid improvement, before it too enters an asymptotic phase (unless AGI makes all of this irrelevant, as one typically adds nowadays).
Comment #57 July 27th, 2026 at 7:49 am
Scott #56
except revolutionary technologies do need some steady return to make the (often exponential) growth self-sustaining.
It’s not like powered flight was a money sink until the very first airline was finally ready to go.
But at least QC is small scale technology, it doesn’t rely on large scale infrastructure like AI, which revenues can’t yet offscale its gigantic investments (recent cost increase per token of over 10x are pretty ridiculous).
QC is similar to nuclear fusion, with no return until it fully works, but nuclear fusion has some well defined goal (more energy out than what goes in… but even that clear definition is being twisted to fool investors) while QC still very much looks like a solution in search of a problem.
99.9% of people who understand CS don’t even understand QC… recently I was discussing the limitations of AI with a very experienced coding manager, at some point he told me “AI will tremendously benefit from quantum computing because all the possible answers will be considered at once”, I told him that’s not how QC works and started to explaining about how the final measured solution path is actually picked randomly and how it all requires careful interferences between the paths, etc but the more I explained the more he was looking at me as if I was making it all up… so I gave up.
Comment #58 July 27th, 2026 at 9:44 am
I hope not the case but the observation that inventions (call it-a physical manifestation of a new idea) have an early growth curve that goes asymptotic could potentially be applied to technology in general. The easy things were done and now technology in general is reaching an asymptotic growth curve with ever greater inputs required for ever smaller impacts. I guess AI could be proposed as a counterexample but no certainty that it will in fact be a counterexample.
A case further could be made that in the early growth phase the tendency is to underestimate rate of progress and real impact but now in the asymptotic phase the tendency is to overestimate rate and impact. There is now an entire infrastructure devoted to profiting from overestimation of new technology by others.
A couple weeks ago I was looking for data with Google and Gemini provided an unsolicited table with maybe ten entries. I immediately saw that all entries were low by the same factor of 10. There was nothing in the text to explain the discrepancy and I concluded it must have duplicated a table but missed the units of the table. I was surprised to see this type of error at this point in AI development.
Comment #59 July 28th, 2026 at 7:31 am
In the end there’s only supply and demand, with value set by bid price vs offer price equilibrium. And then costs have to be lower that demand x value, otherwise you’ll never grow.
No amount of bullshit and hype can overcome those realities in the long run.
If your tech requires trillions in initial investment before you can truly assess the demand and value, that’s very risky to say the least.
Comment #60 July 28th, 2026 at 7:59 am
For the vast majority of people, AI is just going to be an improvement on web searching, which has been a free service for decades now.
They put text in, they get a better answer. But most of the time people don’t even have any meaningful text to put in, certainly not for hours a day – they’re just happy with some infinite stream of random/targeted content served to them.
Then for “professional work” AI is okay assuming you have the mental energy to constantly monitor it to catch the bullshit asap and work around it by putting it back on the right track.
From personal experience I can say that the latest model iterations aren’t that much better at coding than the previous ones from 6 months ago, they’re only better at apologizing/making excuses, or even plain deception when you catch them making mistakes. That was somewhat alright when tokens were near free, but now that a few hours of this kind of back and forth is costing 100$, you may quickly run out of patience.
The best is to use them to learn about various known approaches in an unfamiliar topic, then have them do very specific coding tasks. Don’t trust them to make any good high level design decisions.
Comment #61 July 28th, 2026 at 8:08 am
The Anecdote
About twenty years ago I was in Castellanza, north-west of Milan, for a work project. At lunch we went to a trattoria run by a Roman family – warm, unpretentious people who clearly knew what they were doing – serving “penne all’arrabbiata”. The owner warned me the arrabbiata was very very arrabbiata. I ordered it anyway. The plate arrived steaming, and after a few bites I could no longer tell whether the burning in my gums came from the temperature or from the chili.
Which, it turns out, is roughly where the NISQ debate is.
The Punchline
Hagar: “The dish is excellent – I want to be clear about that. But I can’t tell whether the burn is coming from the heat or from the chili, and neither can you. I should have tasted the sauce on its own first. It would have taken thirty seconds, and we could still do it – there’s a spoon right there.”
Aaronson: “Heat is heat, chili is chili. If you think they conspire, tell me how – what is it about a hot plate that makes the peperoncino stronger? The plate is hot but perfectly edible, and your gums are burning, which is precisely the point: it proves gums can burn.”
Both agree, for the record, that the real test is the next dish.
Comment #62 July 28th, 2026 at 2:29 pm
Matteo Vitturi #61: I confess that I didn’t understand your analogy—like, at all. Then again, I’m not huge on arrabbiata or other extremely spicy food! 🙂
Comment #63 July 28th, 2026 at 3:24 pm
Dear Prof. Aaronson,
I apologize; I realize now that my post is out of place. It won’t happen again.
Regards,
_M
Comment #64 July 29th, 2026 at 6:23 am
S-R #60
My view is that even with the limitations you point out AI’s are better at tasks constrained only by logic (Maths, CS) than open tasks in the physical world. Very specific tasks can be accomplished by specially coded Agents (if you detect X destroy it) but general tasks requiring properly accounting for all the pertinent physical constraints is beyond AI capacity at this time. The rejoinder might be that Agents should be considered tools that AI uses to accomplish physical world tasks but there is still the problem of the decision which Agents are required to properly account for all the messy physical world constraints.
As an example I asked Chat to use a finite element scheme to calculate heat flow in an insulated carbon steel bar. It did so without problem but when I raised the input temperature above the melting point of carbon steel it continued as it had before so no recognition of the phase transition and so no accounting for the thermodynamics of the phase transition nor the change in specific heat of molten carbon steel.
My conclusion based on this and other evidence is that at least currently to get an appropriate answer from Chat is that you must be very specific what you ask for and then carefully check the answer and see if you must goad it to provide a better answer. I think this is similar to your observation that it shouldn’t be allowed to make high level decisions. Ultimately coding performs some real world function and without a reasonable model of the real world then not possible for AI to develop suitable software. I guess that leaves Maths as an area where no need to have a reasonable physical world model.
It seems to me that Sam Altman has created a new event to create a marketing spectacle. It may be true in some sense but the claim that an AI purposefully broke out of its containment and purposely hacked some other system is very difficult for me to believe. What, Chat thought there was information housed there about the government conspiracy to hide ET contact?
Comment #65 July 30th, 2026 at 2:22 am
Hi Scott,
The Jacobian conjecture was disproved, apart from the fact it was by anthropic with AI assistance ( which wasn’t really necessary or too hard, it’s just mathematicians had more important things to do apparently), it has implication on quantum math.
Namely, The 3×3 example means that SU(3) has an endomorphism which is not an automorphism, which can certainly have physics applications.
https://mathoverflow.net/questions/513392/consequences-of-the-disproof-of-the-jacobian-conjecture-on-mathematical-physics
any thoughts on quantum computing implications?
Comment #66 July 30th, 2026 at 3:23 am
Itai #65: Of course I read about the disproof of the Jacobian conjecture and of course it’s very exciting! I have no idea what the physics implications are if any, but anyone who does know is welcome to share here.
Comment #67 July 30th, 2026 at 8:06 am
OhMyGoodness #64
AI is usable for math and cs not so much because of logic but because proposed solutions for those activities are verifiable and comparable.
For example with software you can compare two competing solutions: either they compile or do not. It they run or crash. They pass a series of tests against requirements or don’t. One runs faster than the other (but this may vary with input). So there’s a somewhat robust framework to iterate and improve quality.
That said, once the solution space becomes large enough, math and cs are tough optimization problems, and optimization over concave spaces is np-hard (unlike convex optimization).
Comment #68 July 30th, 2026 at 8:58 am
While this discussion thread has been one of the most informative and with high quality debates, for the general public it leaves some of the important questions open
1. Can current NISQ QCs provenly used with substantial advantages over classical computers, even if it is for a very narrow range of useful applications ?
2. What are those applications that need a tip over to full QFT, other than breaking current cryptography.
3. Given that the current advantage of even full QFT QCs is known to be for 2 categories of applications, i.e. Quantum simulations and breaking cryptography , where is the investment justified from a commercial perspective, specifically which sub areas of Quantum simulations
It would be helpful if someone can provide a pragmatic picture of the current situation and near future.
Comment #69 July 30th, 2026 at 12:20 pm
I’ll go ahead and use Prasanna #68 as an excuse to answer my own question in #46, since it seems no one else is going to:
> Do you know of a paper primarily by condensed matter physicists that treats a result from a QC experiment as providing new insight into the Fermi–Hubbard model?
Phasecraft posted two 2D Fermi-Hubbard papers (https://arxiv.org/abs/2510.26300 and https://arxiv.org/abs/2510.26845) on Oct 30 2025, one using Quantinuum’s hardware, the other using Google’s. ChatGPT 5.6 Sol identified 38 2D Fermi-Hubbard papers, i.e. papers whose main object of scientific interest is the 2D Fermi-Hubbard model, published after Phasecraft’s papers. Out of these, 0 (zero) cited either Phasecraft paper. Among the dozens of papers citing Phasecraft’s, ChatGPT found one condensed matter paper. It cited Phasecraft + Quantinuum once, in the introduction, as a motivation for developing better classical simulation techniques.
Comment #70 July 30th, 2026 at 2:21 pm
S-R #67
I was referring to the broader context so the software works as intended or it doesn’t for the use client. In other areas just the same, the implementation of say an engineering design safely fulfils the intended function or it doesn’t. Certainly if software doesn’t compile it doesn’t work as intended but that is not a sufficient condition that it can accomplish its intended use by a client.
AI’s certainly perform at a very high level on standardized tests now unless the test have been tweaked in a manner inconsistent with a Google search on the topic. If questions are tweaked the performance declines considerably so in that sense equivalent to a lower level check the box engineer with access to Google. You will definitely get an answer and it’s then the obligation of those that have responsibility for quality to carefully check the answer. The recent math finds by AI are way above this level of engineer.
I saw that technical people at SpaceXAI were surprised that Musk told them he wanted them to produce a fully AI software company in a box. He must not much understand the real world limitations of AI at this time.
Weakly related-
I am always amazed at the superior performance of chimps vs humans on computer based number flash tests. It’s amazing to me.
Comment #71 July 30th, 2026 at 3:08 pm
S-R #67
Also it wasn’t my point that math is logical and other areas aren’t but that math is constrained only by logic while physical world endeavours have numerous interacting constraints from physical laws and local conditions as well as regulatory and legal restraints and these last two may or may not be logical.
Comment #72 July 30th, 2026 at 3:49 pm
Sorry but just one other thing-
Waymo is a good example of AI agents in the wild with a very specific function. Its AI’s know the traffic rules better than any human drivers on the road, and cars have better sensors than humans, but it is still puzzled by unusual situations.
I am not demeaning Waymo and very happy they are in the wild (although sadly I have never ridden in one) but they do react improperly to unusual situations. The problems I know about are not reacting properly to police cars with flashers on, reaching flood waters, and improperly responding to construction zones. All of these required new coding.
I understand there is a problem in Austin now with violations of parking markers and they are incurring thousands of dollars in parking fines. The list however is still extensive of unusual situations that could prompt improper actions by Waymo cars.
Comment #73 July 30th, 2026 at 4:43 pm
Waymo should enter a car in F1 with one of their AI drivers. That would be a historic level marketing campaign.
Comment #74 July 30th, 2026 at 6:40 pm
One quantum supremacy thing I’d like to see is whether the very construction of a quantum computer shows a shrinkage of spacetime around the entangled qubits, like in the “gravity from entanglement” movement. Of course that’s quantum supremacy since a classical computer can’t demonstrate the same thing, heh. But IDK how to calculate whether the shrinkage could be experimentally detectable.
Comment #75 July 30th, 2026 at 6:42 pm
Scott #66, John Baez has some Mathstodon posts about physics implications of the Jacobian conjecture being disproved. Something something something about the algebra of the standard model. But, quantum supremacy doesn’t seem to figure in.
Comment #76 August 1st, 2026 at 1:31 pm
off topic: OpenAI Astra has solved ten open math problems, including two from quantum complexity …
Comment #77 August 1st, 2026 at 2:06 pm
Sorry if this was already discussed, but what do you guys think about https://en.globes.co.il/en/article-ibm-teams-with-israels-qedma-for-quantum-breakthrough-1001550907 ?
Comment #78 August 2nd, 2026 at 9:42 am
JoshP #77
The paper behind this story (https://arxiv.org/abs/2607.24937) is practically a textbook example of QC as a tool in search of a problem:
– The model they study is, broadly speaking, a kicked-Ising magnet. There’s some previous work on models in this family, but it’s a tiny subfield, nothing like the Fermi-Hubbard model or quantum chemistry.
– The geometry they study was dictated by the underlying IBM hardware, so, unsurprisingly, this combination of model and geometry appears not to have been studied before IBM adopted heavy-hex connectivity for its quantum processors.
– Both the model parameters and the initial state were fine-tuned using exact classical simulations of small systems to produce behavior that, at larger sizes, would simultaneously lie beyond the reach of approximate classical methods, remain within the reach of existing quantum hardware, and appear interesting.
Props to the authors (disclaimer: I know several of them personally and professionally) for being reasonably upfront about these and other limitations of their work.
Comment #79 August 4th, 2026 at 4:36 am
Vlad #7i
I took a couple quarters of Organic Chem classes with Chem E’s, Chem, and Pre-med students outside my major as an undergrad. I found interpreting NMR to be very pleasing. The measurement curves were so harmonious and beautifully ordered. Unfortunately a subset of the students disliked me for “busting the grading curve” which wasn’t pleasing.
I enjoy seeing your posts again.
Comment #80 August 7th, 2026 at 4:01 pm
I asked ChatGPT for a joke about Anthropic and here is the result-
Anthropic says its AI should be helpful, honest, and harmless.
My group chat read that and said, “Great—now build one that’s available on weekends.”
Or another:
Working at Anthropic must be interesting. Imagine your performance review:
“Excellent work. The AI is brilliant. We just need it to stop apologizing to the office ficus.”
Or a lighter one:
Anthropic and OpenAI are a bit like two neighbors with very smart dogs.
Every few months, one says, “Ours learned a new trick,” and the other quietly opens a laptop.
And about quantum computing
I tried debugging a quantum computer. Every time I found the bug, it insisted it had also been fixed.
Quantum computers are great coworkers. They can work on every possible solution at once—and still tell you, “It depends.”
I asked a quantum computer if my code would compile. It said, “Yes, no, and don’t observe it until the demo.”
A quantum programmer walked into a bar. According to the wave function, they also stayed home.
Quantum computing is the only field where saying, “The problem disappeared when I looked at it,” sounds almost scientifically plausible.
There is actually a book on Amazon, “700 Jokes by ChatGpt”, but why would anyone buy it? Chat GPT is a veritable font of free .jokes.