The Evidence for Quantum Supremacy

A newly revised paper reviews the outstanding evidence for quantum supremacy:

A brief history of quantum vs classical computational advantage
Ryan LaRose

In this review article we summarize all experiments claiming quantum computational advantage to date. Our review highlights challenges, loopholes, and refutations appearing in subsequent work to provide a complete picture of the current statuses of these experiments. In addition, we also discuss theoretical computational advantage in example problems such as approximate optimization and recommendation systems. Finally, we review recent experiments in quantum error correction -- the biggest frontier to reach experimental quantum advantage in Shor's algorithm.

So has it been proved, or not? No, not really.

It seems at this moment in history we are just on the boundary between quantum and classical computational advantage, and in the near future we expect the status of computational advantage to continue shifting between quantum and classical. We hope that this brief history helps to propel readers to the research frontier and develop new ideas which advance both classical and quantum computation.

There is still no convincing experiment that quantum computers are possible.

I would have predicted that by 2026, quantum computing would be proved possible, or investor money would dry up. I was wrong. Investor enthusiasm for QC is stronger than ever. The Trump administration just instested $2 billion into QC, mostly in startup companies. There are about five of these companies worth about $10B apiece. Most of them went public in sneaky financial maneuvers where they did not have to disclose all their risks.

New Scientist magazine just posted a video on Quantum Computers Are More Dangerous Than You Think:

On Q-Day, your privacy will be at stake. This is the moment when quantum computers break the encryption protecting the modern world, bank transactions become readable, private messages get exposed and even state secrets become vulnerable.

For years it sounded like sci-fi, something that was decades away from happening, if it happened at all. But now, research suggests that we may be hurtling towards Q-Day at a rapid speed.

In this video, New Scientist uncovers why many experts think the countdown to Q-Day may already have begun, and explains how quantum computers work and why these machines could both threaten the security of the modern world and unlock breakthroughs that could change our lives. Special thanks to Quantum Motion for letting us film at its facilities.

If and when the countdown to Q-day starts, I think that we will have about ten years. Only the computer security companies, NIST, and the US Dept of War need to prepare now.

For most people, SSL/TLS/SSH is just a way of getting assurance that a web site is real, and that no one is stealing a password or credit card number. If Q-day hits, you will just update your browser and not notice the difference.

The Bitcoin blockchain would have to be restructured, and that is feasible as long as there is a consensus on how to do it. A consensus could take a couple of years.

New Carroll Podcast to Defend Many-Worlds

Sean M. Carroll is frustrated by physicists preferring Copenhagen over many-worlds, so he posted a podcast with his views:

Solo: Looking Quantum Mechanics in the Eyeball | Mindscape 355

One of the major obstacles to understanding quantum mechanics is the difficulty we have in simply accepting what the theory itself is telling us. The problem is that we know what the everyday world looks like -- stuff, arranged in space, evolving through time. So we can't resist the temptation to impose that picture on the quantum description, even if it's not actually there. In this solo episode I talk about what it means to take quantum mechanics at face value, and the difficult work involved in understanding how the everyday world of our experience fits into the picture.

For a more technical description, he refers to his paper, Reality as a Vector in Hilbert Space.

This podcast is a defense of many-worlds theory. He says people believe in textbook QM because they are stupid:

And I suspect that most of the people in the physics survey who said that they're Copenhagenists don't actually have that view themselves, but mostly because they haven't thought about it very carefully.

He has learned that he loses his audience if he talks about the parallel universes too much.

[24:35] Many worlds by contrast and we're not going to get into the worlds aspect of many worlds that much because it's actually not relevant for what we're talking about today. I've often said that many worlds is not mostly about the worlds. The worlds come along. They're there, no doubt. But what many worlds is really about is saying there's no such thing as collapse.

I think the problem here is that he makes several serious conceptual errors.

First, he misunderstands probability. Probability is not a real physical thing, like energy or temperature, but it is essential to all scientific theories. Let me repeat. All scientific theories are based on probability predictions.

You might say: No, when Nasa sent the Artemis II rocket around the Moon, it was all deterministic Newtonian physics.

I say: Not correct. Nasa calculated the splashdown location as a probability distribution.

Next, a probability is a prediction that something will happen, with other things not happening. If I say a coin toss has a 50% chance of heads, I am referring to getting heads, and not getting tails. If I get heads, I can then disregard any possibility of that toss being tails. For example, if I toss a coin three times, and the first is heads, then I can immediately eliminate the possibility of three straight tails.

The core concept behind many worlds does not even have anything to do with QM. It is: Throw away probabilities. Throw away definite outcomes. Assume all possibilities happen, in parallel universes.

If you toss a coin and get heads, it just means that you are in the universe with heads, and a parallel universe has tails. You cannot even say that the universes are equally likely.

When Carroll says (above) that "there's no such thing as collapse", he means that if you toss a coin and get heads, you cannot say that tails did not happen.

Carroll has no evidence for anything he says. His big argument is that it somehow simplifies QM to never predict any probabilities, never do any experiments, never accept any outcomes, and never reject any possibilities.

By eliminating QM's relations to the real world, he says we get more a pure and abstract theory where we do not have to worry about issues like what defines a measurement.

At 1:42:20, he denies that there should be any experimental test for many-worlds theory. He says "that's just not how science works."

On YouTube, a comment points out:

A very good introduction to the subject, but you dodge all the important critiques:

- Probability (Born Rule) is a huge problem for Many Worlds, but I know you are working on that.

- The Schrodinger equation is obviously wrong because spacetime is an assumed background. You dealt with space/locality a few times. There is work on entanglement creating space, and I agree so far, but how can QM/QFT get time to be emergent when it is a parameter not observable? (momentum is just a thick slice of time for mass position? - someone needs to handle that. What is the calculus of position and momentum in background-free local (infinitesimal) proper time?

- It seems that Hilbert Space changes dimension with the number of 'entities' in the system. But we know that 'entities' are variable (n particle quantum number is not defined). So we must immediately leap to the HS of the whole universe: a total matter/field equation that must be fixed, which defines everything (Wheeler/DeWitt). Anything less becomes some strange variable dimensional complex space - I don't buy that. [My personal world is computation and variable size matrices are just ... mathematically impossible. ] What happens with particle creation/destruction and second quantization - hint total hack!

- I don't see any contact with gravity - yes, AdS/CFT and holography, maybe perhaps with actual finite dS boundary defined by SR light cones, etc. but that has to emerge from large (in)finite HS, I don't buy it (yet). My tendency is to trust/believe the criticism from GR gravitationalists (Sir Roger, et al). I don't think you have addressed any of those criticisms (yet). You have to admit that background-free GR is much much more beautiful than background-dependent QFT (yeah, okay, subjective).

- Of all the symmetries in the SM, matter/antimatter and chirality asymmetry are the frontier. Yes, RH/LH neutrinos are vague/undecided/outside SM, and (maybe heavy dark) RH neutrinos could be the answer (cue Neil Turok) but GR people also have tentative answers for the background (Twistors, PIN decompositions, etc) I don't hear solutions coming from pure QFT formalisms.

I could go on, but enough already.

Carroll's excuse for ignoring all these points is "I have to confess that the whole idea of steelmanning is not really my vibe". [10:00]

Einstein's Friend Wrote a Relativity Paper

Hector Giacomini writes a new paper:

This note examines an apparently unpublished manuscript on special relativity written by Conrad Habicht in 1914 and made available online by the ETH-Bibliothek Zürich in December 2024. To the best of my knowledge, no study of its content has yet been published. Habicht was one of Einstein's closest companions during the Bern years. ...

The manuscript offers a clear and pedagogical presentation of special relativity.

Habicht was a friend of Einstein before 1905, so this might have given insights on where Einstein got his relativity ideas. Unfortunately it does not.

Habicht’s manuscript is much closer to the 1907 exposition than to the original 1905 paper. The 1905 article is remarkably austere in its historical framing: it begins with the magnet-and-conductor asymmetry, formulates the two postulates, defines simultaneity, and proceeds directly to the transformation laws and their consequences. It contains no historical reconstruction of Lorentz’s theory, no explicit discussion of the Michelson–Morley experiment, and no narrative account of the ether problem. The 1907 review article, by contrast, restores much of this background. It places special relativity within the history of the conflict between the Galilean principle of relativity, Maxwell–Lorentz electrodynamics, the stationary ether, negative optical experiments, and Lorentz’s work....

Habicht’s manuscript shows that, within a circle personally close to Einstein, special relativity could be presented through the more historical, Lorentz-centered, and electrodynamical framework that Einstein himself had adopted only two years after the 1905 paper. This manuscript reminds us that the history of special relativity was not transmitted only through the paper of 1905, but also through later acts of exposition, recollection, simplification, and reorganization.

When Lorentz's work is presented, it is really hard to understand what Einstein did that was original. In 1907, the theory was known as Lorentz-Einstein theory.

There is no reference to Poincare. This is bizarre, as it is known that Habicht and Einstein read and discussed some of Poincare's papers before 1905. Poincare's 1904-05 relativity papers were widely read in Europe. It is likely that Einstein knew about them in 1905. Even if he did not, he certainly knew in 1907, and Habicht knew in 1914.

The above paper says "the history of special relativity was not transmitted only through the [Einstein] paper of 1905". That 1905 paper was not even historically very significant. Much more important were Lorentz's 1895 and 1904 papers, Poincare's 1898-1905 papers, and Minkowski's 1907-08 papers. Special relativity as we know it came from those papers, and almost nothing came from Einstein's 1905 paper.

I think this Habicht paper is mostly interesting for what it does not say. If Einstein had some of the main ideas behind special relativity before Lorentz and Poincare published them, then Habicht would be the most likely witness. This Habicht paper could have credited Einstein with having some of the ideas before 1905. It does not. It is only known that Einstein told Habicht he was preparing a paper that “provides a new conception of time and space,” in May 1905.

Giacomini wrote other papers on relativity history, discussed here and here. The first paper was just updated.

Distinguishing Newton's First and Second Laws

Isaac Newton's three laws of motion are: (1) if F = 0 then a = 0; (2) F = ma; (3) actions have reactions.

The first law is a trivial consequence of the second. Why did Newton bother to state it as a separate law?

A new paper answers the question:

On the independence problem of Newton's first law Ido Yavetz, Ehud Aharoni Newton's laws of motion pose an apparent problem, sometimes referred to as "the independence problem": the first law seems to be a simple consequence of the second law, raising the question of why it was included as a separate law. Numerous answers to this question have been proposed in the literature. The main contribution of this paper is a novel answer which we call "the formal explanation." Unlike previous accounts it relies on mathematical formalism and argues that the definitions of Euclidean geometry necessitate the inclusion of the first law. We provide evidence in support of this claim. A second contribution is a comprehensive review of previously suggested explanations, which so far have often been treated in a fragmented manner, and a discussion of the plausibility of the various answers.

It turns out that many people have addressed this, and this paper has a new explanation.

Roughly, mathematicians did not always treat zero as a number. There are many examples in Euclid's Elements where an argument gets restated for the zero and nonzero cases, when a modern textbook would unify them. This paper shows that Newton's usage is consistent with Euclid's.

Newton did not have vectors either, so he had to state the directional components of F = ma separately. One version of his second law was:

”A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”

This is similar to Euclid, as he only wrote about nonzero quantities being proportional.

Randomness Cannot be Proved

There are scientists who believe in strict determinism, and say it is necessary to a scientific view. Albert Einstein was such a believer. In particular, they do not believe in free will.

I have criticized this as wrong, and I also point out the opposite view is also wrong.

Roman Schnabel writes in a new paper:

Experiments testing Bell inequalities [12, 13, 15] have proven that there are physical events that occur without a causal reason, i.e., that are truly random. The proof does not make any assumptions, in particular, the proof does not use QT but only pure mathematics and reproducible experimental observation. Regardless of the validity of QT, random numbers can be certified as truly random using an experiment to test Bell’s inequality [27]. It is remarkable that a truly random process can be proven as such. The only assumption made here was the reasonable but, in principle, unprovable one that there is no entity that has predetermined every single microscopic event in the universe in advance [28].

Others also say this -- that randomness has been proved, except for the silly possibility of superdeterminism.

The whole idea is absurd. No experiment or theorem could possibly prove true randomness. At best they could only prove that something is not predictable with the data and methods available.

Since QT is complete, as proven by Bell’s tests, radioactive decay is a truly random process. There is no causal reason, no cause that leads to decay before or after the half-life. If you start observing a single atom at any point in time, there is a genuine, equally weighted quantum mechanical randomness as to whether the atom decays before the half-life expires or only afterwards. ... Radioactive alpha decay occurs in a truly random manner, i.e., without cause, which is referred to as ‘spontaneous’ in quantum physics.

Yes, radioactivity seems about as random as anything could be. K-40 has a half-life of about a billion years. Decay statistics are predictable. But no one can predict when a particular potassium atom will decay.

Maybe the problem is that we do not the physics and technology to measure the K-40 state well enough. If we knew exactly how those quarks were bouncing around the nucleus a billion years ago, maybe we could predict when one will bust out.

I know that seems absurdly impractical, but the Bell argument says something else. It seems to say that some things are unpredictable if we assume a local hidden variable theory. Maybe that K-40 nucleus has a state that can predict the decay without using classical variables. Bell's theorem does not say anything about what can be done in a non-classical theory.

The paper has also been criticized:

The paper repeatedly suggests that Bell-test violations show that quantum theory is complete, that hidden variables cannot exist “in general,” and that some events happen without causal reason and are therefore truly random. We think these claims go too far. Bell’s theorem rules out local hidden-variable models only under a definite set of assumptions, including locality or factorizability, measurement independence, and an ordinary Kolmogorov probabilistic framework in which the relevant joint probabilities and expectation values are defined. It therefore does not, by itself, settle every broader question about causality, ontology, or completeness.

PBS TV just dropped a video on atomic clocks, and Sean M. Carroll makes his usual dopey appearance:

[0:00] [Narrator] Albert Einstein famously said that he didn't believe God plays dice with the universe. ...

[Carroll] [0:42] The basic idea of quantum mechanics, the thing that we really struggle with to get our heads around even as professional physicists, is that unlike any other version of physics, quantum mechanics separates what happens in a system when we're not observing it from what we see when we measure it. ...

[1:50] That opens up a whole world of questions. You know, what happens to the observational outcomes that are not observed? What picks out which outcome is going to happen? This is still what we're thinking about today.

He would argue that what happens is that the observational outcomes that are not observed slip off into a parallel universe.

I do not see how Carroll's struggles with QM relate to atomic clocks, the subject of the video. Yes, atomic clocks depend on the quantum mechanics of atoms having discrete energy levels, but Carroll's philosophy rants are not relevant.

Update: Carroll also has a new podcast on Free Will and Levels of Reality. Both Carroll and his guest are determinists who believe that free will is an illusion. Philosophers call this compatibilism.

Aaronson's Latest Lecture on Quantum Computers

Dr. Quantum Supremacy has posted a new lecture:

Title: The TRUTH About Quantum Computing
Date: 2026-05-13 @5:00PM

Abstract: Yes, scalable quantum computing should actually work! Sooner than many expect, which will create a huge headache when it breaks the encryption currently used to protect the Internet. But no, we don't think quantum computing can do most of what the popular articles promise in AI and optimization and so forth. Come to this talk to learn about why!

Somehow he has gotten to be the academic authority on whether quantum supremacy has been achieved, so I always check his latest opinion. He seems to be getting more confident, but it is still just a prediction. He says it may or may not be achieved. And that not to trust your RSA keys.

And another one:

Title: Scott Aaronson - Theoretical Computer Science and AI Alignment
Date: 2026-05-14 @1:00PM

Abstract: I'll survey some areas where I think theoretical computer science, math, and statistics can potentially contribute to the urgent quest to align powerful AI with humane values. These areas include: the watermarking of AI outputs, mechanistic interpretability (including Paul Christiano's "No-Coincidence Principle," and succinct digests of the training process to aid interpretability), and theoretical guarantees for out-of-distribution generalization.

Also on the subject, Dr. Bee dropped a new one today that starts:

In Einstein’s theory of general relativity, the time an object experiences depends on its acceleration. But time in quantum physics works more intuitively – it’s a universal parameter experienced by every object in the same way. In a new paper, physicists say they want to use a special type of clock to test that difference. Let’s take a look.

0:00 Quantum physics says that objects can be in two places at the same time. A group of physicists now says that they can also be at two times at the same time, ...

No, quantum physics does not say that objects can be in two places at the same time. It does not say that cats can be alive and dead at the same time.

Quantum computers are often explained this way, but QM really just estimates probabilities for different place. Once you observe the object, it is in just one place. Her statement is like saying: probability theory says that a tossed coin can be heads and tails at the same time.

Aaronson is an AI enthusiast: [11:40] AI is what "I would regard as, you know, maybe the most consequential technology, uh, that humans are ever going to be building."

Update: At the other extreme, Brian Greene released a new interview with an AI skeptic. The guy says that the AI LLMs are just a stupid trick of little value.

Sean M. Carroll Lectures on Many Worlds

NewScientist just posted a marathon series of math lectures, but almost half of it is from a 5-year-old lecture, Sean Carroll: The many worlds of quantum mechanics, that is not even on math. He gave a similar lecture last year, The Many Worlds of Quantum Mechanics | Dr. Sean Carroll.

My disagreements start early. Carroll says:

Why does 7:14 quantum mechanics have this reputation of being so hard? Here's the answer. There's an amazing feature of quantum mechanics that was nowhere to be found in classical mechanics which says that what you observe when you look at a system is not what you see.

What you see and what is really there are two different things. There's a difference between what a thing is when you're looking at it and when you're not looking at it. What you can possibly see is much less than what really exists. This sounds weird. This sounds bizarre. like it's very very different than what we had in classical mechanics.

He is trying to say that reality is the wave function, which is not directly observable.

The word see and observe are synonyms. I do not get his explanation. Even in classical physics, there are things we cannot see. We cannot see the center of the Earth.

You might think that in that 14:03 circumstance, since quantum mechanics is the foundational theory for all of modern physics, you might think that the quest to understand quantum mechanics at a deep level would be recognized as one of the most important things we could possibly do in physics. The people who devoted their lives to these would be academic superstars. You would have different universities trying to steal them away with highpriced packages and salaries and so forth. and it would be the highest prestige occupation you could have in physics.

Sadly, no, that is not what we do. It is the opposite of that. We have adopted a strategy of denial where if you're a physicist and you think hard about answering these questions, you are labeled not a physicist or a physicist who is too old to do important work anymore and you're sent off to retirement.

That is because the important issues were settled in 1930. People like Carroll want to be paid to do research on many-worlds, and real physicists consider it a complete waste of time.

36:37 Another what I think incorrect objection is that this idea cannot be tested. Can it be tested Right? It's important in science that we not just have good ideas, but that we compare these important ideas to data. Right? that we experimentally probe our ideas and people say you've invented all these new worlds. How do you ever test that idea?

The response to that is, I didn't invent any new worlds. I just took quantum mechanics seriously. The entirety of the assumptions that go into the many worlds theory is there are wave functions and they obey the Schroinger equation. That's it. Everything else is a consequence, a prediction and implication of those assumptions.

And are those assumptions testable? Hell yes they are. Of course they are. Whenever we do a quantum mechanical experiment, we're implicitly testing the many worlds interpretation.

If you want to falsify the many worlds interpretation, remember that the prediction of many worlds is wave functions don't collapse. They never do. They appear to collapse because of decoherence.

So there is no way to test many-worlds. He says it is logically correct, so everything you see confirms it. That's all.

As he admits, we see wave functions collapses. They would contradict many-worlds, except that he does not believe that they are really collapsing. He calls that a test.

This is all nonsense. I don't know why anyone takes him seriously.

Carroll also has to answer this new survey:

World's largest ever survey of physicists, results & reaction

May 12, 2026
What do physicists really think about the biggest mysteries in the universe?

In this video, leading voices in theoretical physics come together to unpack the results of the Big Mystery Survey—the largest survey ever conducted of professional physicists, prepared in collaboration with the American Physical Society's Physics Magazine." Featuring reactions from experts like Sean Carroll, Niayesh Afshordi and ,Ghazal Geshnizjani we find out what physicists really think about topics such as: What should we think about fine tuning ? What is dark matter? What is dark energy? How should we truly understand the Big Bang?What the right approach to quantum gravity ?

Whether you’re a physics enthusiast or just curious about the universe, this conversation offers a rare glimpse into how experts think about the unknown.

It reports 11% for many-worlds, 6% for Bohm pilot wave. These are the two crackpot interpretations. It is amusing to see how the leading popularizers of theoretical physics have views that are rejected by most physicists.

Carroll also has a lecture in this newly-released video on the physics of time and the history of relativity.

[4:50] All you have to do is entirely jigger your thoughts about what space and time are. And in fact, it wasn't until two years later when Hermann Minkowsky, who was a mathematician who had been one of Einstein's professors, said, "You know, the right way to think about Einstein's theory is to say that space and time aren't separate anymore. To imagine there's one thing called spacetime, and different people, different observers moving in different ways through the universe will divide it up into space and time differently.

There's no objective true fact about when I snap my fingers now what's happening light years away. That's going to depend on who's doing the observing and who is doing the measuring. ...

It can all be explained very beautifully by imagining a single four-dimensional spacetime instead of separate space and time. Einstein himself was not impressed by this move. ...

And when Minkowsky says, "I have some new math that unifies space and time based on Einstein's theories," Einstein himself is like, "I don't need that. That's like extra mathematical nonsense."

Minkowski never referred to "Einstein's theory", but got that 4D spacetime from Poincare. That 1907 Minkowski paper cited Poincare's 1905 paper with the 4D spacetime.

Yes, people like to credit Einstein for spacetime, but that was published by Poincare and Minkowski, and Einstein rejected it.

Carroll wrote a whole book on relativity, so he surely knows the history. It is weird that he gets it so wrong.

Update: The survey has just been posted in a paper.

We present results from the Big Mysteries Survey, a large-scale survey conducted through the American Physical Society's Physics Magazine on foundational and controversial topics in contemporary physics. The survey provides a snapshot of physicists' views on issues in cosmology, black-hole physics, quantum mechanics, quantum gravity, and anthropic coincidences. A central finding is that several positions often described publicly as field-wide ``consensus'' views are, in practice, supported by much narrower majorities or by pluralities rather than majorities.

19% believe string theory is the best hope for quantum gravity. 30% believe that information dropped in a black hole is preserved in Hawking radiation. 24% believe in the dark energy cosmological constant. No consensus on dark matter. 51% believe in cosmological inflation.