Thanks, this is much better than the incredibly vague Wolfram documentation.

Skimming through it, the links between the specific physics and the general statements about graphs seem to me to be rather weak. A typical section looks like setting up a bunch of very general definitions about graphs, and then suddenly jumping into a standard physics derivation in standard physics notation without even using the definitions you set up a page earlier. In other words, the graph stuff seems to not be doing much of the work!

But I do admit that I only skimmed. This could be an unfair assessment. I hope your papers get a good, thorough peer review.

Reading through the paper in (3) above. If I understand the text on page 26 correctly, you predict that quantum computers will not be more efficient than classical computers:

"The class of problems that can be solved efficiently by quantum computers should be identical to the class of problems that can be solved efficiently by classical computers: More precisely, we predict in this appropriately coarse-grained case that P=BQP, where P and BQP denote the complexity classes of polynomial time and bounded error quantum polynomial time, respectively."

And:

"In other words, in order to maintain a causal invariant representation, the observer must perform a sufficient level of coarse-graining to ensure that any apparent advantage obtained through the use of a quantum computer over a classical one is effectively lost."

Am I missing something fundamental (most probably)? Are you predicting that quantum computers will not be able to, for example, factor RSA keys much faster than todays non-quantum machines?

I'm not sure if that is the case or not but if that is the prediction then they are in good company.

Nobel laureate Gerard 't Hooft also has a cellular automaton theory and one of his conclusions is: "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist."

https://arxiv.org/abs/1405.1548

I believe most of these theories essentially suggest that the error correction required to produce a precise and reliable answer from more qubits, will grow faster than the computing power added by those qubits.

> no classical theory can explain quantum mechanics."

Not sure I can agree with 't Hooft on this. A GR-based theory with closed timelike curves can easily have particles travelling through time to interfere with themselves, and thus reproduce the quantum phenomena like the double-slit experiment. There's been some work on this:

https://www.reddit.com/r/Physics/comments/1gjekn/the_logic_o...

In your last sentence, you compare future quantum computers to “today’s” non-quantum computers, which might be a false dichotomy.

[warning: uninformed tangent]

A more optimistic interpretation could be that quantum & non-quantum machines will be similar because we have huge leaps to make in non-quantum computer architecture.

This is strictly a theoretical thought-experiment for me, but it has always intrigued me that quantum computers sort-of model the problem itself in the hardware circuit & shove a bunch of qubits through it.

In digital computers, we mostly model Boolean logical structures & then, in software, translate our problem into that Boolean logic. This translation into discrete steps places a limit on the theoretical efficiency.

However, perhaps there is room in analog computing hardware to more closely model specific types of optimization problems & then shove a bunch of electrons through it (shouldn’t the electrons follow the path of least resistance?).

> In your last sentence, you compare future quantum computers to “today’s” non-quantum computers, which might be a false dichotomy.

Ah, good point.

Though I was more thinking of Shor's algorithm and Grover's algorithm that tells us the theoretical expected performance that could be achieved with quantum computers. Normally these are described as showing the speedup provided by a possible quantum computer (in relation to non-quantum computers).

So, when reading the Wolfram Model paper I cited, I read the statement regarding quantum computers as dismissing the possibility of achieving qantum computers capable of realising Shor's and Grover's.

But one could of course read it in a flip-side way, that there are algorithms out there to be discovered that achieves the same lower bound complexities on non-quantum machines.

Considering that the Wolfram Model is all about graphs and cellular automata, the statement should probably be considered not based on a RAM complexity model, but something like PRAM that considers parallelism.

What you are describing is an analog computer or circuit. These definitely exist, I had to build a circuit to model the physics of a bouncing ball in a Circuits class in college. However, I don't know how often analog computers are used in professional/practical applications these days. Here is some more info: https://spectrum.ieee.org/computing/hardware/not-your-father...

> However, perhaps there is room in analog computing hardware to more closely model specific types of optimization problems & then shove a bunch of electrons through it (shouldn’t the electrons follow the path of least resistance?).

Congratulations, you've rediscovered quantum annealing!

I'm certainly going to look forward to Scott Aaronson's response

I haven't checked the context, but that indicates a flaw in either their framework or the way they draw this conclusion. We know for a provable fact that some problems (not necessarily interesting or useful ones) can be solved exponentially faster on a quantum computer than a classical computer: Deutsch-Jozsa algorithm (or it's generalization: Simon's algorithm) demonstrates this.

We know problems can be solved faster on a "quantum computer" as the term is defined; we don't know that the version of QM that our reality runs on actually allows us to create such a computer, or at least scale it up to a demonstrably (not provably! Demonstrably!) superclassical level. That's what the Quantum Supremacy debate is about.

Could I understand the effort this way? In general any Turing complete set of computational rules should be able to generate any computable expression and hopefully physics can be expressed with computable expressions (at least if it is at all comprehensible to humans). So you are looking for a particular set of rules (instead of the English language and math symbols, e.g.) that meet certain kind of aesthetics. Do you expect only valid physics to be expressed or is the research on the kind of restriction that will lead to only valid physics being expressed?

From the main article, it looks like they believe that relativity and quantum mechanics are both things that directly emerge as necessary consequences from the structure, not that those are arbitrary results that may be computed inside. It wouldn't be very interesting in the latter case; there's no shortage of Turing tarpits.

Could you provide some details on the algorithm used to graph the plots? I'm pretty sure nothing in graphviz would result in such nice looking graphs, so probably not a spring relaxation-type algorithm. Perhaps something using the graph Laplacian eigenvectors? I recall some papers by Yehuda Koren using the technique on massive graphs

Are you guys planning on submitting your novel findings to peer reviewed physics journals? Have you done that? How has that gone?

Our preprints are currently in peer review (for different journals, I should add). Nothing terrible has happened yet.

Why didn't you wait with the announcements until after the pre-prints were accepted by reputable journals?

It's relatively common practice in academia to make announcements about results while they're still in pre-print form (particularly given how slow the peer review process is for some journals).

I've never announced my papers before they were accepted by a conference or journal (other than putting them on arXiv). I would certainly not let my university's press office mention my work if it was not fully peer reviewed. I've never seen this from my colleagues either.

It's common practice to "announce" in the sense that you email colleagues about it and give seminars. It's not common practice to do a press blitz, solely directed at an audience that will be unable to criticize it.

The internet is pretty good at criticizing things.

Well yeah, but a lot of the criticism is baseless. For example, you have people downthread saying things like "this can't be right because it's discrete", or, "it's inherently impossible for a theory of everything to make predictions", and so on. These aren't true at all.

Every physicist knows that if you want good criticism, you need to go to people with relevant expertise. That's what peer review is!

But they're doing that too. Given we live in the information age, why the hell not send it out in both a traditional research publication as well as a forum like this one? A lot of smart people out there in the world and if you can get 10,000 geniuses to look it over, who says it won't lead to either better criticisms or expansion of a potentially sound theory into other discoveries?

In a lot of physics areas, things move very fast, so generally people submit to a journal and arXiv simultaneously, in case someone else posts on arXiv first and goes down in history as first.

However, rarely are arxiv publications accompanied by such fan fare.

Yes, but press releases are only released after papers have been accepted, not only by journals, but overall by the scientific community.

Specially for papers that claim new or bold things.

Why rely on narrow peer review when you can put the ideas out in public and receive much broader feedback. Most of that feedback will be noise, but the Wolfram crew are certainly able to find the signal in it and use that to improve or fix their ideas.

Because they don't need to?

Because they wanted more peer review?

Why didn't you wait for approval of your HN comment?

I forget what kind of fallacy you're arguing, but it's definitely a fallacy of some sort.

Right. Except for all this fanfare. Why is it necessary to celebrate the writing of two papers like this?