Quantum complexity tamed by machine learning | Hacker News Reader

Quantum complexity tamed by machine learning

quantamagazine.org

71 pointsgeorgehill21 comments

>> “I probably won’t put a lot of time into machine learning efforts,” he said, “because although machines can learn, they can’t yet explain to us what they have learned.”

So, as usual with the use of deep learning in the sciences, we had a lot of data that we couldn't understand, then we built a model that represents the data, and now we have a model that we can't understand.

I continue to be reminded of that early Pinky and the Brain episode:

The Brain plans to use a "growing ray" (originally a "shrinking ray") to grow Pinky into super-size while dressed up as Gollyzilla, while Brain would turn himself gigantic and stop him, using the name Brainodo, in exchange for world domination. However, the real Gollyzilla emerges from the ocean and starts to rampage through the city, making Brain think that the dinosaur is Pinky. The episode ends with the ray going out of control and making everything on Earth grow, including the Earth itself, to the point that Pinky, the Brain, and even Gollyzilla are mouse-sized by comparison again.

https://en.wikipedia.org/wiki/List_of_Pinky_and_the_Brain_ep...

A nice video introduction [1] on DFT from PBS SpaceTime.

[1] https://youtu.be/55c9wkNmfn0

DFT as in Density Functional Theory, not the Discrete Fourier Transform. Yes, in the context of the article (quantum physics) it may not need clarification, but to some of us having the acronym expanded helps.

I’m barely even a layman at machine learning or quantum mechanics. But isn’t a large essence of quantum mechanics essentially a love fest between probability and physics? And people keep complaining that AI/ML is just lots and lots of statistics? Should I be surprised that heavy duty statistics computing has a resonance with statistics of physics?

I admit I only skimmed the article past the opening paragraphs (see layman).

> But isn’t a large essence of quantum mechanics essentially a love fest between probability and physics?

Not really.

Quantum physics is about state being represented by a linear combination of vectors in a state space rather than a point in a state space. Additionally, it’s about how that state evolves over time. And finally about how observables are projections of the state onto some ortholinear basis (this is where the probability creeps in and no one really understands why).

Expectation values and psi^2 is literally probability. Quantum mechanics tells us nature is inherently probabilistic at the quantum scales.

QM is perfectly deterministic. Probability only comes into play during measurement. Now here's the thing, nobody knows how does measurement work. Currently, we just assume measurement is a probabilistic black box.

There are theories about measurement that do away with probability, but they have to skirt around Bell's inequality in ingenious ways

So in other words it's not perfectly deterministic at all?

Layman, but: there are perfectly deterministic interpretations. The "default" view (Copenhagen) has randomness, because it's trying to recover a classical measurement, but there's views that discard that entirely, such as many-worlds, which is completely deterministic, including measurement, at the expense of discarding any notion of definiteness. Ie. in MW you can't say that "outcome X happened, and outcome Y did not", only "we the observer have become entangled with outcome X." This does difficult things to probability, though there's approaches to recover a notion of likelihood even in this model, such as the decision theoretic approach https://en.wikipedia.org/wiki/Many-worlds_interpretation#Dec... where they :layman handwave: show that the Born probabilities are the only consistent assignment that exists at all, or something. I also vaguely remember reading an approach that showed that looking back at the ultimate history of the universe, all but a vanishing fraction of branches had experienced histories consistent with the Born rule, but I don't have a link or name for that.

Anyways, in a MW universe there's no probability, because every outcome occurs, but there's still "indexical uncertainty", which is to say you don't necessarily know which branch of the universe you are presently inhabiting.

Addendum: All (surviving) QM interpretations are empirically equivalent, anyways, so this is purely a philosophical question.

In other words you always win lottery, you just happen to be entangled with universe where you don't, sorry.

That's correct.

This is dependent on your point of view.

The Copenhagen interpretation is probabilistic. However, there are reasons to believe that wavefunction collapse is an illusion brought on by something called decoherence. The gist of decoherence is that the interaction of a quantum system with its surroundings couples that system to its environment, bringing about the appearance of wavefunction collapse, when the system + environment is still a single quantum system evolving together.

This is a purely philosophical matter, though, and beyond the scope of science, since such things are not testable. However, there is a mathematical reason to prefer decoherence over Copenhagen, which is that wavefunction collapse is inherently non-unitary, which is to say that it's irreversible. The measurement process in Copenhagen is akin to applying a non-invertible matrix to the wavefunction, resulting in its appearance in a single state.

The problem with this is that all known processes in quantum mechanics evolve according to unitary transformations. Interactions with electromagnetism and the strong and weak forces all involve unitary transformations. So where does this non-unitary behaviour come from? Decoherence theories suggest that when you're performing a measurement, this is a single transformation on the system + environment, which is still unitary, but when you examine the state of the system, for a given state of the environment, it appears to be non-unitary.

In practice, however, measurements are still probabilistic, so in that sense it doesn't really matter; this is mostly just a philosophical question.

However, in that sense, if somebody has this point of view, they could perhaps say that quantum mechanics is just as deterministic and not any more probabilistic than, say, classical statistical mechanics, where there's the appearance of randomness not because of non-deterministic laws of physics, but because of various issues like

- even if they were classical particles, you couldn't hope to measure their positions and momenta

- even if you could do so, calculation would be impractical to the point of impossibility

- even if you had a supercomputer that was up to the feat, minuscule amounts of initial error (or accumulated rounding error over time) would result in drastically different long-term behaviour

These combined would mean that only summary statistics and expectation values could be offered for such a system, even if all of the dynamics were fully deterministic with classical particles.

Decoherence is easiest to see in a MW setting. The basic observed fact is that at some point you need an observer that makes a clear, consistent observation.

Decoherence is a concept about an isolated state (that can be multi-valued, like dead cat / alive cat) that leaks out into the environment by entanglement with more and more environment states, and proceeds to "pull in" versions of you (as the observer) one by one as the versions of you are also entangled with the environment.

You can recurse this analysis and eventually you reach a point where the "leaf" quantum state only involves one outcome and is entangled with a single version of you, and at that point you don't need any collapse anymore. Also this process is completely deterministic.

The Copenhagen interpretation is a shortcut that basically says let's ignore all those intermediate interactions between the original "weird" state and the observers, in a very real sense you "collapse" the chain of entanglements. You also ignore that you have multiple observer versions of yourself and instead explain it as a probabilistic distribution from the point of view of the "pre-split" observer. This has turned out to be a good enough strategy in practical physics since the 1920s!

Note that none of this explains the quantitative aspect of it, the Born rule, or what it actually means that something's more probable than not. It just discusses how you can start with superpositions and end up with observers who don't see the superpositions.

> However, there are reasons to believe that wavefunction collapse is an illusion brought on by something called decoherence.

Decoherence itself doesn't explain the (apparent) wave-function collapse. Decoherence just tells you why the quantum states can't self-interfere after coming in contact with "the environment" (such as in a measurement). You still need to invoke some other explanation why the non-interfering states can't both be observed (or shut up and calculate).

In MWI, this other explanation is the claim that "a classical observer" is an entity that only exists in one "branch" of the state space at one time, and can only perceive the solution to the wave equation they are entangled with. But this is an extra assumption entirely equivalent to the Born rule, though it is more intuitively acceptable in some way.

Well, depends on your interpretation of QM, and whether you consider measurement to come under the purview of QM. I like to keep measurement separate from QM, since we don't have an acceptable theory to explain it. We don't even agree on how to define measurement.

Parent comment saying "nature is inherently probabilistic" is false. At best, you can say "nature may be probabilistic". Saying "QM is perfectly deterministic" is fine because nature ≠ QM (although this is my opinion, maybe others disagree).

It's deterministic in the sense that QM gives you an exact answer about what happens at the quantum scale for any interaction, without any probability involved.

However, the exact values that QM predicts are not real numbers for speed etc, they are a complex numbers describing a wave, with different values for different positions in space-time. These numbers precisely describe how the wave-packet will interact with other wave-packets.

But, if you want to do a classical measurement, then the only known relationship between the wave description and the outcome of your experiment is the Born rule - the amplitude of the wave at a point X in space-time is proportional to the probability that the particle will be detected at that point.

It's the other way round. The vectors-in-state-spaces representation is necessitated by the fact that it is a probabilistic theory, and has no physical content itself besides that.

The first half of "The Structure and Intepretation of Quantum Mechanics" by R.I.G. Hughes [1] lays this out very clearly. He derives most of the framework simply from the premise that it's a probabilistic physical theory. Then he shows how you can add a single extra element to it (eg. unitarity [2]) to turn it into full blown quantum mechanics (i.e. derive Schrodinger's equation), and lists several alternative ways you can do that.

It's a great book, and accessible to the layman.

[1] https://www.hup.harvard.edu/catalog.php?isbn=9780674843929

[2] https://en.wikipedia.org/wiki/Unitarity_(physics)

>The first half of "The Structure and Intepretation of Quantum Mechanics"...

Is this a coincidence, or might that name be inspired by Abelson & Sussman?

I think it's a coincidence - an old comment of mine about that: https://news.ycombinator.com/item?id=19769946

Well after all that was how QM was invented back in the days as well (they had to find underlying explanations for the probabilistic experiment outcomes).

But see the PBR theorem ( https://en.wikipedia.org/wiki/PBR_theorem ) regarding the importance of the quantum state itself and its "physical content".

This kind of work has always made me chuckle, because it's effectively pitting together two "when you have a hammer" kind in of hype against eachother: Deep Learning and Quantum Computing.

If deep learning can solve quantum systems, what do we even need Quantum Computing for?

Due to the way the science startup ecosystem works, neither QC people nor DL for Physics people will even acknowledge that there is a deep contradiction to having both of them be correct.

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