7 ms·

Quantum complexity tamed by machine learning

71 points by georgehill 5y ago

xvilka 5y ago
A nice video introduction [1] on DFT from PBS SpaceTime. [1] https://youtu.be/55c9wkNmfn0 https://youtu.be/55c9wkNmfn0
- dr_zoidberg 5y ago
  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.
travisgriggs 5y ago
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).
- frutiger 5y ago
  > 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).
  - raziel2701 5y ago
    Expectation values and psi^2 is literally probability. Quantum mechanics tells us nature is inherently probabilistic at the quantum scales.
    - mvakde 5y ago
      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
      - arrow7000 5y ago
        So in other words it's not perfectly deterministic at all?
        FeepingCreature 5y ago
        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#Decision_theory 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.
  - omnicognate 5y ago
    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 https://www.hup.harvard.edu/catalog.php?isbn=9780674843929 [2] https://en.wikipedia.org/wiki/Unitarity_(physics) https://en.wikipedia.org/wiki/Unitarity_(physics)
    - _0ffh 5y ago
      >The first half of "The Structure and Intepretation of Quantum Mechanics"... Is this a coincidence, or might that name be inspired by Abelson & Sussman?
      - omnicognate 5y ago
        I think it's a coincidence - an old comment of mine about that: https://news.ycombinator.com/item?id=19769946 https://news.ycombinator.com/item?id=19769946
    - l33tman 5y ago
      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 https://en.wikipedia.org/wiki/PBR_theorem ) regarding the importance of the quantum state itself and its "physical content".
YeGoblynQueenne 5y ago
>> “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_episodes#Season_1_(1995%E2%80%9396) https://en.wikipedia.org/wiki/List_of_Pinky_and_the_Brain_ep...
xmcqdpt2 5y ago
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.

71 points by georgehill 5y ago

xvilka 5y ago

A nice video introduction [1] on DFT from PBS SpaceTime. [1] https://youtu.be/55c9wkNmfn0 https://youtu.be/55c9wkNmfn0

dr_zoidberg 5y ago
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.

travisgriggs 5y ago

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).

frutiger 5y ago
> 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).
- raziel2701 5y ago
  Expectation values and psi^2 is literally probability. Quantum mechanics tells us nature is inherently probabilistic at the quantum scales.
  - mvakde 5y ago
    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
    - arrow7000 5y ago
      So in other words it's not perfectly deterministic at all?
      - FeepingCreature 5y ago
        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#Decision_theory 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.
- omnicognate 5y ago
  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 https://www.hup.harvard.edu/catalog.php?isbn=9780674843929 [2] https://en.wikipedia.org/wiki/Unitarity_(physics) https://en.wikipedia.org/wiki/Unitarity_(physics)
  - _0ffh 5y ago
    >The first half of "The Structure and Intepretation of Quantum Mechanics"... Is this a coincidence, or might that name be inspired by Abelson & Sussman?
    - omnicognate 5y ago
      I think it's a coincidence - an old comment of mine about that: https://news.ycombinator.com/item?id=19769946 https://news.ycombinator.com/item?id=19769946
  - l33tman 5y ago
    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 https://en.wikipedia.org/wiki/PBR_theorem ) regarding the importance of the quantum state itself and its "physical content".

YeGoblynQueenne 5y ago

>> “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_episodes#Season_1_(1995%E2%80%9396) https://en.wikipedia.org/wiki/List_of_Pinky_and_the_Brain_ep...

xmcqdpt2 5y ago

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.