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Quantum computing is difficult to explain because you have to learn a mathematical model to understand it. You cannot make use of metaphors & analogies to famil

Quantum computing is difficult to explain because you have to learn a mathematical model to understand it. You cannot make use of metaphors & analogies to familiar references. Why? Because our language developed in a classical world. It is not equipped to deal with quantum mechanics. Quantum mechanical objects are an entirely new ontological category. Light is not a particle, nor is it a wave; it's a different third kind of thing with which you've had no prior experience. The last time most people encountered a new ontological category was in early childhood, and since then they've been building up knowledge by relating it to what they already know. The only way to surmount this obstacle is to learn a new language - the language of mathematics. All metaphors and analogies will lead you astray; they will only confuse. Thankfully the math is quite easy, it is only basic linear algebra. Learn the math and you will learn quantum computing. Don't learn the math and you will not learn quantum computing. Let's take the simplest phenomenon in quantum computing: superposition. People get very confused about superposition. Something being both 0 and 1 at the same time? Like fuzzy logic? Is it 0 and 1? Is it 0 or 1? No, superposition is a linear combination of 0 and 1 which can be collapsed according to certain measurement rules. It can also be manipulated with quantum logic gates. There is no simpler way of explaining it.

dandanua 5y ago
The math behind quantum mechanics, even though working nicely in practice, doesn't fully connected to the real world because the measurement problem has yet to be solved. I would say this reason is the main source of confusion.
- ahelwer 5y ago
  It's possible some new paradigm will come along which makes the mathematical model of quantum computation obsolete and renders irrelevant the question of interpretation (QC uses naive Copenhagen by convention) but I wouldn't hold my breath. And even then, like Newtonian mechanics, the mathematical model would probably still be worth learning.
  - TchoBeer 5y ago
    I don't think QC uses naive Copenhagen by convention? I remember reading something by a quantum computation scientist (maybe it was Scott Aaronson?) who said he prefers many works.
    - ahelwer 5y ago
      What a researcher prefers is different from how quantum programming languages are structured and how the mathematical model is taught: you have a state vector in superposition that is collapsed probabilistically to classical values on measurement.
      - meroes 5y ago
        It is interesting though behind the scenes of this description, David Deutsch really does think the worlds of MWI are interfering with each other to allow quantum computations.
- PeterWhittaker 5y ago
  Consider reading Carlo Rovelli's "Helgoland", which is a good introduction both to Rovelli (a brilliant, poetic, and humble writer) and to Relational Quantum Mechanics, of which he is a major proponent and likely founder. Why? Because he asserts that there is no measurement problem, and that the EPR paradox and violations of Bell's Inequality don't exist: They are based on misunderstanding what QM is actually predicting and what QM observers are actually observing. Likewise, there is no wave function collapse, no need for MWI, no hidden variables, etc. To sum up the physics, badly.... Background: Relativity took as its principles that physics is universal (the universe is isotropic), that there are no fixed reference frames (all measures of speed, and therefore of a few other things, like energy) are relative to the observer making the measurement), and that the speed of light is a fixed constant. From that we space-time curvature, etc. Relational QM takes this same perspective: Measurement is relative to the measurer, which can mean an observer or anything else affected by whatever is manifesting itself, like another particle, e.g. Manifesting is a deliberate word: Absent manifestation, nothing has properties. Properties only make sense in the context of interactions. What is the charge or spin of an isolated electron? 無 (mu): the question makes no sense, because charge and spin and everything else only arise, are only measurable, in interactions. So take EPR: There is no paradox, because when Alice measures the spin of one of the entangled particles, she may "know" that Bob will measure or will have measured opposite spin, but she doesn't "know" this yet unless and until she interacted with Bob. It is only after this slower-than-light communication that the two opposite spins - and the predictions of QM - are confirmed. Until A and B interacted, entangling their states, the states A-observes-S1 and B-observes-S2 were independent. The interaction between A and B, state "A+B share information re S1+S2", took place without anything ever being FTL, without violations of locality, etc. What I do not yet know, and have not had enough to look into, is whether and how Relational QM might or does change what we expect of quantum computing. At some point, I'll seek out some Aaronson on the subject, e.g. Read the book, well worth it.
drewrv 5y ago
Do you know a good source for someone to learn about it at a high level, if they took linear algebra in college but haven’t touched it in 10+ years?
- ahelwer 5y ago
  I made a lecture aimed at such people (I was such a person!), which has proven popular: https://youtu.be/F_Riqjdh2oM https://youtu.be/F_Riqjdh2oM With a follow-up blog post focusing on entanglement: https://ahelwer.ca/post/2018-12-07-chsh/ https://ahelwer.ca/post/2018-12-07-chsh/
  - juancn 5y ago
    Thanks! Commenting so I don’t lose this.
    - wskinner 5y ago
      You can use the “favorite” button on comments to save them to your profile.
      - juancn 5y ago
        I didn't know you could do it on a comment. It's not on the normal UI. Thanks.
  - nyc 5y ago
    Andrew, that lecture you gave was fantastic. The Deutsch oracle example in the lecture was especially helpful -- I'm surprised it doesn't get used more frequently in other explanations of QC. I think one of the most interesting moments in the video was when the audience (me included) jumped to the conclusion that the QC was more powerful than it actually was and you helpfully brought everyone back to reality.
    - ahelwer 5y ago
      Glad you enjoyed! I do think the Deutsch Oracle problem is the closest thing to a "hello world" problem in quantum computing, or maybe more analogous to the "sum every value in a list of integers" problem in GPU programming. Of course you can shoot holes in it, and a lot of people have trouble with the "rewire the black box to use two wires" thing and think it's cheating. But such an objection would disappear if you just look at the N-bit Deutsch Oracle problem, which is unfortunately too complicated to be the first problem one encounters.
sigsergv 5y ago
Deutsch explained quantum theory in his Fabric of reality book. Not every aspect but basic concepts are presented really well.
fxj 5y ago
For me the following works best: Superposition is like transparency blending of two images together. For 0.5 each you still can see both images, but of course information can be lost. And a superposition of 1% and 99% gives essentially only one picture even though it is a slightly mixed state. A measurement is then the amount of a single picture in the superposition. And quantum gates are just linear operators on the mixed (superposed) image.
- deleted 5y ago
  [deleted]
meroes 5y ago
What I still am left with is, yes we can write down a classical description of superposition, but SOMETHING RANDOM still happens. When you imagine a fair coin being flipped and describing that with a probabilistic mathematical model, you can always imagine a classical story of what actually occurred. How you went from a spread out of possibilities to witnessing a single definite outcome. So I can understand the ontology because there is a classical ontology. What QM is forcing us to do is write down as much classical story as possible, THEN SOMETHING TRULY RANDOM OCCURS. I can't imagine in my head any possible classical story. Both the coin and quantum "measurement" use probability theory in a similar way, but this is an important distinction. When you say develop a new ontology, I really think you mean develop a recipe. I see no way to even comprehend anything but classical ontologies. I'm not sure if it's a limit of our, biology, imagination, or intuition. There is no classical ontology, nor settled ontology for that matter to describe the "measurement" of superpositions process.
- ahelwer 5y ago
  This problem is solved by learning the language of mathematics. The limits of our language are the limits of our world. When we learn the language of vectors obeying the 2-norm manipulated by unitary matrices and collapsing probabilistically according to the Born rule, we have learned how a single qbit works.
  - meroes 5y ago
    But the Born rule required empirical content to come up with. Empirical content which is (possibly) fundamentally random. You can't simulate that (fundamental randomness) purely classically. The classical world can be simulated with Turing machines, however. And we know infinite pen-and-paper maths can simulate any Turing machine. How do I get from pen-and-paper maths (doing simple turing-machine-like operations/computations) to a truly random event, a necessary component for a quantum measurement? So when I'm doing my pen-and-paper maths, I have to go grab a radioactive atom and use the time it decays to somehow seed a random event into my simulation. I do not know of a way to think beyond classically, or beyond the above notion of pen-and-paper maths. Or are you saying some abstract high-dimensional vector really does ontologically exist in some even higher dimensional space? What space? Not spacetime, that is 4D. And even then how do we reduce that spread out WF to definite values in your ontology. Math is not an ontology, unless you want to go the Mathematical Universe route.

dandanua 5y ago

The math behind quantum mechanics, even though working nicely in practice, doesn't fully connected to the real world because the measurement problem has yet to be solved. I would say this reason is the main source of confusion.

ahelwer 5y ago
It's possible some new paradigm will come along which makes the mathematical model of quantum computation obsolete and renders irrelevant the question of interpretation (QC uses naive Copenhagen by convention) but I wouldn't hold my breath. And even then, like Newtonian mechanics, the mathematical model would probably still be worth learning.
- TchoBeer 5y ago
  I don't think QC uses naive Copenhagen by convention? I remember reading something by a quantum computation scientist (maybe it was Scott Aaronson?) who said he prefers many works.
  - ahelwer 5y ago
    What a researcher prefers is different from how quantum programming languages are structured and how the mathematical model is taught: you have a state vector in superposition that is collapsed probabilistically to classical values on measurement.
    - meroes 5y ago
      It is interesting though behind the scenes of this description, David Deutsch really does think the worlds of MWI are interfering with each other to allow quantum computations.
PeterWhittaker 5y ago
Consider reading Carlo Rovelli's "Helgoland", which is a good introduction both to Rovelli (a brilliant, poetic, and humble writer) and to Relational Quantum Mechanics, of which he is a major proponent and likely founder. Why? Because he asserts that there is no measurement problem, and that the EPR paradox and violations of Bell's Inequality don't exist: They are based on misunderstanding what QM is actually predicting and what QM observers are actually observing. Likewise, there is no wave function collapse, no need for MWI, no hidden variables, etc. To sum up the physics, badly.... Background: Relativity took as its principles that physics is universal (the universe is isotropic), that there are no fixed reference frames (all measures of speed, and therefore of a few other things, like energy) are relative to the observer making the measurement), and that the speed of light is a fixed constant. From that we space-time curvature, etc. Relational QM takes this same perspective: Measurement is relative to the measurer, which can mean an observer or anything else affected by whatever is manifesting itself, like another particle, e.g. Manifesting is a deliberate word: Absent manifestation, nothing has properties. Properties only make sense in the context of interactions. What is the charge or spin of an isolated electron? 無 (mu): the question makes no sense, because charge and spin and everything else only arise, are only measurable, in interactions. So take EPR: There is no paradox, because when Alice measures the spin of one of the entangled particles, she may "know" that Bob will measure or will have measured opposite spin, but she doesn't "know" this yet unless and until she interacted with Bob. It is only after this slower-than-light communication that the two opposite spins - and the predictions of QM - are confirmed. Until A and B interacted, entangling their states, the states A-observes-S1 and B-observes-S2 were independent. The interaction between A and B, state "A+B share information re S1+S2", took place without anything ever being FTL, without violations of locality, etc. What I do not yet know, and have not had enough to look into, is whether and how Relational QM might or does change what we expect of quantum computing. At some point, I'll seek out some Aaronson on the subject, e.g. Read the book, well worth it.

drewrv 5y ago

Do you know a good source for someone to learn about it at a high level, if they took linear algebra in college but haven’t touched it in 10+ years?

ahelwer 5y ago
I made a lecture aimed at such people (I was such a person!), which has proven popular: https://youtu.be/F_Riqjdh2oM https://youtu.be/F_Riqjdh2oM With a follow-up blog post focusing on entanglement: https://ahelwer.ca/post/2018-12-07-chsh/ https://ahelwer.ca/post/2018-12-07-chsh/
- juancn 5y ago
  Thanks! Commenting so I don’t lose this.
  - wskinner 5y ago
    You can use the “favorite” button on comments to save them to your profile.
    - juancn 5y ago
      I didn't know you could do it on a comment. It's not on the normal UI. Thanks.
- nyc 5y ago
  Andrew, that lecture you gave was fantastic. The Deutsch oracle example in the lecture was especially helpful -- I'm surprised it doesn't get used more frequently in other explanations of QC. I think one of the most interesting moments in the video was when the audience (me included) jumped to the conclusion that the QC was more powerful than it actually was and you helpfully brought everyone back to reality.
  - ahelwer 5y ago
    Glad you enjoyed! I do think the Deutsch Oracle problem is the closest thing to a "hello world" problem in quantum computing, or maybe more analogous to the "sum every value in a list of integers" problem in GPU programming. Of course you can shoot holes in it, and a lot of people have trouble with the "rewire the black box to use two wires" thing and think it's cheating. But such an objection would disappear if you just look at the N-bit Deutsch Oracle problem, which is unfortunately too complicated to be the first problem one encounters.

sigsergv 5y ago

Deutsch explained quantum theory in his Fabric of reality book. Not every aspect but basic concepts are presented really well.

fxj 5y ago

For me the following works best: Superposition is like transparency blending of two images together. For 0.5 each you still can see both images, but of course information can be lost. And a superposition of 1% and 99% gives essentially only one picture even though it is a slightly mixed state. A measurement is then the amount of a single picture in the superposition. And quantum gates are just linear operators on the mixed (superposed) image.

deleted 5y ago
[deleted]

meroes 5y ago

What I still am left with is, yes we can write down a classical description of superposition, but SOMETHING RANDOM still happens. When you imagine a fair coin being flipped and describing that with a probabilistic mathematical model, you can always imagine a classical story of what actually occurred. How you went from a spread out of possibilities to witnessing a single definite outcome. So I can understand the ontology because there is a classical ontology. What QM is forcing us to do is write down as much classical story as possible, THEN SOMETHING TRULY RANDOM OCCURS. I can't imagine in my head any possible classical story. Both the coin and quantum "measurement" use probability theory in a similar way, but this is an important distinction. When you say develop a new ontology, I really think you mean develop a recipe. I see no way to even comprehend anything but classical ontologies. I'm not sure if it's a limit of our, biology, imagination, or intuition. There is no classical ontology, nor settled ontology for that matter to describe the "measurement" of superpositions process.

ahelwer 5y ago
This problem is solved by learning the language of mathematics. The limits of our language are the limits of our world. When we learn the language of vectors obeying the 2-norm manipulated by unitary matrices and collapsing probabilistically according to the Born rule, we have learned how a single qbit works.
- meroes 5y ago
  But the Born rule required empirical content to come up with. Empirical content which is (possibly) fundamentally random. You can't simulate that (fundamental randomness) purely classically. The classical world can be simulated with Turing machines, however. And we know infinite pen-and-paper maths can simulate any Turing machine. How do I get from pen-and-paper maths (doing simple turing-machine-like operations/computations) to a truly random event, a necessary component for a quantum measurement? So when I'm doing my pen-and-paper maths, I have to go grab a radioactive atom and use the time it decays to somehow seed a random event into my simulation. I do not know of a way to think beyond classically, or beyond the above notion of pen-and-paper maths. Or are you saying some abstract high-dimensional vector really does ontologically exist in some even higher dimensional space? What space? Not spacetime, that is 4D. And even then how do we reduce that spread out WF to definite values in your ontology. Math is not an ontology, unless you want to go the Mathematical Universe route.