Cartoon aided design: The lighter side of computing

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It’s true that the usual formulation of the uncertainty principle involves a peculiarity of the Schrödinger equation—namely, that position and momentum are conjugate observables—but I prefer the more abstract formulation, which applies to any pair of conjugate observables, in Hilbert spaces of any dimension (the finite case probably being the clearest). And in the latter case, yes, it’s just a logical consequence of the basic axioms of QM, the ones that talk about amplitudes. Ajit #43: When you say “I haven’t so far studied the density matrix formalism at all”, do you mean that you have never seen density matrices before, or just that their ultrashort treatment found in introductory QM textbooks gave you no indication why they are useful? By ultrashort, I mean a short talk about mixed states followed by some basic facts like: So should we say, on that basis, that you don’t need any nontrivial math to do physics: no complex numbers, no linear algebra, no calculus, not even arithmetic? Alas, not if you actually want to understand what the theories say, which David Deutsch reminds us is more important than calculating with them…

I often have trouble understanding what you are saying. When I do think I understand it seems wrong in strange ways. For example: I think that it is not the preferred basis which is primarily problematic with ppnl #66’s model. (Problematic, in the sense, what makes it unlike the actual QM.)

won’t interest me, I am sure. The application would be of interest to information theory/TCS folks, but it is not, to me. My interests are mainly in the QM foundations and then, may be, some software simulations of some basic QM phenomena and/or applications to some topic here and there, may be, from condensed matter physics (i.e., if at all). Of course, the aliens simulating our universe might be fine with that nonlocality, and you might be fine with it too! But what it does is to push the alleged pseudorandomness of quantum measurement outcomes to a level that’s disconnected from what we actually know about physics. Note, in particular, that it’s extremely important that none of us ever discover the pattern to the pseudorandomness, since if we did, we could break the whole structure of QM, communicate faster than light, etc. Personally, I’d say that it’s of limited interest to postulate a theoretical superstructure that has to be so intentionally sequestered from everything we know about the workings of the world, but YMMV. Asolutely brilliant Scott – cystal clear, simple and entertaining- ALL profound insights should look exactly like this when correctly stated – if they don’t, the theorist is doing it wrong.

Overall, (1) is absolutely great to have. This property by itself does motivate me to “pre-pone” my studies of density matrices to an earlier date (even if it won’t be right away—not right this week or next week!). Are you sure that for real amplitudes just the 1-norm won’t be enough? … Ummm… But wait… Energy of a wave is proportional to the *square* of its amplitude… So, yes, if measurements via eigen-states were still to be necessary, and were still to depend on energy, then it would still have be a 2-norm. … So, yes, you are right, in that sense. Please don’t tell that to the thousands of unmotivated CS students in the university. They’ll think they can get a job without learning mathematics as long as they’re fine with not understanding what they’re doing.EXPERIENCE SOME ASPECTS OF SOFTWARE DEVELOPMENT (SUCH AS FIXING BUGS, TESTING AND ITERATIVE DEVELOPMENT) DEVELOP COLLABORATIVE SKILLS THROUGH WORK WITH A PARTNER YOU WILL NEED… No, by deterministic I mean deterministic. As in the current state follows precisely from the previous state. Like Conway’s game of life for example. Now chaos may result from following the rules. But first that chaos does not change the fact that it is fully deterministic. And secondly that chaos is irrelevant to any point about quantum mechanics.

A model is a mathematical construct that describes some aspect of the material world. It’s purpose is to make visualization easy and give us an intuition for it. On the topic of experimental demonstration of quantum supremacy, in your initial paper on Boson Sampling with Alex, you proved that BS being efficiently solvable by a classical computer implies that the polynomial hierarchy collapses to the third level. Is there any hope for reducing the collapse level further? It seems like the primary barrier is that the universal hashing scheme gives rise to BPP Stella #68: Thanks for your comment! I’d be happy to help you, but maybe you could help me first. What kinds of problems are you looking for? In “Why Philosophers Should Care About Computational Complexity”, I did mention a bunch of underexplored issues that I found interesting. Is that the kind of problem you wanted? Or did you want something more concrete? Just point me in a direction. In any case, essentially every known theory in physics can be “compiled down” to where its predictions can be calculated to arbitrary accuracy by a computer toggling 0’s and 1’s—the only exceptions (not coincidentally) being the theories that aren’t yet fully defined or understood. So should we say, on that basis, that you don’t need any nontrivial math to do physics: no complex numbers, no linear algebra, no calculus, not even arithmetic? Alas, not if you actually want to understand what the theories say, which David Deutsch reminds us is more important than calculating with them… 🙂 but while we’re on this topic of what is sufficient for describing QM, what about getting rid of reals too? Could you just describe QM in terms of rationals, floating point, or some finite theory?QM needs L2 norm but I was referring to ways of representation. You can do QM even without our notion of complex numbers but you’d need something equivalent and I conjuncture that that other form would be harder for humans to parse. The von Neumann entropy must be computed from the density matrix (or rather from the eigenvalues e_i of the density matrix p as S(p) = Σ e_i ln(e_i)). Taking the probabilities from the Born rule instead (or the p_k from the definition of the density matrix) simply gives the wrong result. From this perspective, the Martinis/Google group’s recent preprint “Characterizing quantum supremacy in near-term devices” (2016) might alternatively been titled “Characterizing the spukhafte Fernwirkungen associated to large-dimension metric isomorphisms in quantum dynamics”. Further discussion of this thought-provoking preprint would be welcome by many Shtetl Optimized readers (including me). gasarch #41: I can say from experience that Oded Goldreich does indeed know a lot, but the lot that he knows is not about QC (and he readily admits as much).

I don’t expect that his book will ever be translated into English, but I hope that at least his concept of dynamic information and his conjecture that this dynamic information is conserved just like energy will find its way into discussions about quantum information theory. Maybe those discussions will show that his concept and conjecture is trivial or wrong, but I think that those discussions would be beneficial for highlighting to role of time dynamics in quantum mechanics. Not sure whether those are important for quantum information theory or not. (I hope I didn’t ran into that “damned by faint praise” issue again. In the part of Germany where I come from, praise is used “sparingly”.) In ppnl’s model, presumably, not just the updating rules but also the measurement rules which the observer cell uses in making its measurements, follow a classical, deterministic criterion. If the criterion is deterministic, it will impart a preferred basis.I realise parents can be embarrased, in previouas generations superposition was done in private and entanglement was practically a taboo, the end result is people too embarrassed to talk about real problems, 58.567% of all left handed american men can’t sustain an entanglement long enough to satisfy their spouses. By “information is energy”, he means that this type of dynamic information is conserved in basically the same way energy is conserved. He investigates a great number of situations, both situations which should confirm his conjecture and make it more understandable, but also situations which seem to contradict his conjecture at first sight. Most of his solutions for those contradictory situations felt good (and sometimes enlightening) to me, but sometimes his solutions didn’t convince me.