Cartoon aided design: The lighter side of computing

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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. John B #5 and Roy Badami #19: I think linking to the top of Shtetl-Optimized is correct. The blog almost always talks about quantum computing, and the misconceptions about how quantum computing come up so often that it’s even in the tagline and the previous tagline.

It’s true that technically, the program would need a random number generator to make the final selection of a measurement outcome, and have it “really” be random (rather than pseudorandom). But I’ve never seen that as such a big deal—as a challenge to the Church-Turing Thesis or whatever—because even a deterministic program can easily output a list of probabilities, so that the only thing left for you to do would be to “spin the wheel.” Zach #33: I’ve already decided that I’m not going to get upset when Lubos calls me “the most corrupt moral trash,” urges my students to spit in my face, etc. So by symmetry, I shouldn’t be gratified either if he happens to like something that I was involved with.One part of the force between moving charges we call the magnetic force. It is really one aspect of an electrical effect. One thing that surprised me when I first took a Physics course is the importance Physicists give to intuition.

describe how they’ve used the software to create their animation then comment on the finished product and evaluate how successful it is. 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. base 12 is obviously the better choice, it makes daily calculations much easier but we have 10 fingers and so we have an intuition for base 10 and we need to develop an intuition for base 12. 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. In case Born did say that: Born was not God—merely a Nobel laureate. This position (i.e., pre-emptying any possibility of there being any deeper mechanism) is not worthy of any serious attention—not in physics. May be (and just may be) Born shares a philosophic point with you, that’s all—at the most.Looking toward the quantum future, the preceding considerations provide reason to foresee that practical large-scale demonstrations (or not) of quantum supremacy— whether achieved by photonic BOSONSAMPLING, DWAVE-style SQUID arrays, ion traps, or any other foreseen scalable quantum technology— will rely crucially upon MEEP-like computational tools and philosophical/social insights like Voevodsky’s. Actually electrical engineers do use complex numbers to talk about electrical pulses. So yes you could use electrical impulses to talk about complex numbers. The definition of the entropy was the reason why John von Neumann introduced the density matrix. The description of subsystems was the reason why Lev Landau independently invented the density matrix. And the absence of global phase is a good reason for physics students to not worry too much about the global phase.

The same argument goes the other way: six months from now its going to be just as hard for someone reading this blog post to find the particular comic (unless they read comment #19 of course!). Either way, I think it’s better to provide full information — doing otherwise just offends my nerdish OCD. 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. I don’t quite understand right away, but never mind. (I don’t want to put you through the trouble of explaining something to me at a time that I am not even ready to understand it!) It’s not really the fact of linear operators (i.e. linearly evolving amplitudes) which gives QM its peculiar character. The peculiarity of QM lies in the necessity of measurement, and the collapse postulate which an act of measurement involves. In other words, the peculiarity of QM lies in the “quantum jumps.” Schrodinger was unhappy only with this part of QM; and it is only this part that makes QM as we know it, incomplete. Scott, what are the hard questions that this kid could have asked his Mom where she would not have been able to give him an answer that he’d be satisfied with?

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OK. There are two different flavors of deterministic theories. One is linear, another nonlinear. The nonlinear theory (viz. that at least for some regimes of the input data, the output does not scale linearly with the input) is a good candidate for producing randomness. (Oh, BTW, “randomness” is “random-ness”: it is a matter of degrees.) All pseudo-random number generators rely precisely on such a (deterministic) nonlinearity. They do have some relevance to some points “related to QM.” All software simulations of QM phenomena rely on the pseudo random number generators—i.e. on the nonlinear determinism. If they thus are practically useful, so is the linear vs. nonlinear distinction, esp. in the context of a software model like CA. You failed to make it. I therefore had trouble understanding what you had in mind. And I don’t understand what you mean by measurement rules being deterministic. Quantum measurements are always irreducibly ontogicaly random. That randomness simply is. There is no underlying mechanism. That is the point of the Born rule.

Even if both the categories of rules (updating and measurements) are kept deterministic, the machine would still show certain similarities to the quantum mechanical (i.e. the actually existing) world—viz., a reduction in the number of input states required to get to a given observed state. Either this, or that, but not both. Equivalent to the XOR logic gate. Example: “Give me liberty, or give me death” Gentzen’s remarks on density matrices (#24) are well-conceived and clearly stated (as they seem to me). Thanks! I got all the way to the bottom of the SMBC thinking I should possibly point it out to you before I saw your name on it. It just seemed so much like what you’ve been saying! Niraj #27: Not sure if I understand the error. Had the OR/XOR distinction been relevant given the context, the mom could’ve added, “superposition doesn’t mean AND, and it doesn’t mean OR, and it doesn’t mean XOR either.” 🙂

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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. Scott: Is tunneling, Heisenberg uncertainty, and action at a distance really consequences of complex amplitudes? I would think to predict tunneling you’d need to know Schrodinger’s equation, to understand the uncertainty principle you need to know [x,p], and to get action at a distance you need entanglement. Can’t all those things exist independently of complex amplitudes? Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication [we simulate] a protein containing over a thousand nuclear spins…