It's rare that you find an article that explains something as complex as Quantum Computing in such a friendly and...
It's rare that you find an article that explains something as complex as Quantum Computing in such a friendly and easy to understand manner. Great read.
http://investigate.ingress.com/2018/01/11/the-next-machines/
http://investigate.ingress.com/2018/01/11/the-next-machines/
Oh, for heaven's sake: a quantum system cannot be in two states at once! That's not what a superposition is. The guy they did the interview with presumably knows better, but if he wrote that stuff on an undergraduate quantum exam he'd fail. It would be nice to see someone write popular explanations of these things that weren't so deeply misleading. Quantum computing in principle has some advantages, but it's not magic - and given the many failed attempts to make it practical over the decades, I think one ought to view it with a certain measure of skepticism.
ReplyDeleteIncidence Matrix Why don't you do us a favor and explain what he supposedly didn't.
ReplyDeleteArnold Schwarzenegger I started writing a description of how states work, but realized that it was going to be too long for anyone to read. I elected instead to try offering another metaphor, and that ended up also being long - but I'll give it a try anyway. (Like all metaphors, this one is imperfect, but I think it captures the essence of the phenomenon more clearly.) Imagine you have a friend named Sally. Sally likes two things: sandwiches, and playing woodwind instruments. If you ask Sally what sandwich she is eating, she'll tell you - and if she wasn't eating one before, she'll pull one from her copious pockets and start doing so. Likewise, if you ask Sally what instrument she is playing, she'll point to it annoyedly, and if she wasn't already playing she'll grab an instrument from her pocket and start doing so. That's just how she rolls.
ReplyDeleteNow, when Sally grabs at a sandwich or instrument, she's pretty careless, and you can never be sure exactly which one she's going to end up with. Sometimes it's pastrami on rye, or a BLT...or a trumpet, or a clarinet. It's random. (You notice that she's more likely to grab some things than others, depending on what she is currently doing, but if she has to grab something there's always an element of randomness.) On the other hand, once she's started doing something, Sally tends to keep doing it until something intervenes to change her behavior. If Sally is eating a ham sandwich and you ask her what she is eating, she'll continue with that sandwich (and tell you). If Sally is playing the trumpet, she's not going to switch when you ask her about her instrument. She'll just be annoyed.
Let's now imagine that you ask Sally about her sandwich, and she pulls out a grilled cheese and chows down. You keep asking her about it and she keeps giving you the same answer (grilled cheese), and you are getting bored. You think back to your quantum mechanics class, and realize that Sally is just like a quantum system that is in a so-called "pure state" (or eigenstate) with respect to a "sandwich mesaurement operator." When you "measured" her sandwich eating, her state "collapsed" into one associated with the grilled cheese, and there she stays until something happens to change her behavior. You now muse about what would happen if you asked her what instrument she was playing (you used an "instrument measurement operator"). She might pull out a trumpet, or she might pull out an oboe - who knows? You realize that, in quantum mechanics, you would say that she is in a superposition state with respect to instrument playing. She's not in the "playing trumpet" state, nor in the "playing oboe" state, although she might end up in either if you measured her - her state (as she eats her sandwich) is something else again.
(Note that it would be absurd at this point to say that Sally is both playing the trumpet and the oboe. She's eating a damn sandwich. It only makes sense to talk about what instrument she is playing when she plays one.)
OK, at this point you want to hear a song, so you ask Sally what instrument she is playing. She now spits out her sandwich, pulls a trumpet from somewhere, and starts performing. Sally is now in an eigenstate ("playing trumpet") of the "instrument measurement operator." It occurs to you that if you asked her about sandwiches, there is no guarantee that she's go back to the grilled cheese - she'd pull something out, and it might be a different sandwich entirely. She is no longer in an eigenstate of the "sandwich measurement operator," and is in a superposition of sandwich eating states. Again, this doesn't mean that she is eating different sandwiches at once - she is not eating any sandwiches - but that if you made her eat one, it's not clear which one she would start eating. This is due to a deep truth: you can't eat sandwiches and play wind instruments at the same time. Sandwich and instrument measurement are incompatible operators. The eigenstates of one are not eigenstates of the other, so if you measure Sally with respect to sandwich eating she has dump her instrument and if you measure her instrument playing she has to dump her sandwich. She can't do both types of thing at the same time.
ReplyDeleteAs you contemplate this, it occurs to you that there are things that Sally can do while playing the trumpet. You ask her which song she is playing, and she points you to a card mounted on her trumpet (which you have never noticed before) with the music to "Miles Ahead." She doesn't stop playing, nor does she change her tune. This is because the "song measurement operator" is compatible with the "instrument measurement operator" - they share common eigenstates (like "playing Miles Ahead on trumpet"). You realize that if you had asked her about the song she was playing while she was eating, Sally would have again had to spit out the sandwich and grab an instrument, so "song measurement" is not compatible with "sandwich eating." It doesn't make any sense to contemplate what song Sally is playing when she is eating, and it is equally senseless to ask what sandwich Sally is eating when she is playing Miles Ahead on trumpet. The incompatibility of states expresses the idea that these are things that Sally cannot do at the same time.
And this is, in essence, how eigenstates and superposition states work. When we say that a quantum system is in a superposition state with respect to some operator (and such a statement must always be in reference to an operator, or more generally a basis set ), we are saying (among other things) that we are uncertain what the system will do if we measure it in the way that the operator defines. We are most certainly not saying that the system is doing two different things at once. Indeed, that's because, if the system is in superposition, it is essentially doing something else, that is incompatible with the measurement we are contemplating. This is not mysterious: we have no problem with it when we think about eating a BLT versus playing a bassoon. The thing that is odd about quantum mechanics is that many things we think of as being "properties" of a system turn out to be more like "behaviors" at the microscopic level.
So, angular momentum is a thing that an electron "does," not a thing that it "has." And, moreover, if an electron is busy "doing" angular momentum about the Z axis, it can't also be "doing" angular momentum about the X axis. If you measure its angular momentum about the Z axis, it will collapse into a Z eigenstate...but then it must be in a superposition state with respect to the X axis. The state itself is well-defined, just like Sally and her trumpet, but it entails uncertainty about what you would see if you performed the other measurement (just like you don't know what sandwich Sally would grab if you prompted her to do so). That uncertainty isn't because we don't know what the X-axis angular momentum is, but because it isn't doing X-axis angular momentum in the sense of our measurement. Asking about it makes about as much sense as asking what type of sandwich Sally is eating while she plays the trumpet.
ReplyDeleteAnd that is one attempt at explaining how states work in quantum mechanics, using only sandwiches and wind instruments. As forewarned, no metaphor is perfect, and neither is this one. However, I personally view it as being much closer to what the theory says (and how the math involved works) than the usual "quantum systems can be in two places at once" nonsense. I hope it also gives insight into the dominant view that one cannot meaningfully speak of certain quantum mechanical properties existing when they aren't measured. This seems esoteric, until you think of those properties as behaviors rather than attributes. There are things you just can't do at the same time, and when doing one it makes no sense to speak of your doing the other. As for quantum computing, that is yet another level of complexity, but again it is not magic. QM is sometimes strange, but in my view it is usually less bizarre than popular accounts make it sound.