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First Quantum Computing Gate on a Chip

An anonymous reader writes "After recent success in using quantum computing for superconducting qubits, researchers from Delft have formed the first Controlled-NOT quantum gate. 'A team has demonstrated a key ingredient of such a computer by using one superconducting loop to control the information stored on a second. Combined with other recent advances, the result may pave the way for devices of double the size in the next year or two--closer to what other quantum computing candidates have achieved, says physicist Hans Mooij of the Delft University of Technology in the Netherlands. Unlike today's computers, which process information in the form of 0s and 1s, a quantum computer would achieve new levels of power by turning bits into fuzzy quantum things called qubits (pronounced cue-bits) that are 0 and 1 simultaneously. In theory, quantum computers would allow hackers to crack today's toughest coded messages and researchers to better simulate molecules for designing new drugs and materials.'"

41 of 166 comments (clear)

  1. Double the size of a single not gate? by Spazntwich · · Score: 5, Funny

    I know grammar has been taking a hit in society as of late, but now even our computers are blatantly spewing out double negatives?

    We're not in for an unrough ride, gentlemen.

    1. Re:Double the size of a single not gate? by Jazz13 · · Score: 2, Funny

      Rodney McKay steps through the resulting tear in space time and smacks you up the back of the head.

  2. A solid milestone... by teebob21 · · Score: 5, Interesting

    I find it interesting that the first electronic computing gates devised were the AND/OR gates, using basic diode logic. Quantum computing research develops the NOT gate first. I think this has something to do with the esoteric nature of quantum computing. AND/OR gates require two inputs to change to a single value, where NOT is merely an inverter. The idea of entanglement makes the inversion process a likely first step in quantum research.

    For those wondering why this is important, the first true electronic gates were invented in the early 1920's. This predates point-contact transistors by about 20 years, invented in 1947. 60 years later, here we are with transistor computing in every aspect of our lives.

    At the rate quantum computing is advancing, I think we can expect to see quantum transistors (in the lab, at least) by 2020. A true useful quantum computer may be available less than 50 years from now. Hopefully by then someone will pick up the slack and have the Linux kernel ported to the Q-CPU architecture!

    --
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    1. Re:A solid milestone... by Ant+P. · · Score: 2, Interesting

      What is a quantum computer good for, anyway? So far all I've seen is cracking encryption and other stuff involving gigantic calculations. Is there anything in the mainstream market it'd be useful for, like sound/video processing?
      Come to think of it, arithmetic encoding is a bit like encryption...

    2. Re:A solid milestone... by Simon80 · · Score: 2, Insightful

      I wouldn't know for sure, but I don't think it's valid to compare any form of computing based on binary logic with quantum computing. I searched for "quantum transistor" and found this, which makes use of the term to refer to transistors that rely on principles of quantum mechanics to function properly. This would be relevant to conventional computing, but not quantum computing. If I understand correctly, quantum computing is not a replacement for binary logic computing, but an alternative or supplement.

    3. Re:A solid milestone... by pablob · · Score: 5, Informative

      I find it interesting that the first electronic computing gates devised were the AND/OR gates, using basic diode logic. Quantum computing research develops the NOT gate first. I think this has something to do with the esoteric nature of quantum computing. AND/OR gates require two inputs to change to a single value, where NOT is merely an inverter. The idea of entanglement makes the inversion process a likely first step in quantum research.

      Keep in mind that this is a Controlled-NOT gate (a two-input gate) and not a simple NOT gate (a one-input gate). It has been proven that if you can implement two-qubit C-NOT and arbitrary one-qubit operations, you can implement a universal quantum computer (that is, one that can run an arbitrary "quantum program").

      There is a deeper reason for quantum computers not to use AND/OR gates, which is their irresibility (AND and OR are two-input to one input gate, which makes them irreversible). Quantum Mechanics is intrinsically reversible, so a quantum computer should be reversible too and that's why it is not common to hear about Quantum AND or Quantum OR.

      Pablo B.

    4. Re:A solid milestone... by asuffield · · Score: 5, Interesting

      For those wondering why this is important, the first true electronic gates were invented in the early 1920's. This predates point-contact transistors by about 20 years, invented in 1947. 60 years later, here we are with transistor computing in every aspect of our lives.


      However, it is important to realise that the theory of computation had been in development since the early 1800s (and the logic underlying that had been around for centuries); by the time the first electronic devices were created, we already had a good understanding of what they could be used for, because we had been doing exactly the same things by hand for over 50 years at that point (the word "computer" originally meant a person who performed such computations, and an "electronic computer" was just a device to replicate the task that person was doing).

      We can't do quantum computations by hand, so we have no real experience with the theory, and the underlying statistical methods are relatively recent developments: quantum computers do not use the classical logic that we're all familiar with. This is a massive setback compared to the development of the electronic computer - and advances in theory usually can't be accelerated all that much. It is likely to be between 50 and 100 years before we know enough to build non-trivial applications out of quantum computers. Not because we can't build the hardware, but because we don't know how to write any software to run on them. The entire field of software development will have to be reinvented, and we don't actually know that it will be useful for anything. Unlike the first electronic computers, which had very real and obvious applications performing the tasks that were currently being done by hand, we have only vague theories and ideas about what quantum computers might be useful for. (Even the much-quoted method for breaking certain encryption algorithms is based on various assumptions that aren't proven; we don't know for sure whether quantum computers will actually be able to run it, yet)

      We'll get there eventually, but it will probably take a long time and we can't really predict at this stage whether it'll be particularly useful. From what we know so far, these things are going to be incredibly arcane and obtuse to work with, and that is going to make it difficult. We might see it in our lifetimes, but I wouldn't place any bets on it, it might take much longer. The things we're playing with today may turn out to be the Babbage engines of quantum computing.
    5. Re:A solid milestone... by Anonymous Coward · · Score: 2, Insightful

      Most of the hard logistics problems are forms of nonlinear optimization and usually reduce to integer programming, which is solved by a pretty blind search (excluding tricks like branch and bound, pruning; it's still a tree search). Improving these solutions by a few percent translates into a lot of money very quickly.

      Esoteric, maybe (it'll be a computer in a lab, not a PC), but usable nonetheless.

    6. Re:A solid milestone... by jp102235 · · Score: 4, Interesting

      Well, inverting logic is well, logical (no pun intended) to most modern digital logic designers of the CMOS type. CMOS logic (and its variants) are inherently inverting. That is, the basic gate in CMOS is an inverter. The next higher complexity of gates in CMOS is a NAND and NOR (AND NOT / OR NOT). To make an AND gate requires a NAND and an Inverter... same thing for OR : a NOR and an Inverter. Although the quantum abstraction of computation may not be the same as CMOS (inverting layers of logic) it is not surprising at all that the designers tried to make an inverter first. Had they started during the days of relays, we might have had a different gate altogether. JP

      --
      jp
    7. Re:A solid milestone... by fatphil · · Score: 2, Informative

      Controlled-Not is not Not. Controlled-Not is "if the control line is 1, then not the input, else preserve the input", i.e. XOR. (But being quantum, it must also output the control line too, so that the operation can be reversed.)

      --
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    8. Re:A solid milestone... by Schemat1c · · Score: 2, Funny

      What is a quantum computer good for, anyway? You could use it to store your recipes.
      --

      "Nobody knows the age of the human race, but everybody agrees that it is old enough to know better." - Unknown
    9. Re:A solid milestone... by pablob · · Score: 3, Informative

      Is there a reason why it's called a NOT gate rather than XOR? Is there some quantum wierdness that makes the thing asymmetric and causes A-inverts-B to mean something different to B-inverts-A?

      I guess it's mostly historical, and that XOR is usually associated with a two-input/one-output gate. Controlled-NOT looks pretty intuitive (the target is negated only if the control is 1), but probably XOR is better because A-inverts-B is exactly the same as B-inverts-A (which seems counterintuitive when you think of it as a CNOT, but it's reasonably simple to see that is the case by just looking at the corresponding truth table).

      But I would venture that most people working on trying to build quantum computers would be more familiar with CNOT than XOR in the context of quantum computation (QXOR sounds weird, doesn't it?)

      Pablo B.

    10. Re:A solid milestone... by pdbaby · · Score: 2, Funny

      Regex pedantry here, but you're being overly permissive - you allow semantically invalid words: as, ars & arss.

      As a side-note, if you like hearing from your local regex pedant, please remember to donate g(ener|ratuit)ously: we survive only through your funding

      ...it's like I know I should be ticking 'Post Anonymously' but I just can't stop myself

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    11. Re:A solid milestone... by Dantu · · Score: 2


      We can't do quantum computations by hand, so we have no real experience with the theory, and the underlying statistical methods are relatively recent developments: quantum computers do not use the classical logic that we're all familiar with


      I'm not an expert on Quantum computers, but I think the math/computer science is WAY ahead of the physics on this one. Please correct me if I'm wrong, but I think a Quantum computer is to a normal computer as a NFA is to an DFA (http://en.wikipedia.org/wiki/Nondeterministic_fin ite_state_machine). In this case it's really not a new idea at a fundamental logical level. I realize these only apply to regular languages, not general Turing problems, but that's because you can convert one to the other, so in THEORY they are equivalent anyway. Similarly, conventional computers can solve the same set of problems that quantum computers can solve, they just require an expansion of the problem which in the real world requires much more time and/or space to complete.

      Of course, we don't have (that I know of) nice high-level compilers for them yet, but I think that's a whole different issue.

    12. Re:A solid milestone... by afaik_ianal · · Score: 2, Funny

      you allow semantically invalid words: as, ars & arss.

      No they don't. The only matches are ass, ase, arss and arse, but your point still stands. When being a pedant, it's also polite to provide a correction. The regex they were after is: a(rse|ss).

      ...it's like I know I should be ticking 'Post Anonymously' but I just can't stop myself

      At least tick "No Karma Bonus", please :).
    13. Re:A solid milestone... by afaik_ianal · · Score: 3, Informative

      You're getting confused between the distinction between bits/transistors, and qubits/quantum gates. The difference between tubes and transistors is nothing like the difference between transistors and quantum gates. Bits and qubits are just as dissimilar.

      Like transistors, tubes are just amplifiers. Contrary to popular belief, both are analogue components, but they have quite different responses to changes in current (the graphs are a different shape). Many people consider tube amplifiers to produce better sound quality than transistor amplifiers, and tubes will almost always handle clipping better than transistors. There's actually not much a transistor can do that a vacuum tube can't.

      Either tubes or transistors can be used to implement logic gates. These gates can be built up to store and process bits of information. In the digital world, they are functionally similar. The advantages of tubes from the analogue world go out the window, and the advantages of transistors (size, speed and cost) come into their own.

      Quantum computers are another thing entirely. The computers you and I are using at the moment are deterministic Turing machines. Quantum computers are non-deterministic. Quantum gates deal not in bits, but in qubits. They don't think in terms of binary data, they work with quantum states.

      There are many things that these quantum components can do that conventional transistors cannot, but I don't think we'll be seeing quantum gates implementing binary logic in computers any time soon (if ever). The article unfortunately confuses the issue by making it sound like they've implemented a binary operation. CNOT is not a binary operation - it is a quantum operation.

      I hate analogies as much as the next guy, but if tubes are the horse and cart, and transistors are our cars, then quantum computing is going to be our interstellar space craft - they suck for doing the weekly shopping.

    14. Re:A solid milestone... by Short+Circuit · · Score: 2, Interesting

      Really? I know they can get close, and it's possible to prove that power must be consumed to change state, but I'd love to see a device with no leakage. Gates such as those used in NAND flash devices (dual MOSFETs) get pretty close, but I'm pretty sure even they leak, especially on read operations. You got me there. I'd forgotten about leakage across the insulating layer due to quantum tunneling. OTOH, a vacuum tube doesn't work well without power to the heating element. Come to think of it, though, one could still get current flow at ambient temperatures; It just wouldn't be nearly as large as when you have a hot cathode.

      My point is that quantum computers are not just special transistors with slightly different properties. They really are a completely different thing. You're never going to make an amplifier out of quantum gates, and you're never going to make a quantum computer out of transistors Point taken and noted. I'm still not very clear on how quantum computing works, but I'm looking forward to reading more discussions like this one in the future.
    15. Re:A solid milestone... by tsa · · Score: 3, Funny

      There will be a small market. I think the world needs only 5 or so quantum computers.

      --

      -- Cheers!

    16. Re:A solid milestone... by tbo · · Score: 2, Insightful

      Disclaimer: I am a quantum information scientist.

      If you re-read the article, you'll see that the gate is a controlled-NOT (aka CNOT) gate, rather than a simple NOT gate. CNOT is a two-bit (or, in this case, two-qubit) gate. Simply being able to make and maintain single qubits is challenging (at least, for superconducting systems), manipulating single qubits is more challenging, and performing two-qubit operations is extremely hard. It's worth noting that this result is not the first example of a two-qubit gate in a superconducting system; rather, it appears to be the most complete so far.

      It's also worth noting that quantum CNOT gates were achieved years ago in other physical systems (NMR, ion traps, etc.). Part of the reason people are so excited about this is that, by virtue of it being on a chip, we may be able to apply the enormous amounts of chip-fab technology we already posses to scaling up the system.

    17. Re:A solid milestone... by Cope57 · · Score: 2, Funny

      What is a quantum computer good for, anyway? So far all I've seen is cracking encryption and other stuff involving gigantic calculations. Is there anything in the mainstream market it'd be useful for, like sound/video processing?
      Come to think of it, arithmetic encoding is a bit like encryption... It was probably created to handle the high demands of the Microsoft Vista operating system.
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    18. Re:A solid milestone... by tbo · · Score: 3, Informative

      I'm not an expert on Quantum computers, but I think the math/computer science is WAY ahead of the physics on this one. Please correct me if I'm wrong, but I think a Quantum computer is to a normal computer as a NFA is to an DFA (http://en.wikipedia.org/wiki/Nondeterministic_fin ite_state_machine). In this case it's really not a new idea at a fundamental logical level.

      I am an expert, and I don't think CS is ahead here; rather, I'd say CS and physics are moving forward in a partnership. As best as we understand the relevant complexity classes, quantum computer are not equivalent to an NFA. To put it another way, as far as we know, quantum computers cannot efficiently solve NP-complete problems. I say "as far as we know" because we don't even know for sure whether classical computers can efficiently solve such problems. Quantum information is a fundamentally new concept to CS, however.

      Similarly, conventional computers can solve the same set of problems that quantum computers can solve, they just require an expansion of the problem which in the real world requires much more time and/or space to complete.

      If you look simply at the domain of solvable computational problems, and don't care about efficiency, then yes, there's no difference. There are, however, communication problems and quantum "games" that cannot be solved with classical information but can be with quantum information.

    19. Re:A solid milestone... by Stefanwulf · · Score: 2, Funny

      Or you could store the superposition of all possible recipes simultaneously. It would simply decohere into the one you wanted once you began cooking.

      The trick is going to be figuring out the right first interaction to generate the recipe you're searching for.

  3. Like in Borat? by SilentOneNCW · · Score: 2, Funny

    Not Jokes:

    It's a Quantum Gate.... NOT!

  4. They say that it works by zmollusc · · Score: 4, Funny

    but how can they test it when the output is always either 0, meh, pfft or 1?

    --
    They whose government reduces their essential liberties for temporary security, receive neither liberty nor security.
    1. Re:They say that it works by Joebert · · Score: 2, Funny

      That's why they built a NOT gate, even if they failed, they'd still succeed.

      --
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  5. Quantum states by arashi+no+garou · · Score: 4, Interesting

    I'm no quantum theory expert by a very long shot, but it was my understanding that there are 32 quantum states of electrons, not just on/off (1/0) like in the binary computer world. So, if we now have a quantum NOT gate, doesn't that mean there are 32 possible states of the NOT gate? Also, according to the article the CNOT gates they created can be both 0 and 1 simultaneously. In my mind this would cause errors and actually stop the flow of information instead of speeding it up.

    Someone with some understanding of this stuff please elaborate, before my head asplodes.

    1. Re:Quantum states by LighterShadeOfBlack · · Score: 4, Funny

      but it was my understanding that there are 32 quantum states of electrons, not just on/off (1/0) like in the binary computer world. So, if we now have a quantum NOT gate, doesn't that mean there are 32 possible states of the NOT gate? Well, yes and no...

      *ba-dum-tsch* Thank you very much, I'll be here all week.
      --
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    2. Re:Quantum states by pablob · · Score: 4, Informative

      32? They should be 42!

      More seriously, a qubit (short for "quantum bit") has two well defined states, 0 and 1 (|0> and |1> for those QM buffs) just as a regular (classical) bit. The difference is that the classical bit has to be in either 0 or 1, while the qubit can be in what is called a "superposition" of those. So you could have a qubit in the 0 state, or in the 1 state, or in the "x% 1 and y% 0" state (where x+y=100). Part of the magic of quantum computers comes from this fact: using the proper operations, you can feed your quantum computer a register which is set up to "all possible inputs" so that it applies the algorithm to all possible values. Some people call this "Massive parallelism". You have to be careful, because Quantum Mechanics does not allow to extract the result of all those calculations (that would be great), so you have to go through some tricks to get useful information out of that "parallel processing".

      I hope this helped some!

      Pablo B.

    3. Re:Quantum states by mindriot · · Score: 5, Informative

      Note: I am not a physicist, this is just what I remember from a quantum computing lecture I attended years ago. Of course, rather than believing 100% in what I wrote, you're probably better off double-checking on Wikipedia and Google...

      The quantum states you're referring to do have something to do with this. However, their number isn't what's important.
      The interesting thing about the quantum computing world is that such states can be in superposition, that is, it is unclear whether or not the state is one or the other. You can only know that if you measure the state, the outcome will be state A in, say, 30% of the time, and state B in 70%. Now, you could probably extend this to 32 different states, but since we're used to bits, we'll build something where we just use two (for instance linearly polarized photons -- 0 degrees = 0, 90 degrees = 1).

      Now, there exist methods (or they're being researched) that allow you to put your bit into a superposition of its states. This could, for instance, be so that measuring the state will produce a 0 exactly half the time. Maybe you could put your Schroedinger cat in the box -- dead=0, alive=1...

      This by itself is not particularly exciting. But you could do that for multiple bits (say a 32-qubit word) so that measuring it, you get uniform probability to measure any number between 0 and 4294967295. Where it really gets interesting is when you apply quantum operators to your state: They can transform the state without destroying the superposition, i.e. without measuring it. For instance, if your superposition currently gives you 30% chance for measuring a 0 and 70% for a 1, then a CNOT gate would reverse that probability.

      Note, however, that a CNOT is a "controlled not": it has two inputs, the control and the target. The control passes through unchanged, but the target is flipped if and only if the control is 1 (i.e. the target output value is identical to the XOR of the input values). In a quantum world, this lets the two bits be entangled: For instance, if the target bit is 1, then the output of the target is 1 iff the control is 0 (target = NOT control). Now suppose that we create a superposition on the control input -- then the control output will be that same superposition, but the target output will be (NOT control) for all control values. In other words, we've just computed a function for all possible input values at once. And you can build these things larger, to do more useful things, such as with a 32-qubit input.

      The problem is, you thus get all possible results at the same time, but it's a superposition, and after measuring, you'll only have one result. Why is this useful? Because for one, you can construct some algorithms that transform the problem in such a way as to give a guaranteed result; in other cases, you'll do multiple samples and after a while you'll get your result -- and for some problems, you'll get it orders of magnitude quicker, on average, than on classical computers.

      For instance, the Deutsch-Josza algorithm is such an example. Assume I have a function that does one of two things -- it is either constant over the whole input domain, or it is balanced, that is, it returns 0 for exactly half the possible inputs and 1 for the other half. The function, to you, is a black box. How do you determine quickly whether the function is constant or balanced? On a classical computer, you have to test one more than half the inputs, in the worst case, to find out whether the function is balanced or constant. Using the Deutsch-Josza algorithm, you can solve the problem in *constant* time on a quantum computer.

      In other words, quantum computing may be interesting for some number-crunching applications. Of course the true capabilities of such a system are not yet completely understood. But I would think that for desktop computing it's probably not too relevant...

  6. Cracking by z-man · · Score: 4, Informative

    In theory, quantum computers would allow hackers to crack today's toughest coded messages.

    That's an overstatement. A quantum computer will not suddendly magically crack the strongest codes. Yes, certain algorithms designed for quantum computers, like Grover's algorithm, will reduce the time needed to find the key of a symmetrical cipher with about half the number of bits in the key. However, given for example a 256-bit key you would still have ~2^128 keys to check and afaik 2^128 still takes quite sometime to crack....

  7. Quantum gates? by Mikachu · · Score: 5, Funny

    They're opening the quantum gates now? They're insane! Who knows what might pour out of them... I hope they're at least doing it on the moon.

    The future of the human race is up to one lone marine now. Thanks a lot, scientists.

  8. Re:Fuzzy qubits of unknown distinction? by Joebert · · Score: 2, Funny

    Tribbles & Qubits: The new Pacman

    --
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  9. Used for what? by symbolset · · Score: 3, Funny

    At home you will use these for ever more sophisticated rendering of artificially intelligent virtual reality porn.

    At work it will be more useful in the advanced simulation of a mechanical process for imprinting letter glyphs on sheets of wood fiber.

    --
    Help stamp out iliturcy.
  10. Inversed qubit? by Lobais · · Score: 2, Interesting

    If a qubit is both 0 and 1 at the same time, what is the point of inversing it? Would it then be 1 and 0 at the same time?

    1. Re:Inversed qubit? by bh_doc · · Score: 2, Informative

      Absolutely correct. The way it's written in the text is a bit misleading. A qubit can be 0, 1, or some proportion of 0 and 1. It's like a continuum between 0 and 1, and a qubit can take any place along that continuum.

      The tricky thing is, quantum mechanics won't let you measure anything other one of two values (not strictly true, but go with me on this). But those values don't necessarily have to be 0 and 1, just so long as they are orthogonal to each other.

      Okay, to understand that last bit you need to bring in the fact that the proportions of 0 and 1, x and y say, can actually be any complex number, positive, negative, imaginary, whatever, just so long as their magnitudes-squared add to 1. So, then, instead of measuring for the 0 and 1 states, you could measure for "0.5" and "-0.5" states.

      This isn't even getting to the confusion of putting these things into gates.

  11. NOT Moore's Law by VisceralLogic · · Score: 3, Funny
    the result may pave the way for devices of double the size in the next year or two

    Hmm, seems like they've successfully performed a NOT on Moore's law.

    --
    Stop! Dremel time!
  12. Imagine slashdot on a quantum server! by EmbeddedJanitor · · Score: 3, Funny

    You'd never know if an article was a dupe or not.

    --
    Engineering is the art of compromise.
  13. Wow. ? by DoofusOfDeath · · Score: 3, Funny

    This is awesome no it's not!

  14. Really freaking fast processing by estimation by Wrexs0ul · · Score: 2, Interesting

    IAMAQP (I am not a quantum physicist) but the theory I read explains a system gaining processing power from shared computing of a single processor replicated across multiple realities. Each qubit is a calculated answer by a machine in one reality and the culmination of those answers assumedly gives you the correct response. David Deutsch wrote a book on this called "The Fabric of Reality" that works through the concept of a basic Turing machine - where computers all come from - and how this can be re-worked into a quantum processor.

    There's a lot more math to it than that, but the idea is a simpler approximation formula replicated infinitely across realities gives an accurate response much faster than any single reality calculating the absolute answer.

    Cooler yet is that if they're actually making functional quantum gates does this mean the processor power is actually being derived from other realities? That would be awesome and totally Outer Limits material.

    -Matt

    --
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  15. Re:Qubits? by tbo · · Score: 2, Insightful

    Disclaimer: I am a quantum information scientist

    Qubits represent a probability of being a 0 or 1. Observing a qubit destroys that probability, and you "read" only a zero or a one.

    This is at best an incomplete description of what happens. Qubits are quantum states, not probabilities. Quantum states are sometimes called "probability amplitudes", in that taking the square of the magnitude of the coefficient for a particular basis state gives you the probability of getting that state if you measure in that basis. There are a few very important points: (1) we're dealing with complex numbers, and things work in such a way as to give us the possibility of "interference" of probability amplitudes; (2) quantum states are real states, not just probabilities representing our ignorance of which classical state you'll find when you measure.

    A brief intro to the math:

    Let's take some qubit in some arbitrary state, which we'll call | psi > (I'm using Dirac notation). We can completely describe the state as follows:
    | psi > = a | 0 > + b | 1 >,
    where a and b are complex numbers, and have the property that |a|^2+ |b|^2 = 1. We see that we have an uncountably infinite number of possible states for just a single qubit. If psi were a classical bit instead of a quantum bit, we could use essentially the same description, except that the requirement on a and b would then be that exactly one of them is 1, while the other is 0 (only two possible states). If psi were a "classical" analog "bit" or a probabilistic bit, the requirement would be that a, b in [0,1], and a+b=1.

    What happens if we measure psi? It depends on the basis we choose to measure in, but if we go to measure psi in the {| 0 >, | 1 >} basis, we'll get | 0 > with probability |a|^2, and | 1 > with probability |b|^2. Figuring out probabilities for other bases requires only a basis transformation (simple linear algebra).

    Now, this qubit business seems horribly messy--we have an infinite number of states for a single qubit--how can we possibly describe the action of a two-qubit gate like controlled-NOT (CNOT)? Fortunately, quantum mechanics is linear, which means that if we describe how a gate operates on each of the possible input basis states, we've completely specified the gate. For two qubits, we can use the following basis: {| 00 >, | 01 >, | 10 >, | 11 >}. Labeling the rows and columns in that order, we get the following truth table for the CNOT gate:

    1 0 0 0
    0 1 0 0
    0 0 0 1
    0 0 1 0

    In other words, if the first bit is 0, do nothing to the second bit. If the first bit is 1, flip the second bit.

    It turns out that CNOT plus a bunch of different single qubit gates is universal, meaning you can use that set of gates to implement any "quantum circuit".

  16. Re:Quantum Not? by m1h41 · · Score: 2, Informative

    here's a simple representation of a C-Not on two qbits:
      ______
    -| NOT|-
    -|____|-

    the gate has two inputs and two outputs
    in direct computation the the inputs are on the left, the outputs on the right
    in reverse computation the other way around

    let's take direct computation,
    say the inputs(left side) are in_x(top) and in_y(bottom) and the outputs(right) out_x(top) and out_y(bottom)

    the C-Not performs the following function:
    out_x := in_x;
    out_y := ((not)in_y and in_x) or (in_y and (not)out_x)

    BUT it performs this functions simultaneously on a superposition of inputs,
    a superposition of inputs for a qbit roughly translates to: something like if I measure the qbit I may get 0 with p probability and 1 with (1-p) probability

    algebraically you would express this using in_y = sqrt(p) |0> + sqrt(1-p) |1>

    so literally the gate works like this: in the cases when in_x is 1, out_y will be 1 with a probability of p and 0 with a probability of (1-p) - exactly the inverse probabilities of in_y

    this is all roughly speaking, there are other more subtle aspects...