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Hadamard Gate

Discussion in 'Microcontrollers, Programming and IoT' started by quantumtangles, Sep 8, 2013.

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  1. quantumtangles

    quantumtangles

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    Dec 19, 2012
    Qwires are two dimensional lines of say copper atoms, or any conductor, provided its not 3-dimensional. Left and/or right, but not up, down or diagonal. Intuitively fine.
    The input is always the same as the output because all it does is...well...nothing much. It allows the input to travel along the single layer or line of copper atoms. A two-dimensional wire.

    The next component is at least mathematically intuitive. NOT gates simply invert the input, whatever it may have been. Accordingly, two NOT gates in series reverse the input 'twice'...so the output is the same as the initial input. Groovy.

    Finally, Hadamard Gates I find the most difficult to understand. After spending hours doing sums, two Hadamard Gates in series perform precisely the same function as two NOT gates in series. The output is also identical to the original input.

    Accordingly, Qwires; 2 x NOT gates in series; and 2 x Hadamard gates in series all give identical output to that which was the original input.

    Questions:

    1. How can I make a NOT gate?
    2. How can I make a Hadamard Gate?
    3. What possible benefit arises from using two Hadamard Gates in series over and above a QW and/or over and above two NOT gates in series?
     
    Last edited: Sep 8, 2013
  2. KrisBlueNZ

    KrisBlueNZ Sadly passed away in 2015

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    Nov 28, 2011
    Let me preface my answer by saying that I have no specific knowledge of Qwires, nor Hadamard gates.

    A NOT gate, also called an inverter, is an electrical circuit that accepts one logic-level signal (0 or 1) at its input, and produces one logic-level signal at its output which is the logical opposite of the input; in other words, output = (1 - input).

    In the process of performing this inversion, the NOT gate introduces a propagation delay; that is, the output does not change immediately when the input changes. The delay depends on the technology used, including the feature size (which affects the capacitance), the specifics of the components and design used in the NOT gate, the supply voltage and operating current used, the nature of the circuits driving the input and receiving the output, and probably a lot of other factors.that I don't know about and/or can't think of right now. If two NOT gates are cascaded, their propagation delays add together.

    Secondly, a NOT gate also performs some amount of cleaning up of the input, when you view the input as a voltage rather than a perfect logic 0 or logic 1. That is, as the input voltage rises from logic 0 to logic 1, or falls from logic 1 to logic 0, there will be a range of voltages over which the output transitions. For example in a 5V circuit, if the input voltage is raised steadily from 0V (low, "0") to 5V (high, "1"), the output will be initially high, then (for example) when the input reaches 2.4V the output starts to fall from 5V towards 0V, and when the input has reached 2.6V the output reaches 0V. So the input is "cleaned up". Cascading two NOT gates improves this "cleaning up" behaviour. A gate with a Schmitt trigger input performs a different kind of cleaning up; look them up if you're interested.

    Thirdly, a NOT gate provides buffering. That is, the output can (or may be able to) drive a heavier load than the input could. This load could be resistive, capacitive, or a combination of both. For more information, look up the term "fan-out".

    Compared to two cascaded NOT gates, a simple wire has none of these three features.

    I have no idea what a Hadamard gate is. I found "Hadamard product" on Wikipedia and it appears to relate to matrix calculations, which have multiple inputs and outputs. (A matrix calculation with one input and one output is just a unary operator; not a matrix calculation at all.)

    If you can explain these other terms in more detail I may be able to help, but I think the above is probably all I can tell you.
     
  3. Harald Kapp

    Harald Kapp Moderator Moderator

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    Nov 17, 2011
    Kris,
    I think the OP's question is outside the scope of classical electrical engineeering. He seems to be talking quantum mechanics. A Hadamard gate is a kind of quantum gate.
    That's why he refers to the almost infinitesimal thin "wire".

    I'm afraid this forum is not the right place to answer these questions (unless we have a physicist among us, that is).
     
  4. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    I know just enough about physics to suggest he speak to a real physicist. :D
     
  5. quantumtangles

    quantumtangles

    152
    3
    Dec 19, 2012
    Probably the wrong place to ask non-classical questions, sorry.

    This is the Youtube video that led to me looking at this



    Thanks ChrisNZ for such helpful detail on classical NOT gates. It answers the question to a large extent... by analogy with decoherence. Decoherence essentially means external interference [the environment messing with the stability of superpositions]. Internal interference in classical NOT gates is the same thing inside out...the other way round [internal rather than external] which I had not thought of.

    It is how the microscopic and macroscopic worlds interact that interests me. Quantum computers are useful in some ways but they will be used in tandem with classical computers. Some researchers use optics [high end lasers and beam splitters] to make their circuits. But what fascinates me involves silicon chips. A single phosphorous atom inside a sandwich of silicon...(atomic numbers 15 and 14 respectively) where the valence electron does the work [the Kane Qcomputer, University of New South Wales], and they might look just like a regular IC but for the problem of decoherence analogously described by Chris. I think the boundary between classical computing and quantum computing is going to become increasingly blurred.
     
    Last edited: Sep 10, 2013
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