Answers.Body: <p>I don't know of anything that quite mimics it in regular life, though you could go through a sort of imagined construction that mimics the idea fairly well:</p>
  <p>There is a beach ball, and it is formed by a circular bit at one end, and the strips of plastic, like so:</p>
  <p><a href="https://i.sstatic.net/75c3A.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/75c3A.png" alt="Beach Ball from https://www.senteqdirect.co.uk/wp-content/uploads/2019/04/GiantBB.jpg" /></a></p>
  <p>Let's imagine that the circle on the other side is black, so we have a white circle and a black circle on opposite ends, and delightful, rainbow strips of plastic for the rest of the ball.</p>
  <p>I'll put a strong magnet on the white circle, and on the black circle on the other side.  Now they're magnetized!  But we've faced the magnets in opposite directions, so that either side of the ball will be attracted or repelled the same way by any magnet we hold nearby.</p>
  <p>I want to know whether the white circle is facing north or south.  And this is one of the key ideas: those are the only two possible answers!  North, or south.</p>
  <p>If I put it like so, then it will be facing north.  If I turn it around, the white circle is now facing south.</p>
  <p>Now I spin it haphazardly, and it winds up facing mostly towards the floor and a bit that way, we can again the question: is it facing north or south?  But now it's more complicated, of course.</p>
  <p>You might first object, and say it is not facing north or south at all. We even just <em>said</em> that it is facing towards the floor and a bit that way.  But I will point out that we stipulated that there are only two possible answers.  There is only North, and there is only South.  So, is it facing north?  Or south?</p>
  <p>The answer is... sort of north... and sort of south... and, we call this superposition.  In a world in which everything must be characterized purely by north and by south, it is some of both.  That's what superposition means.  It means it's facing a different way entirely.</p>
  <p>When we do this with real quantum states, we can't see the balls with our eyes.  Instead, we must make a measurement.  For that, we have to go back to those two magnets we placed onto the black and white circles.</p>
  <p>What we can do is essentially place a stick with a powerful magnet on the end in the direction we want to measure.  The magnet is powerful enough that the ball will definitely rotate to meet the stick.</p>
  <p>Once it's on the stick, I can look at the end and see if I have captured the black end or the white end, and now I know whether it's facing north or south.</p>
  <p>If the ball is rotated 90% before we start, there's no way to know what answer I'll get out.  In fact, assuming my ball is really good, there's essentially a 50/50 shot that I will find the white circle facing north or south.  There's no way to know which way it will turn.  That's a perfect superposition.</p>
  <p>So a few takeaways: if I can only read the state with a magnetic stick like this, is there any way to read the state of the qbit without also modifying the state?</p>
  <p>No?  Well, there <em>is</em> a way, actually.  The only way is if it already happens to be facing due north or due south.  Otherwise, my reading the qbit will force it to conform to the reading stick.  In other words, figuring out which way the ball is facing will also change which way the ball is facing.  It will face it either exactly towards, or exactly away from, the magnet I'm using to read its position.</p>
  <p>Second, is there any way to tell, just by placing our magnet stick, where the ball was actually facing before we started to measure?  What do you think?</p>
  <p>The answer is no.  We have to choose an orientation, and then make our &quot;read&quot; along that orientation.  What we get out of that read is probabilistic.  We hope that whatever program we ran on this qbit faced the qbit sufficiently north or south that we can rely on our reading, but in truth we probably have to run our program a bunch of times before we can get a firm sense about the result with any confidence.</p>
  <p>Thirdly, and finally, there's actually a key difference between a qbit in superposition and this beach ball: we said that if the superposition is 90 degrees off, there's a 50/50 shot that the ball will read as north or south.  That remains true for qbits as well.</p>
  <p>But if you only rotate 15 degrees from north, this life-sized beach ball will always read as north, because that is the closest magnet.  But this part is a bit different for real qbits.  Our qbit will only read as north 85% of the time, and the other 15% it will read as south.</p>
  
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Body: <p>An early step of building students' QIS knowledge is understanding superposition in a 2-state system. What are effective metaphors and actual systems for teaching the concept of uperposition, that a thing is actually in both states?</p>
  
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Comments.Text: Ooh, the course I took on quantum computing with Qubit by Qubit last summer will finally come in handy!
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Comments.Text: Also, welcome back :)  We've missed you.
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Tags: <quantum-computing>
Title: To introduce quantum computing, what metaphors/actual examples of 2-state systems work for teaching, and what misconceptions might they introduce?
ThreadText: # To introduce quantum computing, what metaphors/actual examples of 2-state systems work for teaching, and what misconceptions might they introduce?
  
  (Asked by: username_0 on 2022-08-02)
  
  An early step of building students' QIS knowledge is understanding superposition in a 2-state system. What are effective metaphors and actual systems for teaching the concept of uperposition, that a thing is actually in both states?
  
  **Tags:** quantum-computing
  
  > **Comments:**
  > **username_1**: Ooh, the course I took on quantum computing with Qubit by Qubit last summer will finally come in handy!  
  > **username_1**: Also, welcome back :)  We've missed you.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-08-04. Score: 1
  
  I don't know of anything that quite mimics it in regular life, though you could go through a sort of imagined construction that mimics the idea fairly well:
  
  There is a beach ball, and it is formed by a circular bit at one end, and the strips of plastic, like so:
  
  [![Beach Ball from https://www.senteqdirect.co.uk/wp-content/uploads/2019/04/GiantBB.jpg](https://i.sstatic.net/75c3A.png)](https://i.sstatic.net/75c3A.png)
  
  Let's imagine that the circle on the other side is black, so we have a white circle and a black circle on opposite ends, and delightful, rainbow strips of plastic for the rest of the ball.
  
  I'll put a strong magnet on the white circle, and on the black circle on the other side. Now they're magnetized! But we've faced the magnets in opposite directions, so that either side of the ball will be attracted or repelled the same way by any magnet we hold nearby.
  
  I want to know whether the white circle is facing north or south. And this is one of the key ideas: those are the only two possible answers! North, or south.
  
  If I put it like so, then it will be facing north. If I turn it around, the white circle is now facing south.
  
  Now I spin it haphazardly, and it winds up facing mostly towards the floor and a bit that way, we can again the question: is it facing north or south? But now it's more complicated, of course.
  
  You might first object, and say it is not facing north or south at all. We even just *said* that it is facing towards the floor and a bit that way. But I will point out that we stipulated that there are only two possible answers. There is only North, and there is only South. So, is it facing north? Or south?
  
  The answer is... sort of north... and sort of south... and, we call this superposition. In a world in which everything must be characterized purely by north and by south, it is some of both. That's what superposition means. It means it's facing a different way entirely.
  
  When we do this with real quantum states, we can't see the balls with our eyes. Instead, we must make a measurement. For that, we have to go back to those two magnets we placed onto the black and white circles.
  
  What we can do is essentially place a stick with a powerful magnet on the end in the direction we want to measure. The magnet is powerful enough that the ball will definitely rotate to meet the stick.
  
  Once it's on the stick, I can look at the end and see if I have captured the black end or the white end, and now I know whether it's facing north or south.
  
  If the ball is rotated 90% before we start, there's no way to know what answer I'll get out. In fact, assuming my ball is really good, there's essentially a 50/50 shot that I will find the white circle facing north or south. There's no way to know which way it will turn. That's a perfect superposition.
  
  So a few takeaways: if I can only read the state with a magnetic stick like this, is there any way to read the state of the qbit without also modifying the state?
  
  No? Well, there *is* a way, actually. The only way is if it already happens to be facing due north or due south. Otherwise, my reading the qbit will force it to conform to the reading stick. In other words, figuring out which way the ball is facing will also change which way the ball is facing. It will face it either exactly towards, or exactly away from, the magnet I'm using to read its position.
  
  Second, is there any way to tell, just by placing our magnet stick, where the ball was actually facing before we started to measure? What do you think?
  
  The answer is no. We have to choose an orientation, and then make our "read" along that orientation. What we get out of that read is probabilistic. We hope that whatever program we ran on this qbit faced the qbit sufficiently north or south that we can rely on our reading, but in truth we probably have to run our program a bunch of times before we can get a firm sense about the result with any confidence.
  
  Thirdly, and finally, there's actually a key difference between a qbit in superposition and this beach ball: we said that if the superposition is 90 degrees off, there's a 50/50 shot that the ball will read as north or south. That remains true for qbits as well.
  
  But if you only rotate 15 degrees from north, this life-sized beach ball will always read as north, because that is the closest magnet. But this part is a bit different for real qbits. Our qbit will only read as north 85% of the time, and the other 15% it will read as south.
  
  > **Comments:**
  > **username_1**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/139016/discussion-on-answer-by-ben-i-to-introduce-quantum-computing-what-metaphors-ac).  
  
  ---
  
  