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Our first task in learning how quantum computers work is to understand the basic nature of waves. We’re all familiar with the waves at the beach and the ripples in a pond. The most basic kind of wave is a sine wave moving through space, a source that wiggles up and down or back and forth is sending out a wave and so anywhere that the wave goes also wiggles up and down or back and forth. Sound in the air, light, radio, microwaves, even the shaking of the ground in an earthquake; they are all waves of one form or another. Let’s look at what happens when we make waves in a rope.
The distance between two peaks in our wave is called the “wavelength.” The time between two peaks passing a point is called the “period”, and the number of times that peaks pass a point in one second is called the “frequency.” Our frequency with this rope is about two cycles per second, so our period is about half a second. There’s a special type of wave known as a “standing wave.” First, let’s send a wave down our rope. You can see that the wave starts at my end, and when it gets to Satoh’s end of the rope, it turns around and comes back. That reflection is just like light reflecting off of a mirror or an echo reflecting off a mountain.
If the wave is of a certain frequency and reflects properly, you wind up with a wave that appears to move up and down in place without going anywhere. We can have standing waves that look like halfwave or a whole wave or even higher multiples. Standing waves hold a special place in quantum mechanics and quantum computing. When we get to qubits or quantum bits shortly, if you want, you can think of a qubit as a box with waves in it that holds two different kinds of standing waves. We could for example make the half wave be our zero state and the full wave be our one state. When you study physics, you will spend a lot of time working with waves.
Both the mathematics and the images are beautiful and result in some unexpected effects. We will study those next.


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