1.1 The mysterious quantum bit
Suppose I am standing in a room with a single overhead light and a switch that turns the light on or off. This is a normal switch, so I can’t dim the light. It is either entirely on or entirely off. I can change it at will, but this is the only thing I can do to the switch. There is a single door to the room and no windows. When the door is closed, I cannot see any light.
I can stay in the room, or I may leave it. The light is always on or off based on the position of the switch.
Now, I’m going to do some rewiring. I’m replacing the switch with one located in another part of the building. I can’t see the light from there, but once again, whether it’s on or off is determined solely by the two positions of the switch.
If I walk to the room with the light and open the door, I can see whether it is lit or dark. I can walk in and out of the room as many times as I want. The status of the light is still determined by that remote switch being on or off. This is a “classical” light.
Let’s imagine a quantum light and switch, which I’ll call a qu-light and qu-switch, respectively.
When I walk into the room with the qu-light, it is always on or off, just like before. The qu-switch is unusual in that it is shaped like a sphere, with the topmost point (the “north pole”) being OFF and the bottommost (the “south pole”) being ON. A line is etched around the middle, as shown in Figure 1.1.
The interesting part happens when I cannot see the qu-light when I am in a different part of the building from the one the qu-switch.
I control the qu-switch by placing my index finger on the qu-switch sphere. If I place my finger on the north pole, the qu-light is off. If I put it on the south, the qu-light is on. You can go into the room and check. You will always get these results.
If I move my finger anywhere else on the qu-switch sphere, the qu-light may be on or off when you check. If you do not check, the qu-light is in an indeterminate state. It is not dimmed, it is not on or off; it just exists with some probability of being on or off when seen. This is unusual!
You remove the indeterminacy when you open the door and see the qu-light. It will be on or off. Moreover, the switch is forced to the north or south pole, corresponding to the state of the qu-light when you see it.
Observing the qu-light forced it into either the on or off state. I don’t have to see the qu-light fixture itself. If I open the door a tiny bit, enough to see if any light is shining, that is enough.
If I place a video camera in the room with the qu-light and watch the light when I put my finger on the qu-switch, the qu-switch behaves like a normal switch. I am prevented from touching the qu-switch anywhere other than the top or bottom, just as a normal switch only has two positions.
If you or I are not observing the qu-light in any way, does it make a difference where I touch the qu-switch? Will touching it in the northern or southern hemisphere influence whether it will be on or off when I observe the qu-light?
Yes. Touching it closer to the north pole or the south pole will make the probability of the qu-light being off or on, respectively, higher. If I put my finger on the circle between the poles, the equator, the probability of the light being on or off will be exactly 50–50.
We call what I just described a two-state quantum system. When no one observes it, the qu-light is in a superposition of being on and off. We explore superposition in section 7.1. superposition two-state quantum system
While this may seem bizarre, evidently, nature works this way. For example, electrons have a property called “spin,” and with this, they are two-state quantum systems. The photons that make up light itself are two-state quantum systems via polarization. We return to this in section 11.9.3 when we look at polarization (as in Polaroid® sunglasses).
More to the point of this book, however, a quantum bit, more commonly known as a qubit, is a two-state quantum system. It extends and complements the classical computing notion of a bit, which can only be 0 or 1. The qubit is the basic information unit in quantum computing. qubit quantum$bit Bloch sphere
This book is about how we manipulate qubits to solve problems that currently appear intractable using just classical computing. It seems that just sticking to 0 or 1 will not be sufficient to solve some problems that would otherwise need impractical amounts of time or memory.
With a qubit, we replace the terminology and notation of on or off, 1 or 0, with the symbols |1⟩ and |0⟩, respectively. Instead of qu-lights, it’s qubits from now on.
In Figure 1.2, we indicate the position of your finger on the qu-switch by two angles, θ (theta) and φ (phi). The picture itself is called a Bloch sphere and is a standard representation of a qubit, as we shall see in section 7.5.
