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 just a normal switch, and so I can’t dim the light. It is either fully on or fully off. I can change it at will, but this is the only thing I can do to it. 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 that is in another part of the building. I can’t see the light at all but, once again, its being 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 and the status of the light is still determined by that remote switch being on or off. This is a ‘‘classical’’ light.

Now 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. There is a line etched around the middle.

The interesting part happens when I cannot see the qu-light, when I am in the other part of the building with 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 definitely off. If I put it on the south, the qu-light is definitely 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!

The moment you open the door and see the qu-light, the indeterminacy is removed. It will be on or off. Moreover, if I had my finger on the qu-switch, the finger would be forced to one or other of the poles corresponding to the state of the qu-light when it was seen.

The act of 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 or not, that is enough.

If I place a video camera in the room with the qu-light and watch it when I try to place my finger on the qu-switch, it behaves just like a normal switch. I will be prevented from touching the qu-switch at anywhere other than the top or bottom. Since I’m making up this example, assume some sort of force field keeps me away from anywhere but the poles!

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, be 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.

What I just described is called a two-state quantum system. When it is not being observed, the qu-light is in a superposition of being on and off. We explore superposition in section 7.1.

While this may seem bizarre, evidently nature really works this way. 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. We return to this in section 11.3 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 bit, which can only be 0 or 1. The qubit is the basic information unit in quantum computing.

This book is about how we manipulate qubits to solve problems that currently appear to be 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 of on or off, 1 or 0, with |1⟩ and |0⟩, respectively. Instead of qu-lights, it’s qubits from now on.

In the diagram above, the position of your finger on the qu-switch is now indicated by two angles, θ and ϕ. The picture itself is called a Bloch sphere and is a standard representation of a qubit, as we shall see in section 7.5.