The Qubit

In this chapter, we start with the very basics of quantum computing–the quantum bit. And we will write our first quantum circuit. A quantum circuit is a sequence of quantum bit transformations–the quantum program. Let’s start with the basics.

The world of quantum mechanics is different. A quantum system can be in a state of superposition. A popular notion of superposition is that the system is in different states concurrently unless you measure it.

For instance, the spin of a particle is not up or down, but it is up and down simultaneously. But when you look at it, you find it either up or down.

Or, let’s say we flip a quantum coin. In the air, it has both values, heads and tails. If and only if we catch it and look at it, it has a specific value. Once landed, it is a normal coin with heads up or tails up.

Another notion of superposition is that the system is truly random and distinguishes it from the systems we know. Tossing a (normal) coin, for instance, seems random because whenever we do it, the conditions are slightly different. And even tiny differences can change the outcome from heads to tails. The coin is sensitive dependent to initial conditions.

If we were able to measure all conditions precisely, we could tell the outcome. In classical mechanics, there is no randomness. Things in our everyday world, such as the coin, seem random. But they are not. If measured with infinite precision, randomness would disappear. By contrast, a quantum system is truly random.

Maybe we wonder: Okay, it’s random. What’s the big deal?

The big thing is the consequences. In a classic system, a system sensitive dependence on initial conditions, the answer to a question is already determined before asking it.

Rather than watching the baseball match tonight, you spend the evening with your friends. When you return home, even though you don’t know the results, the match is over, and there is a definite result. There could be different results, but you don’t know the result until you look at it.

Contrarily, in a quantum system, the answer to a question is not determined up until the time you ask it. And since it is not determined yet, we can still change the probabilities of measuring distinct states.

Do you have doubts? Good! Not even Einstein liked this notion. It led him to his famous statement that God does not play dice.