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Let me start this series of lectures by telling you something that is trivial. obvious perhaps to most of you, but nonetheless it has to be stated. Information is physical. If you think about information, there's always underlying carrier of information. And therefore any information processing, any computation in fact, is a physical process. So do remember, this is the mantra for this series of lectures. Computation is a physical process. Computation is a physical process. Computation is a physical process. So in order to understand computation, you really have to understand it. and underlying physics.

So what our colleagues, computer scientists, or theoretical computer scientists, were doing, looking at different models of computations, in fact, whenever they captured something that really happened in the process of real computation, they were discovering something interesting about physics. Well, don't tell them that all computer scientists are physicists, they wouldn't probably like it, but nonetheless, there is certainly truth in order to fully understand what's going on. computation, you have to understand the underlying physics of computation. And any realistic model of computation has to take into account the physics of computation. Of course, you can study any mathematical model of computation for its logical consistency and so on and so forth.

But in order for this model to reflect something that you can really set up in nature, that model has to somehow reflect what we know about it. than nature has to reflect the laws of physics. Now, as it happens, the laws of physics are written in the language of quantum physics or quantum theory. It is a thing about quantum theory for the purpose of this series of lectures as a kind of a new probability theory. It tells you how to calculate probabilities that something happens. And it does it in a way that can be probably summarized in three basic rules. So the essential. The essential ingredient is a probability amplitude. It is a complex number.

And whenever you want to get a probability, you take this complex number, let me just call it alpha, and the associated probability is mod square of alpha. So you take the absolute value, square it, and that is your probability. So let's call it rule number one. We play with probability amplitudes and we get probabilities by squaring probabilities. amplitudes. Now whenever something can happen in a sequence of independent ways so suppose you have a physical system that evolves in two steps from this configuration to this configuration and then to this configuration and if you associate amplitudes say alpha 1 and alpha 2 with the corresponding steps, then the probability amplitude that you associate with the whole process is the product of the two.

So alpha in this case is equal to alpha 1 times alpha 2. So you simply just multiply the probability amplitudes corresponding to each segment of this evolution. And the third rule, probably the most interesting one, is that if something can happen in mutually exclusive ways. So if there are two alternatives for the system to go from one configuration to another, and if you associate probability amplitudes, again, alpha 1 and alpha 2, then the probability for this system to evolve from this state to this state, or from this configuration to this configuration, is the sum of the two. So your alpha in this case is equal to alpha 1 plus alpha 2. So essentially, the whole quantum physics, well, of course, I'm simplifying a little bit.

But pretty much the whole quantum physics can be summarized by stating the three rules that I have just stated, namely that we play with probability amplitudes. And whenever we want to calculate probabilities, we take the mod square of probability amplitudes. When something can happen in a sequence of two independent consecutive ways, then we simply multiply the corresponding probability amplitudes. And when we have two alternatives or more for something to happen, we just simply add corresponding probability amplitudes. And this set of rules essentially is perfect. all we have in quantum physics but actually we can get a long mileage out of that as you will see in a moment. .