Superposition. How it is determined and what properties it has.

Scientific materials on the Internet create a kind of oppressive, hopeless impression. This is especially true for materials on the quantum worldview. They obviously tire not only me, but many others as well. So, for example, Gordon left the field of science. It can be seen on the rollers, with some melancholy in his eyes, he listens to the scientist, who, with some strained persistence, explains the phenomenon of superposition. He sees that the scientist does not understand this, does not feel this event, and he does not need it as a natural phenomenon. For him, superposition is needed only in order to explain some phenomenon that is not clear to him, for example, a quantum computer. It can be seen that the narrator does not understand the philosophy of an ordinary computer, but tries to explain the principles of building a quantum computer through superposition.

Indeed, how can you understand this "Schrodinger's cat"? Who is in superposition: a cat or an observer? Or are they both in superposition? Or is the cat in superposition because there is an observer? There is no observer and there is no superposition for physical objects. The cat understands that he is alive, if he is not so sick that he feels: I'll die now. If the death of a cat requires destruction from poison, for example, 100 liver cells when he dies for sure, then the destruction of 20 or 77 liver cells gives us the opportunity to say that the cat will die with a 20 or 77 percent probability. The box in which the cat is located also knows whether the cat is alive or not, as long as thermal photons of a certain energy are sent to its walls from the cat or while the cat is scratching it.

But then Schrodinger appears and says that we cannot say whether the cat is alive or dead. Why can't we tell? Because we do not know whether this unfortunate element has disintegrated or not? Why don't we know about it? Because we do not have the slightest idea of how this element works, despite the “most wonderful” wave function of the same Schrodinger. Moreover, it is not necessary to arrange this performance with disintegration, but it is enough not to feed the cat and in a few days the cat will be in superposition: it may be alive or has already given God its soul.

Well, good. Schrodinger's cat is sitting in a box with poison - everything that is supposed to be in superposition. I opened the drawer and see that the cat is alive. According to this science, the superposition has disappeared. The cat is alive. I closed the drawer. What happened? There should be only one answer: superposition has arisen again, another answer is nonsense. After a while, I opened the drawer again and see a lifeless cat. The superposition has disappeared: the cat is alive with a confidence level of 0, that is, dead. I closed the drawer again. I think no Schrodinger would argue that a cat is simultaneously in two states at the same time: alive and dead. That is, an interesting matter: the superposition applies to a live cat, but, alas, not to a dead cat.

Of course, such scientists are dodgy and he can say that the cat has switched to another superposition: I cannot say that the cat has decomposed completely or only partially, whether the rats have eaten it or not. That is, there is scope for creativity, and such a scientist will have bread and butter. No superposition is allowed here: will I get my salary or not. I keep a close watch on the salary and do not let her dive into superposition.

These are extreme and observable superposition states. They refer to the same object, such as an electron. Or rather, to all objects of the microworld. This phenomenon can be applied to objects of the macrocosm with certain reservations, as we have seen from the cat. That is, for the macrocosm, the state of superposition is not a law, but for the microcosm, scientists believe it is a law. If we assume that this assumption is true, then the question arises, where does the superposition law begin to work? From a cell, from a molecule, from an atom, from a particle? Does the water molecule obey the law of superposition completely or not?

Here's how scientists view the phenomenon of superposition:

“ A particle - an atom or an electron - is used as a memory cell of a quantum computer. This unit of quantum information is called a qubit. The possible states of the particle will be called | 0> and | 1>, which corresponds to two possible values of its spin. But in quantum mechanics, everything is more complicated than in ordinary mechanics, and a particle is capable of being in two states simultaneously, and in each of them - with some probability. Therefore, the closest analogue of a qubit is not a bit at all, but a vector on a plane. Hidden in this comparison is the nature of the amazing performance of quantum computers - after all, there are only two possible states for a bit, and there are many possible directions for a vector. When new qubits are added to the system, the dimension of the space of possible states grows exponentially, and the final result of a computational operation on such a system contains the probability distribution of each of the possible answers. This gives rise to parallelism - we perform calculations not for a specific state of the system, but for all its possible states at once ”. I read this on the net.

So, as you can see, the atom can be in superposition. And this should be so, because, for example, Academician S.S. Gershein claims. in his lectures on You-Tube, superposition is one of the fundamental laws of quantum mechanics. This conviction was conveyed to him through a handshake by Niels Bohr, who expressed the brilliant idea that an electron moving in a certain orbit in an atom does not emit anything. But as soon as it moves a little out of orbit, it will immediately light up, that is, it will begin to radiate. Bohr's thought is worthy of superposition.

In general, moving from atom to molecule, cell, tissues, and so on, we come to the conclusion that some atoms in the inanimate cat will be in superposition, but the whole cat will not. Even if you shake the box, at least turn it over, do not do it, but if you put a dead cat in the box, then it will be dead. Of course, for the sake of reliability, you can send for living water, but it is in superposition, either it is, or it is not, or it is dead and alive at the same time with different probability. Probably, our water is like that.

It's easier with an electron - it has two obvious states in the form of a spin. Spin up and spin down. We observe this by the polarization of light. And an amazing third state, or rather an infinite set of states, in the form of the so-called superposition. We cannot see these states in any way or get them in physical form and even ask about them is not correct, because this is the mystery and wisdom of quantum mechanics. In mathematics, please: write ax + iby and here's a state for you. It is precisely here that the spin up with the probability a , and the spin down of the same electron in this place with the probability b ... Change parameters and variables and get a plane of states, but in nature it is impossible to find these states. The main thing is that you can get a lot of such planes of states. Each qubit adds its own plane to the state array.

Imagine: each qubit (like one binary) in the form of a memory bit. The states of such a qubit are not mega, not tera, not femto, but many, many more. That is, this qubit can encode everything in the world. Want - 0, there is 0. If you want to remember 1, you can too. If you want to write 782 into it - no problem. Maybe you would like to store your photo on this qubit? Here it is: photo “I” is located at 568 + i66778. Read it and forward it to your beloved, and she will certainly place it in the front corner at 1 + i1.

And it's a pleasure to get out of the maze or to extract roots on such a computer: quickly and as accurately as you like. Indeed, no matter how large the number is, even a billion characters, the value of its root can be written in a given qubit. Naturally, this should only be one value in this case. Whatever the outlandish laws of quantum mechanics, no academician would dare to write all kinds of numbers into one and the same qubit. We do not know the root of what degree, and from what number, and with what precision we will extract. Try to write down all the results of extracting the square root of the number 3. And in one qubit. Difficult, but if you want, you can.

Okay, let them write it down. And now let's carry out “… calculations not for a specific state of the system, but for all its possible states at once ”. And what are we to calculate here? We already know that this qubit contains the desired answer. Ah, we do not know which state of the system corresponds to the desired answer. Well, then let's calculate the specific state of the system that corresponds to a given result. The priest had a dog, he loved her ...

Even if you carry out all the calculations at once, then among them you need to choose the required one. Try to pick an apple of a given size from a box of apples if the sizes are about the same. This is a little less, then a little more, and so on. You can't do without a tool.

If we do not go crazy and do not appeal to the fact that quantum mechanics is a delicate thing and it allows such events to take place that are not subject to comprehension, then we must admit that at each moment in time we can write only one value ... You can also write two numbers into one qubit, but then you need to know the addresses of these numbers in the qubit, otherwise their sum is immediately obtained. Note that this happens in nature, but we (arguing about superposition) do not yet know this. Of course, we may not know exactly what we wrote there.

Anyway, any computer requires more than one digit. To add two numbers, you must have at least two digits. These numbers can be small or large, but each has its own category. Naturally, to select the result of extracting the square root of the number 3 of a certain accuracy, an almost infinite number of digits is required. If we take into account that each qubit is in superposition, that is, until we count its value, then we do not know what is stored in it, then the speed of this computer due to parallelism can be lost due to comparison or testing of these computational results.

In addition, such not very pleasant things happen with the phenomenon of superposition. If an electron has two understandable states in the form of a spin, then what states of an atom are we talking about, especially an atom with a large number of electrons? About all possible positions of an atom in space? About the mutual arrangement of electrons in it? About whether any electron of a given atom emitted any photon? And if it did, what kind of photon? Or maybe the atom itself is in a superposition: does it exist, or is it not?

But the superposition must be all-encompassing at least in the microcosm. This means that if an atom is in superposition, then its constituent protons, neutrons and electrons must also be in superposition. That is, it is not known where. And in the protons themselves, the quarks and the substrate (field) itself, in which the quarks are located, must be in a superposition.

What kind of computer can be built on such an ideology? Yes, no. Try to enter some data into it. The same number from which you will extract the root of one degree or another in a parallel way. In any case, the extraction algorithm itself must be exactly stored somewhere. And each step of this algorithm should be read not with some probability, but with probability 1 and without destroying this state, because the cycle can repeat itself many times. And this reading will take place through certain channels, to which various spies can connect, from which we need to defend ourselves. Learns that protection should follow the path of protecting information from destruction, that is, keeping the system in superposition all the time, and from theft as such.

In conclusion, we can say that if we are guided by the principles of superposition, which are stated something like this:

“ The main difference between the principle of superposition in quantum theory and its classical counterpart is that the states that“ overlap ”each other in quantum theory are alternative, mutually exclusive states, when one of them completely denies the other. If we are somewhere in one place, it means that we are not in another place - this is suggested by common sense. But in quantum theory exactly such mutually exclusive states are formed, and the system can be in such states at the same time! ”, then common sense will have to be abandoned at every step of a quantum computer, from inputting information to delivering it to the consumer in processed form.

Unfortunately, to convince someone of the presence or absence of the phenomenon of superposition is the same as to convince someone or, on the contrary, to dissuade someone in the presence or absence of God or Allah. This is a very complex problem. Here you need authority or strength, or time, when everything will be learned piece by piece.