[dropcap]W[/dropcap]e all know very well that it is not easy to precisely locate in time the exact moment in which quantum computing began to make noise beyond the academic and research fields. Perhaps the most reasonable is to accept that this development began to be known by the general public about two decades ago, a period during which the classic computers have experienced a very remarkable development.

## What is Quantum Computing And How It Works?

It is not easy to precisely locate in time the exact moment in which quantum computing began to make noise beyond the academic and research fields. Perhaps the most reasonable is to accept that this development began to be known by the general public about two decades ago, a period during which the classic computers have experienced a very remarkable development.

But, there are scientists who defend with a certain intensity that the quantum computation to which we aspire is impossible, like Gil Kalai, an Israeli mathematician who teaches at Yale University, the truth is that he has advanced a lot during the last years.

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From the outside it may seem like an “eternal promise”, but the advances we are witnessing, such as the construction of the first 50-bit functional prototype IBM is working on, invite us to be honestly positive. Yes, the challenges facing mathematicians, physicists and engineers are almost large, but this makes this development even more exciting.

### Quantum computing: What it is and how it works?

Quantum computing is reputed to be complicated, and, therefore, difficult to understand and it is true that if we go deep enough in it, quantum computing becomes very complex. The reason is that its foundations are based on principles of quantum physics that are not at all natural because their effects cannot be observed in the macroscopic world in which we live.

The first concept that we want to know is that is the cube or qubit, which is nothing else than the contraction of the words. And to understand what a qubit is, it is good for us to review previously what is a bit in classical computing.

In computers that we currently use a bit is the minimum unit of information. Each of them can adopt at any given time one of two possible values: 0 or 1. But with a single bit, we can hardly do anything, hence it is necessary to group them in sets of 8 bits known as bytes or octets. On the other hand, the bytes can be grouped into “words”, which can have a length of 8 bits (1 byte), 16 bits (2 bytes), 32 bits (4 bytes), and so on.

If we carry out the simple calculation about which just I have spoken, we will verify that with a set of two bits we can encode four different values (2 2 = 4), which would be 00, 01, 10 and 11. With three bits our options are increased to eight possible values (2 3 = 8). With four bits we will get sixteen values (2 4 = 16), and so on.

Of course, a set of bits can only adopt a single value or internal state at a given time. It is an absolutely reasonable restriction that seems to have a clear reflection in the world that we observe, as a thing can not have both properties simultaneously.

This obvious and basic principle, curiously, does not occur in quantum computing and the qubits, which are the minimum unit of information in this discipline, unlike the bits do not have a single value at a given time; what they have is a combination of the zero and one states simultaneously.

Basically, the physics that explains how the quantum state of a qubit is encoded is complex. It is not necessary to go deeper into this part to continue with the article, but it is interesting that we know that the quantum state is associated with characteristics such as the spin of an electron, which is an essential property of elementary particles, just like the electric charge, derived from its moment of angular rotation.

These ideas are not intuitive, but they have their origin in one of the fundamental principles of quantum mechanics, known as the principle of superposition of states. And it’s essential because it largely explains the enormous potential that quantum processors have.

In a classical computer, the amount of information that we can encode in a particular state using N Bits, which has size N, but in a quantum processor of N qubits, a particular state of the machine is a combination of all possible collections of N ones and zeros.

Each of these possible collections has a probability that indicates, in some way, how much of that particular collection is in the internal state of the machine, which is determined by the combination of all possible collections in a specific proportion indicated by the probability of each of them.

As you can see, this idea is somewhat complex, but we can understand it if we accept the principle of quantum superposition and the possibility that the state of an object is the result of the simultaneous occurrence of several options with a different probability.

A very important consequence of this property of quantum computers is that the amount of information that contains a particular state of the machine has size 2 n, and not n, as in classical computers. This difference is essential and explains the potential of quantum computing, but it can also help us to understand its complexity.

If in a classic computer we go from working with n bits to doing it with n + 1 bits we will be increasing the information that stores the internal state of the machine in a single bit. However, if in a quantum computer we go from working with n qubits to doing it with n + 1 qubits we will be duplicating the information that stores the internal state of the machine, which will go from 2 n to 2 n + 1. This means, simply, that the increase of the capacity of a classical computer as we introduce more bits is linear, whereas in the case of a quantum computer as we increase the number of qubits is exponential.

We already know that bit and qubit are the minimum units of information that classical and quantum computers handle. The elements that allow us to operate with bits in classic computers are the logic gates, which implement the logical operations of Boolean Algebra.

The latter is an algebraic structure designed to work on expressions of the propositional logic, which have the peculiarity that they can only adopt one of two possible values, true or false, hence this algebra is also perfect to carry out operations in systems digital binaries, which, therefore, can also be adopted at a given time only one of two possible values “0 or 1”.

The logical operation AND implements the product, the OR operation, the sum, and the NOT operation invert the result of the other two, with which it can be combined to implement the NAND and NOR operations.

These, together with the operation of exclusive addition (XOR) and its negation (XNOR) are the basic logical operations with which the computers that we all use at present work at a low level. And with them, they are able to solve all the tasks we carry out.

We can surf the Internet, write texts, listen to music and play games, among many other possible applications, thanks to the fact that our computer’s microprocessor is capable of carrying out these logical operations. Each of them allows us to modify the internal state of the CPU so that we can define an algorithm as a sequence of logical operations that modify the internal state of the processor until it reaches the value offered by the solution to a given problem.

A quantum computer will only be useful if it allows us to carry out operations with the qubits, which, as we have seen, are the units of information that it handles. Our goal is to use them to solve problems, and the procedure to achieve it is essentially the same as we have described when we talked about conventional computers, only that, in this case, the logic gates will be quantum logic gates designed to carry out quantum logical operations.

Moreover, we all know that the logical operations carried out by the microprocessors of classic computers are AND, OR, XOR, NOT, NAND, NOR, and XNOR, and with them, they are able to carry out all the tasks we do with a computer nowadays, as we told earlier.

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While the quantum computers are not very different, but instead of using these logic gates they use the quantum logic gates that we have managed to implement at the moment, which are CNOT, Pauli, Hadamard, Toffoli or SWAP, among others.

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