Quantum computing is at the heart of the debate. During 2019 and 2020 we have dedicated many articles to it in Technoeager because there have been very relevant advances in this discipline in which it was worth investigating. The advent of quantum supremacy is the most surprising of them all and has placed it at the center of the discussion, but experts in computers and quantum algorithms unambiguously acknowledge that much work remains to be done.

So much, in fact, that there are those who believe that all this effort is going nowhere. One of the members of the scientific community most critical of quantum computing is the Israeli mathematician Gil Kalai, a professor at Yale University. According to this researcher, the increase in the number of states of quantum systems and their complexity will cause them to end up behaving like classical computers, so the superiority of the former will eventually evaporate.

However, the absence of unanimous support from the scientific community should not cloud the effort and notable progress that many research groups are making, some of them in Spanish institutions such as the CSIC and others integrated into the structure of companies that they have very large resources, such as IBM, Google or Intel, among others. We have good reasons, not to toss the bells, but to look with reasonable optimism towards the innovations to come.

This brief review of the status quo of quantum computers is the prelude to an article in which we have set out to collect all the information we need to have the most accurate picture possible of the state of quantum computing. We trust that this text will be useful to readers who are curious about this discipline and want to have a solid base without having to go through all the articles that we have published so far one by one.

## What is a qubit

The word ‘qubit’ comes from the contraction of the English terms *quantum bit*, or quantum bit. In the computers that we currently use, a bit is the **minimum unit of information**. Each of them can take one of two possible values at any given time: 0 or 1. But with a single bit we can hardly do anything, hence it is necessary to group them into sets of 8 bits known as bytes or octets.

On the other hand, bytes can be grouped into “words”, which can be 8 bits (1 byte), 16 bits (2 bytes), 32 bits (4 bytes), and so on. If we want to know how many different values a set of bits can take, which can be any size (so we’ll call it n), we just have to raise 2 to n (2 ^ n). The two, which is the base, comes from the fact that each bit can take one of a maximum of two values, hence the notation used by digital systems in general is called **binary notation**.

The notation that we use in our day to day is decimal because we use a set of ten different values that go from 0 to 9, and not just two values (0 and 1), like the binary notation. If we carry out the simple calculation that I just told you about, 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 increase to eight possible values (2 ^ 3 = 8). With four bits we will get sixteen values (2 ^ 4 = 16), and so on. Of course, a given set of bits can only adopt a single internal value or state at a given moment. It is an absolutely reasonable restriction that seems to have a clear reflection in the world we observe because a thing is or is not, but it cannot have both properties simultaneously.

This obvious and basic principle, curiously, does not occur in quantum computing. And is that qubits, which are the minimum unit of information in this discipline, unlike bits do not have a single value at any given time; what they have is a combination of states zero and one simultaneously. They can have a lot of state zero and little of state one. Or a lot of state one and little of state zero. Or the same of both. Or any other combination of these two states that you can think of.

## What are quantum states

The physics that explains how the quantum state of a qubit is encoded is complex. It is not necessary that we delve 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 intrinsic property of elementary particles, just like the electric charge, derived from its angular rotational moment.

This idea is not intuitive, but it has its origin in one of the fundamental principles of quantum mechanics known as the principle of superposition of states. And it is 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 specific state using n bits has size n, but in a quantum processor of n qubits a specific 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 tells us, in some way, how much of that particular collection there is in the internal state of the machine, which is determined by the combination of all the 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 intuit 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 different probability. A very important consequence of this property of quantum computers is that the amount of information that a specific state of the machine contains 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 intuit its complexity, which we will explore a little later. If in a classic computer we go from working with n bits to working with n + 1 bits, we will be increasing the information stored by the internal state of the machine in a single bit.

However, if in a quantum computer we go from working with n qubits to working with n + 1 qubits, we will be doubling the information stored by the internal state of the machine, which will go from 2 ^ n to 2 ^ n + 1. This simply means that the increase in capacity of a classical computer as we introduce more bits is linear, whereas that of a quantum computer as we increase the number of qubits is exponential.

We already know that the bit and the qubit are the minimum units of information that classical and quantum computers handle, so we can take a step further and review how we do operations with them. The elements that allow us to operate with bits in classical computers are logic gates, which implement the logical operations of Boolean Algebra.

This algebra is a structure designed to work on expressions of propositional logic that have the peculiarity that they can only adopt one of two possible values, true or false, hence it is also perfect to carry out operations in binary digital systems, which Therefore, they can also adopt at a given moment only one of two possible values: 0 or 1.

The logical AND operation implements the product; the OR operation, the addition, and the NOT operation reverses the result of the other two, with which they can be combined to implement the NAND and NOR operations. These, together with the exclusive sum operation (XOR) and its negation (XNOR), are the basic logical operations with which the computers that we all use today work at a low level. And with them they are able to solve all the tasks that we carry out.

Each one of them allows us to modify the internal state of the CPU, in such a way 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 that offers us the solution to a given problem. A quantum computer will only be useful to us if it allows us to carry out operations with qubits, which, as we have seen, are the units of information it handles.

Our goal is to use them to solve problems, and the procedure to achieve this is essentially the same as what we described when we talked about conventional computers, only, in this case, the logic gates will be quantum logic gates designed to carry out quantum logic operations..

We 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 capable of carrying out all the tasks that we do with a computer today.. 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 today, which are CNOT, Pauli, Hadamard, Toffoli or SWAP, among others.

We are not going to delve into its mathematical basis because it is complex and we do not need to know it to understand the basic ideas of this article, but it is interesting to know that quantum logic gates are represented in the form of matrices.

In this way, to calculate the result that we will obtain at the output of the quantum gate we have to make the product of the matrix and the vector that represents the internal state in a given instant of our quantum computer.

## What is quantum decoherence and why do quantum computers look so strange

If we design an algorithm that uses a given sequence of quantum logical operations, we will be able to modify the internal state of our quantum computer until we obtain the result of the problem that we have initially set for it. This strategy, as you can see, is identical to the one we use in classic computers.

However, we know that due to the principle of superposition, a quantum bit adopts several values simultaneously, so when performing a quantum logic operation from several quantum bits we will not obtain a single result; we will simultaneously arrive at multiple results as a consequence of the multiplicity of states adopted by the bits involved in the quantum logical operation.

We are taking up once again the idea that we developed a few paragraphs above, when we saw that the computing power of quantum computers increases exponentially as we are able to carry out operations with more qubits.

And this allows us to reach a first conclusion with which we have been flirting since the first paragraphs of the article: quantum computers are more powerful than classical computers to the extent that each of the logical operations that we can carry out with them returns us more results than a classic logical operation.

This capacity accumulates as we carry out more and more quantum logic operations until we complete the sequence established by our algorithm to solve a specific problem, which makes a huge difference from classical computing. So far everything looks very good, but there are two very compelling reasons that explain why quantum computing has not yet finished with traditional computing.

The logical thing would be to think that if the first is so efficient it should have managed to displace classical computing and impose itself with overwhelming clarity in some use scenarios. And it has not been so. At least still. The first reason is that at the moment we have few quantum algorithms because these machines are very difficult to program, and therefore we are still able to solve few problems using quantum computing.

The second reason is that it is very difficult to preserve the state of a quantum system because the superposition is easily broken by quantum decoherence. Before we see what this phenomenon consists of, we need to introduce one more concept that is nothing more than an essential property of quantum systems: entanglement.

This phenomenon does not have an equivalent in classical physics, and it consists in that the state of the quantum systems involved, which can be two or more, is the same. This means that these objects are actually part of the same system, even though they are physically separated. In fact, the distance does not matter.

If two particles, objects or systems are entangled by this quantum phenomenon, when we measure the physical properties of one of them we will be instantly conditioning the physical properties of the other system with which it is entangled. Even if it is at the other end of the Universe.

It sounds like science fiction, it is true, but as strange and surprising as this phenomenon may seem to us, it has been empirically proven. In fact, it is, together with the superposition of states that we have talked about, one of the fundamental principles of quantum computing. Let us now return to quantum decoherence.

This phenomenon occurs when the necessary conditions disappear for a system that is in an entangled quantum state to maintain itself. Perhaps a slightly simpler way of describing it is to see it as a system that stops behaving as dictated by the rules of quantum mechanics when certain conditions are met, starting from that moment on behaving as dictated by the rules of classical physics. .

When quantum decoherence appears, the quantum effects disappear . And, therefore, also the advantages that they bring in the context of quantum computing. This phenomenon is very important because it helps us understand why many macroscopic physical systems do not exhibit quantum effects. Or, what is the same, why in our everyday environment we cannot observe the counterintuitive effects of quantum mechanics.

If we keep in mind what we have just seen, we can intuit that if superposition and entanglement are affected as a consequence of the decoherence of the quantum system involved in the operation of a quantum computer, errors will occur and the algorithms will not return the correct results.

Quantum states are maintained for a limited period of time, and this time is precisely what we have to carry out quantum logical operations with the qubits of our computer. Also, as we add qubits, it is more difficult to keep errors under control while preserving the quantum state of the system.

To prevent qubits from changing their quantum state spontaneously as a result of disturbances introduced by thermal energy, current quantum computers work at an extremely low temperature . In fact, it is very close to absolute zero, which is -273.15 degrees Celsius.

The working temperature of the quantum equipment that companies such as Intel, Google or IBM have is about 20 millikelvin, which is approximately -273 degrees Celsius, which allows us to intuit that the cooling system that is necessary to fine- tune to reach and maintaining such an extremely low temperature is complex.

It is precisely this sophisticated cooling system that is responsible for the strange appearance that quantum computers have, which do not resemble the classic computers with which we are all familiar.

The importance of working at a temperature as close as possible to absolute zero lies in the fact that in this state the internal energy of the system is the lowest possible, which causes the fundamental particles to lack movement according to the principles of classical mechanics.

However, even if we are able to reach absolute zero, there will still be a residual energy, known in quantum mechanics as zero point energy , which is the lowest energy level that a physical system can have.

## What can quantum computers do and what problems they solve

The advances in the design of quantum computers are encouraging, there is no doubt, especially if we look back for a moment and contemplate how underdeveloped this discipline was only two decades ago. However, the capacities of the machines of a few tens of qubits are far from allowing us to carry out really relevant calculations.

James Clarke, the director of Intel’s quantum computing laboratory, confessed to us during our visit to his facilities in Delft (Netherlands), that for a quantum computer to be significantly better than a classical one, it will have to work with about 1000 qubits. Only then will they become truly relevant. And to achieve this goal there are still years of research to help us find the solution to the challenges that are still on the table.

Is it really worth all the effort? Yes, it certainly deserves it. In some scenarios, and far from all, quantum computing is exponentially faster than classical, so scientists trust it to make a difference in cryptography, artificial intelligence , machine learning and other scientific disciplines, such as medicine, physics, engineering or chemistry, which may also benefit from the very high efficiency that quantum computers are expected to put in our hands in the future.

Even so, it is reasonable for us to be realistic and bear in mind that scientists are currently working with very few algorithms that can run correctly on a quantum processor. In fact, they usually work on simulators and not on real quantum machines.

It is not even entirely clear how the process of programming a quantum computer should be approached, although platforms for the development of quantum algorithms are already available, such as those from Microsoft , IBM or Google, which invite us to look to the future with reasonable optimism. .

## What is quantum supremacy

Understanding this concept is not difficult. In reality, it is only the milestone that we will reach when a quantum computer is faster in practice than a classical computer when both are faced with solving the same problem. However, this definition admits of nuances. How fast should the quantum computer be? A lot of? Is it enough that it be just a little bit?

The commonly accepted idea proposes that the quantum machine can solve a problem in an understandable period of time that a classical supercomputer would solve in an unaffordable period of time given its extension.

So far the only two research teams that have claimed to have reached this milestone have been the one led by John Martinis at Google and the one led by Jian-Wei Pan at the China University of Science and Technology and the Tsinghua University in Beijing.

The article that the Google researchers published at the time in Nature is a scientific text, and as such, its content is complex . Still, there are a number of interesting ideas worth digging into without going into overly complicated details.

The first one is that the Sycamore quantum processor used by Google incorporates 53 superconducting qubits , which means that a specific internal state of this machine has a size of 2 ^ 53.

To intuit what this means, we only have to remember that in a classic n-bit processor the amount of information that we can encode in a specific state using those n bits has size n, but in a quantum processor of n qubits, a specific state of the machine has size 2 ^ n.

Another interesting idea put forward by the Google researchers in their article explains why they decided to use a pseudo-random number generator in their experiment. According to them, their choice is the correct one when it comes to testing the capacity of their quantum computer because this procedure lacks structure and guarantees a computational effort high enough for a classical supercomputer not to be able to solve it in a manageable period of time..

The latest explanation by the researchers from John Martinis’ team that is worth a moment’s attention details what method they have used to make sure that both their quantum processor and algorithm have worked correctly. In their article they explain that they have resorted to a method known as the cross-entropy test that roughly compares the frequency with which each quantum computer output is experimentally observed with the probability distribution calculated by simulation on a classical computer.

The strategy used by the Asian researchers is radically different from that used by John Martinis’ team. And it is that the Jian-Wei Pan group has developed a quantum system that uses an optical circuit capable of taking advantage of the quantum property that allows photons to travel randomly in different directions to carry out extraordinarily complex calculations.

What interests us is not so much to know in detail how the experiment carried out by Chinese researchers works as to note that it is possible to achieve quantum supremacy using very different approaches and technologies .

In fact, it is very likely that during the coming months other research groups and other companies will also carry out an achievement comparable to the one that these Chinese and American researchers already have on their curricula.

## What are the challenges facing quantum computers

Everything we have seen so far helps us to intuit some of the challenges that quantum computing has ahead of it, a reality that in no way obscures the enormous potential that this discipline has.

Still, we must be cautious and trust that researchers will continue to work hard so that one day quantum computers will help us find the solution to some of the challenges humanity faces.

These are the four biggest challenges researchers are working on:

- We need higher quality qubits . The quantum information with which quantum systems operate is destroyed in a short period of time, so having higher quality qubits will allow us to extend the useful life of quantum information and carry out more complex operations with it.
- An error correction system will help us to guarantee that the results that our quantum computer gives us are correct. As we’ve seen, we don’t have it yet, and as research groups integrate more qubits into quantum computers, it becomes more difficult to preserve the integrity of the quantum state of the system.
- In addition to having higher quality qubits and error correction systems, it is necessary to develop new tools that allow us to control them with precision and carry out more logical operations with them. Its manipulation becomes much more complex as the number of qubits of quantum systems increases.
- It is also necessary to further develop the architecture of quantum computers, such as control electronics, the quantum control processor or quantum compilers. One of the most daunting challenges facing researchers is implementing new quantum algorithms that are capable of helping us tackle problems that we cannot solve with the most powerful classical supercomputers we have today. These algorithms are what will allow quantum computers to make a difference.

They do not aspire to reach our homes, but they are already reaching our lives

Classical and quantum computations are doomed to understand each other. Quantum computers do not aspire to replace classical computers; They intend to complement them by drastically reducing the time invested in the execution of those algorithms that currently have an unaffordable computational cost if we stick to the time they require.

Correcting errors is probably the most complex challenge we will have to solve for quantum computers to achieve real supremacy, and technicians working in this discipline recognize that this moment is still far away.

James Clarke, the director of Intel’s quantum computing laboratory, and Lieven Vandersypen, a researcher and professor of quantum technology at the University of Delft, believe that, if the current pace of development continues, we will have interesting quantum computers in five years.

They will be machines with tens of qubits, probably even more than a hundred qubits, which will prove very useful as a testing ground. They will help us further advance error correction methods and will likely also bring new applications within our grasp where quantum computing can make a difference.

However, these same experts recognize that quantum computers will not have a forceful impact on our lives, and therefore clearly perceptible, for no less than fifteen years.

This vision is interesting because it comes from people who are fully involved in the design and implementation of quantum computers, but it is still an estimate, so it may or may not be fulfilled.

If we stick to the current scenario, IBM, Intel, Google and Honeywell seem to be in a relatively comfortable position because they all have functional quantum computers with interesting capabilities as a test and research environment.

But we should not at all underestimate the role that other companies, such as Microsoft, which are also making significant efforts in the field of quantum computing, can play.

The power of a quantum computer is not only defined by the number of qubits with which it is capable of working, but also by its quality, understood as the ability of these qubits not to be disturbed by noise, and by the efficiency of the algorithms that we can run on this hardware.

In any case, they are already sufficiently advanced that some supercomputing centers, such as the French and German, have decided to introduce them into their infrastructure as one more specialized processor that can make a difference in the search for the solution to some of the problems that arise. those facing humanity.