# Quantum computer: a big promotion game. Lecture in Yandex

We hear every now and then that the era of the active use of quantum computing is not far off, that such systems will soon become available to specialists, including data analysts. But how much is really left to wait? Alexei Fedorov, a researcher at the Russian Quantum Center, brings up to date and talks about how things are going with the development of quantum computers.

Under the cut - decoding and part of the slides of Alexei.

Good day to all. I want to thank the organizers. Since quantum technologies have become a topic of discussion in this format, then this topic is perceived, begins to sound at a fairly high level. Companies such as Yandex are leaders in the IT industry, and it is great that quantum technology appears on their agenda and in their area of interest. This is a kind of global trend. I am very glad that we are playing here today.

I work at the Russian Quantum Center and represent the team that is involved in the development of IT products within the framework of the Russian Quantum Center. The quantum center started as a fundamental scientific institute, but very quickly in the process of development began to engage in applied research in the field of quantum technologies, one of them is quantum cryptography, a project that we are engaged in. And our speakers - I, Eugene, Maxim, Nikolai - we all represent this team, so we will be happy not only to formally talk about the declared topic, but also to interact from the point of view that our interests overlap quite a lot. We will be glad to any questions in the field of quantum technologies, not limited to quantum computers.

I put this picture on my central slide. Do you know what this symbol is?

This statue, which is located next to the Frankfurt Stock Exchange, and means two strategies for how you can play on the market: increase and decrease. Quantum computer is the cornerstone of quantum technology, and now not only the state as the main investor in basic research, but also IT companies and large manufacturers of information technologies are connecting to its development. In this sense, they play to increase, invest heavily and effort in the development of a quantum computer, because they see in it some new opportunity for a revolution in information technology. And the main message of my report is why quantum technologies and a quantum computer are very cool, and why it is not just an interesting and beautiful idea, but really provides great opportunities for the development of the entire IT industry.

What did I, as a person who spent most of my time in physics, hear from programming and IT specialists? I have heard about the following trends.

We often hear about a large number of new startups or projects of existing companies such as the Internet of things, machine learning, big data and information security. These trends sound everywhere, set informational reasons, but behind them, in addition to the beauty of algorithmic solutions, the beauty of mathematics, the beauty of programming, is real iron. And this iron is already quantum.

If you look at the development trends of quantum technologies rather than information, then now this is a transition from the control of collective quantum phenomena that underlie devices such as transistors and lasers to the control of individual quantum properties.

Roughly speaking, a laser is controlling a large number of light particles, a large number of photons, and now we have learned how to control light, atoms, and matter at the level of individual microscopic elements. Such a trend is observed year after year, there are more and more experiments, proposals that use the laws of quantum physics already at the level of individual fundamental particles of matter. And here for me the most amazing thing is that it does not just come from the desire to learn fundamental science, but is also in demand in technological trends.

Quantum particles allow you to build a computer that will solve its problems faster. Quantum computers allow you to build communication systems that are better protected from listening. Quantum technology allows you to create more miniature sensors.

And all this underlies such applications as GPS, future medical sensors, new materials, which are in demand in information technology trends.

All technologically successful countries are currently actively engaged in the development of quantum technologies. A huge amount of money is invested in these studies, special programs for supporting quantum technologies are being created. If we go back to history, we all remember the space race between the USSR and the USA.

The quantum race involves not only states, but also private companies. In total, Google, IBM, Intel and Microsoft have invested about $ 0.5 billion in the development of quantum computers in recent years, created large laboratories and research centers.

Quantum technologies are still interesting in that they imply a kind of research format, where fundamental science is very closely linked to applied research.

Here is a map of the world's quantum centers, which are points of competence and points of growth. In 2011, the Russian Quantum Center, which I represent, appeared on this map. This is a fundamental scientific institute that has turned into an ecosystem where fundamental research coexists and stimulates the development of applied technologies.

However, today we are talking about a quantum computer, and within the framework of this lecture we would like to create a context that allows us to understand why quantum computers are generally interesting and necessary.

Here is the well-known Moore’s law, which expresses a certain trend in the productivity growth of existing computers. We know that from year to year computers are becoming more powerful, but behind this is a reduction in the elemental base, its miniaturization. Thanks to our progress in the development of transistors, we can create less and less, and place them more densely on an elementary unit of area.

But, of course, this trend has a fundamental limit. It is due to physics.

It is unlikely that we will be able to create a transistor the size of one atom. This requires at least a few atoms. As far as I know, the smallest transistor in the world consists of seven atoms. However, if Moore’s law continues as it continues, then in 2020 we will need to create computers with a single atom transistor. And that seems impossible.

What can be done here? You can increase productivity through other technologies, through cloud computing, parallelization, come up with some kind of element base that will allow you to get as close to the limit of Moore’s law as possible, that is, create the smallest transistor in the world. This is a very cool task.

However, even if we come very close to Moore’s law, we will still have problems that a classical computer does very poorly. It’s not for me among IT specialists to talk about this, but I will give examples of several tasks.

The first is the search optimization task. It is poorly resolved on classic computers.

The second, closest and most important to me is modeling of complex physical systems. For example, using modeling from first principles, it is very difficult to model some rather complex physical system. This requires a huge amount of resources.

There are various applied problems that seem quite distant from practice for a wide audience, such as factorization. However, everyone knows their fundamental importance for various technologies.

And even if we get close to the limit of Moore’s law, we won’t be able to solve such problems.

Of course we can. But it will take a lot of time.

I would like to get a physical system that will allow us to solve these problems in a more optimal way. It turns out that it exists, and arises in the context of a quantum computer.

I noticed in a Nobel lecture by Andrei Geim, one of the creators of graphene, such an interesting idea. He told how he came up with the idea of doing research in the field of graphene, using mental clouds. He heard about something, it was somehow processed in his head, and when he accumulated enough mental clouds, he created the concept that it is very interesting to deal with two-dimensional carbon and graphene.

I believe that three mental clouds led to the concept of a quantum computer.

The first one. It is not clear how to deal with computationally complex tasks. Will it always be really difficult for us to model some kind of physical system? Or does the prime factorization problem not have a sufficiently effective classical algorithm?

The second point is more physical. It is connected with the study of the question of what quantum physics as one of the most accurate physical theories imposes on the computation process. For example, Richard Feynman and Charles Bennett investigated the question of what minimum amount of energy or heat is released when one elementary operation is performed. Is it possible to create a computer that is the most productive and most economical in terms of energy release? How to create the smallest computer?

The third question is more about math. It is connected with the study of the question of what interesting properties the information theory acquires if we go from the description of classical objects in the classical theory of probability to the description of quantum objects, to the quantum theory of information. The banknote pictured here illustrates the idea of quantum money. This is one of the first concepts, which implies the use of some practical information technology. The fact is that if you create banknotes in which authenticity will be ensured by the creation of special quantum states, then due to the specific properties of quantum systems, such banknotes cannot be faked.

The second portrait here is a portrait of our compatriot Alexander Holevo. He is known worldwide as the creator of one of the fundamental theorems - the quantum information theorem or the Holevo theorem. Here, at the base of the quantum theory of information, we have something to be proud of. Russian researchers maintain a good tradition of interesting publications and interesting results in this area.

What does quantum physics give? What interesting consequences and chips does it have that could be useful from the point of view of information theory or future calculations?

In the classical world, we are accustomed to thinking that if we have a state of some kind of physical system, then it must be unambiguously defined by something. If we have a point in space, then we know that the system is at this point in space. In quantum physics, such a concept cannot be introduced. The fact is that a quantum system, if it is not observed, is in a superposition of all possible states. In particular, if she has two valid states, an eagle and a tails, then until we have measured this state, this is both an eagle and a tails at the same time. And only measurement gives us a guaranteed answer, in what condition the system is. Before measurement, the system is in a superposition state.

The second property is the property of quantum entanglement. In the quantum world, particles can exhibit very strong correlations, that is, their properties can be very closely linked, even if these particles are spatially sufficiently removed. Explaining the concept of quantum entanglement, they often give an example of a thought experiment, when we had some particle with spin 0, it decays into two particles, one we leave in our laboratory, the second we send to the Andromeda Nebula, and, measuring the spin of the first particle, we will definitely recognize the spin of a particle in the Andromeda Nebula. In a sense, this is a manifestation of the properties of quantum entanglement, strong quantum correlations, which can be useful from the point of view of calculations.

The third thing is fragility. Quantum states are rather fragile in comparison with classical ones. And the measurement process is precisely the process of perturbation. The question is whether this disturbance process is deterministically occurring. This is one of the key challenges to creating quantum technology. It is very difficult to create a large quantum system, the elements of which, on the one hand, will interact well enough with each other and at the same time will be well protected from the environment that can destroy them.

Another interesting aspect is the prohibition of cloning theorem. This is a forbidding theorem. If there is an arbitrary quantum state in the quantum world that is not known in advance, then it cannot be copied, unlike classical information. If there is a classic signal, you can always copy it. In the quantum world, an arbitrary quantum state cannot be copied. And this is a radical difference between quantum information and classical information.

What is the concept of quantum computing based on? In principle, one can abstract to a certain extent from the complex laws of quantum physics and imagine the concept of quantum computing as follows.

The system of bits, which is familiar to us in classical computers, is replaced by a system of qubits. This is a two-level quantum system or an eagle-tails system, when there are two possible states, and until the moment of measurement the system is in superposition: at the same time in this state, and in this with some kind of probability.

All the bits that we have are replaced with qubits. All logic elements from classical processes are replaced by quantum processes, and the result of the calculations is obtained by measurement. Thus, in a quantum computer, processing of all possible implementation variants is obtained at once, that is, you submit not one bit, not zero or one, but all possible combinations to the input - and carry out all operations on this superposition. The result is a certain quantum state. Measure it and get an answer.

In principle, on a conceptual level, this is the whole concept of quantum computing. Bits were replaced by qubits, classical operations were replaced by quantum operations, as a result we get what we need to measure, we measure many times and we get an answer.

This is what qubits can consist of. The fact is that qubits can consist of a huge variety of different physical systems. We are used to the fact that the bit is encoded due to the voltage level. In quantum physics there is a variety of physical systems. This is a particle of light, and a particle of matter, and nuclear spins, and solid-state systems that can be in such an interesting state of superposition. They have various advantages and disadvantages. Here is the key fact for today: no one fully understands what physical, elemental base a quantum computer will be built in the end. There is confidence that the so-called solid-state systems or systems with superconducting qubits are among the leaders, but about a month ago a competition was held between two quantum computers, built on different physical principles, and it did not reveal any radical advantage of one system over another. Some systems scale better, others are easier to control, others are better protected from decoherence, from the process of interacting with the environment.

Let us confine ourselves to two possible pictures as part of the lecture. The first is the polarization of light. It is very simple to imagine, a particle of light is a very simple two-level physical model, and it is very popular in another application of quantum technologies: in the so-called quantum communications. The second picture is spin. Spin can be up or down, this is qubit. Until we have measured, this is a state of superposition. Plus or minus one second.

What I have already said is an interesting process that arises as a result of quantum computing. A new quantum state arises.

Some superposition of zero and one was applied to the input, we performed multiple procedures with it. The output is a superposition of zero and one.

To get the answer, we need to take a measurement, and it needs to be done many times. Quantum computing implies that a predetermined quantum state is repeatedly applied to the input. A conversion procedure and then a measurement are performed on it. And the measurement eventually gives an answer.

This procedure of quantum measurements is quite complicated. This is a holistic topic even for specialists in the field of quantum physics. I draw your attention to the fact that we have a regular column on the N + 1 website called “Quantum Alphabet”, and we discuss such subtle issues there, including questions of quantum computing.

Why do we need all this? What will help us make a quantum computer, what interesting features will it give us? Why all this whistle-blowing with replacing bits with qubits, replacing logical operations and the final results of calculations? What does it give?

This provides benefits in the whole class of tasks. The most interesting problem for me that a quantum computer solves well is the factorization of discrete logarithms, since it underlies systems with asymmetric cryptography. And every time we buy something on the Internet, our credit card details are encrypted using asymmetric cryptography algorithms, public key cryptography. They, in turn, are based on such problems, in particular, as a discrete logarithm and factorization. And in this sense, the Shore quantum algorithm is the most important and most interesting example of a quantum algorithm, because it solves a practical problem exponentially faster than a classical computer. In this sense, a quantum computer is a threat to the existing information security infrastructure.

As soon as it appears, any open key distribution system that is based on such tasks can be hacked. On the one hand, this is bad, it can lead to a revolution, and often a quantum computer is called the information bomb of the 21st century. But on the other hand, at the moment, there is very little need to worry, because the Shore algorithm requires a universal quantum computer that can solve any algorithmically formulated problem, and this is very difficult. Yes, this gives tremendous advantages, but precisely because of the fact that quantum systems are fragile to external influence, it is very difficult to create a system from a sufficiently large number of qubits to carry out all operations and then measure them.

A quantum computer, in order to ensure, for example, hacking systems with asymmetric cryptography, must have a sufficient number of qubits operating in such a quantum mode. And it requires the creation of effective control methods for these quantum systems.

Today, Evgeny Kiktenko will tell you about a universal quantum computer in the context of algorithms. What algorithms are interesting for a quantum computer in terms of application? And Maxim Anufriev - from the point of view of solving the problem of machine learning on a universal quantum computer.

A universal quantum computer is a difficult task, and it is very important to understand. There is not even a clear time estimate when it appears. This year there is a lot of hype around this topic, even the first issue of Nature magazine has been released, one of the articles is “Quantum computers jump out of the laboratory” with the forecast that in 2017 some kind of commercial quantum computer will appear that can solve really useful tasks. Moreover, the forecast is so optimistic that a full-fledged universal commercial quantum computer will appear to solve practical problems.

Although this is a very controversial issue. Estimates of experts vary from 5 to 25 years. And in this sense, it is very difficult to say when a quantum computer will really arise.

The quantum computer that already exists was built by D-Wave. It is good for solving a very narrow class of problems that are interesting today: machine learning and artificial intelligence. Such a computer is very easy to scale, but it does not work fully in quantum mode and cannot solve any arbitrary task. It gives acceleration only in a certain class of problems due to a very interesting mechanism that Nikolay Pozhar will talk about today , precisely in the context of training not with a universal quantum computer, but with the example of D-Wave.

There is another kind of quantum computer called a quantum simulator. It is designed to solve an even more specific class of problems - namely, to simulate other types of physical systems. There are quite large prospects here, for example, for the search for high-temperature superconductors. These are materials that can conduct electrical current without loss at room temperature. So far, the theory for such systems is known only for very low temperatures. There are experimental studies that suddenly discover some materials that conduct current at different temperatures, for example, at –100 degrees Celsius. However, there is no full-fledged theory of high-temperature superconductors, because it is a computationally difficult task. Quantum simulators are designed to reproduce some properties of such physical systems and give some clue in which direction such materials can be sought. But simulators are also not universal quantum computers.

As I said, IT companies are already investing in quantum computer research. A very cool example is Google, which simply lured John Martinis, one of the leading experts in the field of quantum computing on superconducting qubits. John Martinis simultaneously leads several directions. One of them is the creation of a full-fledged universal quantum computer. Another is the study of the existing D-Wave quantum computer and the search for those tasks in which it gives an advantage.

By the way, John Martinis will be at the conference of the Russian Quantum Center this year . There will be an open lecture, where he can tell just about a quantum computer being developed by Google.

Another big player is IBM. She recently announced her open online platform for working with their five-qubit quantum computer. In this sense, anyone can write programs for a quantum computer, but, of course, its potential is limited by the fact that there are quite few qubits.

Other players in this market are Microsoft and Intel, and they have the longest shot - the creation of an anthropological quantum computer. Due to decoherence, due to the fact that the environment introduces errors into the process of quantum computing, part of the resources of a quantum computer must be spent on correcting them. Topological quantum systems avoid this. At the moment, this is a very fundamentally complex scientific concept, behind which there is a lot of interesting mathematics. This is very far removed at the moment from any practical implementation. In particular, the predicted topological states of matter, which are interesting from the point of view of calculations, have not yet been discovered experimentally. However, in 2016, the Nobel Prize was awarded for basic research in the field of the consequences of topologies for physics.

The following fact is very interesting: we are used to the fact that a classic computer is actually the same system, a solid body, which is responsible for all its functionality. We carry out both memory and calculation, in fact, on the same element base. However, a quantum computer allows us to make the so-called hybrid system, which will take the best from various forms of quantum matter from nature. For example, it is known that processors at the moment seem to be best built using superconducting qubits. All interfaces, all that is why quantum computers and their various elements will communicate with each other, can be built using photons - particles of light. This is the best agent for transmitting information.

Of course, in the process of calculation, sometimes it is necessary to store intermediate results, then carry out further operations with them. The best indicators in terms of storing quantum states show atomic systems. Therefore, a quantum computer is a big and interesting fundamental task that will allow you to combine, take the best from nature and build the most attractive, productive and interesting hybrid system.

At the moment, our main activity is work not on a quantum computer, but on a quantum communication system in the framework of the QRate project. And we will still be happy to talk about quantum communications. Quantum communications is a shield that allows us to defend ourselves against the sword of a quantum computer and create a key distribution system whose strength does not depend on the attacker's computing resources. Thanks for attention.

Under the cut - decoding and part of the slides of Alexei.

Good day to all. I want to thank the organizers. Since quantum technologies have become a topic of discussion in this format, then this topic is perceived, begins to sound at a fairly high level. Companies such as Yandex are leaders in the IT industry, and it is great that quantum technology appears on their agenda and in their area of interest. This is a kind of global trend. I am very glad that we are playing here today.

I work at the Russian Quantum Center and represent the team that is involved in the development of IT products within the framework of the Russian Quantum Center. The quantum center started as a fundamental scientific institute, but very quickly in the process of development began to engage in applied research in the field of quantum technologies, one of them is quantum cryptography, a project that we are engaged in. And our speakers - I, Eugene, Maxim, Nikolai - we all represent this team, so we will be happy not only to formally talk about the declared topic, but also to interact from the point of view that our interests overlap quite a lot. We will be glad to any questions in the field of quantum technologies, not limited to quantum computers.

I put this picture on my central slide. Do you know what this symbol is?

This statue, which is located next to the Frankfurt Stock Exchange, and means two strategies for how you can play on the market: increase and decrease. Quantum computer is the cornerstone of quantum technology, and now not only the state as the main investor in basic research, but also IT companies and large manufacturers of information technologies are connecting to its development. In this sense, they play to increase, invest heavily and effort in the development of a quantum computer, because they see in it some new opportunity for a revolution in information technology. And the main message of my report is why quantum technologies and a quantum computer are very cool, and why it is not just an interesting and beautiful idea, but really provides great opportunities for the development of the entire IT industry.

What did I, as a person who spent most of my time in physics, hear from programming and IT specialists? I have heard about the following trends.

We often hear about a large number of new startups or projects of existing companies such as the Internet of things, machine learning, big data and information security. These trends sound everywhere, set informational reasons, but behind them, in addition to the beauty of algorithmic solutions, the beauty of mathematics, the beauty of programming, is real iron. And this iron is already quantum.

If you look at the development trends of quantum technologies rather than information, then now this is a transition from the control of collective quantum phenomena that underlie devices such as transistors and lasers to the control of individual quantum properties.

Roughly speaking, a laser is controlling a large number of light particles, a large number of photons, and now we have learned how to control light, atoms, and matter at the level of individual microscopic elements. Such a trend is observed year after year, there are more and more experiments, proposals that use the laws of quantum physics already at the level of individual fundamental particles of matter. And here for me the most amazing thing is that it does not just come from the desire to learn fundamental science, but is also in demand in technological trends.

Quantum particles allow you to build a computer that will solve its problems faster. Quantum computers allow you to build communication systems that are better protected from listening. Quantum technology allows you to create more miniature sensors.

And all this underlies such applications as GPS, future medical sensors, new materials, which are in demand in information technology trends.

All technologically successful countries are currently actively engaged in the development of quantum technologies. A huge amount of money is invested in these studies, special programs for supporting quantum technologies are being created. If we go back to history, we all remember the space race between the USSR and the USA.

The quantum race involves not only states, but also private companies. In total, Google, IBM, Intel and Microsoft have invested about $ 0.5 billion in the development of quantum computers in recent years, created large laboratories and research centers.

Quantum technologies are still interesting in that they imply a kind of research format, where fundamental science is very closely linked to applied research.

Here is a map of the world's quantum centers, which are points of competence and points of growth. In 2011, the Russian Quantum Center, which I represent, appeared on this map. This is a fundamental scientific institute that has turned into an ecosystem where fundamental research coexists and stimulates the development of applied technologies.

However, today we are talking about a quantum computer, and within the framework of this lecture we would like to create a context that allows us to understand why quantum computers are generally interesting and necessary.

Here is the well-known Moore’s law, which expresses a certain trend in the productivity growth of existing computers. We know that from year to year computers are becoming more powerful, but behind this is a reduction in the elemental base, its miniaturization. Thanks to our progress in the development of transistors, we can create less and less, and place them more densely on an elementary unit of area.

But, of course, this trend has a fundamental limit. It is due to physics.

It is unlikely that we will be able to create a transistor the size of one atom. This requires at least a few atoms. As far as I know, the smallest transistor in the world consists of seven atoms. However, if Moore’s law continues as it continues, then in 2020 we will need to create computers with a single atom transistor. And that seems impossible.

What can be done here? You can increase productivity through other technologies, through cloud computing, parallelization, come up with some kind of element base that will allow you to get as close to the limit of Moore’s law as possible, that is, create the smallest transistor in the world. This is a very cool task.

However, even if we come very close to Moore’s law, we will still have problems that a classical computer does very poorly. It’s not for me among IT specialists to talk about this, but I will give examples of several tasks.

The first is the search optimization task. It is poorly resolved on classic computers.

The second, closest and most important to me is modeling of complex physical systems. For example, using modeling from first principles, it is very difficult to model some rather complex physical system. This requires a huge amount of resources.

There are various applied problems that seem quite distant from practice for a wide audience, such as factorization. However, everyone knows their fundamental importance for various technologies.

And even if we get close to the limit of Moore’s law, we won’t be able to solve such problems.

Of course we can. But it will take a lot of time.

I would like to get a physical system that will allow us to solve these problems in a more optimal way. It turns out that it exists, and arises in the context of a quantum computer.

I noticed in a Nobel lecture by Andrei Geim, one of the creators of graphene, such an interesting idea. He told how he came up with the idea of doing research in the field of graphene, using mental clouds. He heard about something, it was somehow processed in his head, and when he accumulated enough mental clouds, he created the concept that it is very interesting to deal with two-dimensional carbon and graphene.

I believe that three mental clouds led to the concept of a quantum computer.

The first one. It is not clear how to deal with computationally complex tasks. Will it always be really difficult for us to model some kind of physical system? Or does the prime factorization problem not have a sufficiently effective classical algorithm?

The second point is more physical. It is connected with the study of the question of what quantum physics as one of the most accurate physical theories imposes on the computation process. For example, Richard Feynman and Charles Bennett investigated the question of what minimum amount of energy or heat is released when one elementary operation is performed. Is it possible to create a computer that is the most productive and most economical in terms of energy release? How to create the smallest computer?

The third question is more about math. It is connected with the study of the question of what interesting properties the information theory acquires if we go from the description of classical objects in the classical theory of probability to the description of quantum objects, to the quantum theory of information. The banknote pictured here illustrates the idea of quantum money. This is one of the first concepts, which implies the use of some practical information technology. The fact is that if you create banknotes in which authenticity will be ensured by the creation of special quantum states, then due to the specific properties of quantum systems, such banknotes cannot be faked.

The second portrait here is a portrait of our compatriot Alexander Holevo. He is known worldwide as the creator of one of the fundamental theorems - the quantum information theorem or the Holevo theorem. Here, at the base of the quantum theory of information, we have something to be proud of. Russian researchers maintain a good tradition of interesting publications and interesting results in this area.

What does quantum physics give? What interesting consequences and chips does it have that could be useful from the point of view of information theory or future calculations?

In the classical world, we are accustomed to thinking that if we have a state of some kind of physical system, then it must be unambiguously defined by something. If we have a point in space, then we know that the system is at this point in space. In quantum physics, such a concept cannot be introduced. The fact is that a quantum system, if it is not observed, is in a superposition of all possible states. In particular, if she has two valid states, an eagle and a tails, then until we have measured this state, this is both an eagle and a tails at the same time. And only measurement gives us a guaranteed answer, in what condition the system is. Before measurement, the system is in a superposition state.

The second property is the property of quantum entanglement. In the quantum world, particles can exhibit very strong correlations, that is, their properties can be very closely linked, even if these particles are spatially sufficiently removed. Explaining the concept of quantum entanglement, they often give an example of a thought experiment, when we had some particle with spin 0, it decays into two particles, one we leave in our laboratory, the second we send to the Andromeda Nebula, and, measuring the spin of the first particle, we will definitely recognize the spin of a particle in the Andromeda Nebula. In a sense, this is a manifestation of the properties of quantum entanglement, strong quantum correlations, which can be useful from the point of view of calculations.

The third thing is fragility. Quantum states are rather fragile in comparison with classical ones. And the measurement process is precisely the process of perturbation. The question is whether this disturbance process is deterministically occurring. This is one of the key challenges to creating quantum technology. It is very difficult to create a large quantum system, the elements of which, on the one hand, will interact well enough with each other and at the same time will be well protected from the environment that can destroy them.

Another interesting aspect is the prohibition of cloning theorem. This is a forbidding theorem. If there is an arbitrary quantum state in the quantum world that is not known in advance, then it cannot be copied, unlike classical information. If there is a classic signal, you can always copy it. In the quantum world, an arbitrary quantum state cannot be copied. And this is a radical difference between quantum information and classical information.

What is the concept of quantum computing based on? In principle, one can abstract to a certain extent from the complex laws of quantum physics and imagine the concept of quantum computing as follows.

The system of bits, which is familiar to us in classical computers, is replaced by a system of qubits. This is a two-level quantum system or an eagle-tails system, when there are two possible states, and until the moment of measurement the system is in superposition: at the same time in this state, and in this with some kind of probability.

All the bits that we have are replaced with qubits. All logic elements from classical processes are replaced by quantum processes, and the result of the calculations is obtained by measurement. Thus, in a quantum computer, processing of all possible implementation variants is obtained at once, that is, you submit not one bit, not zero or one, but all possible combinations to the input - and carry out all operations on this superposition. The result is a certain quantum state. Measure it and get an answer.

In principle, on a conceptual level, this is the whole concept of quantum computing. Bits were replaced by qubits, classical operations were replaced by quantum operations, as a result we get what we need to measure, we measure many times and we get an answer.

This is what qubits can consist of. The fact is that qubits can consist of a huge variety of different physical systems. We are used to the fact that the bit is encoded due to the voltage level. In quantum physics there is a variety of physical systems. This is a particle of light, and a particle of matter, and nuclear spins, and solid-state systems that can be in such an interesting state of superposition. They have various advantages and disadvantages. Here is the key fact for today: no one fully understands what physical, elemental base a quantum computer will be built in the end. There is confidence that the so-called solid-state systems or systems with superconducting qubits are among the leaders, but about a month ago a competition was held between two quantum computers, built on different physical principles, and it did not reveal any radical advantage of one system over another. Some systems scale better, others are easier to control, others are better protected from decoherence, from the process of interacting with the environment.

Let us confine ourselves to two possible pictures as part of the lecture. The first is the polarization of light. It is very simple to imagine, a particle of light is a very simple two-level physical model, and it is very popular in another application of quantum technologies: in the so-called quantum communications. The second picture is spin. Spin can be up or down, this is qubit. Until we have measured, this is a state of superposition. Plus or minus one second.

What I have already said is an interesting process that arises as a result of quantum computing. A new quantum state arises.

Some superposition of zero and one was applied to the input, we performed multiple procedures with it. The output is a superposition of zero and one.

To get the answer, we need to take a measurement, and it needs to be done many times. Quantum computing implies that a predetermined quantum state is repeatedly applied to the input. A conversion procedure and then a measurement are performed on it. And the measurement eventually gives an answer.

This procedure of quantum measurements is quite complicated. This is a holistic topic even for specialists in the field of quantum physics. I draw your attention to the fact that we have a regular column on the N + 1 website called “Quantum Alphabet”, and we discuss such subtle issues there, including questions of quantum computing.

Why do we need all this? What will help us make a quantum computer, what interesting features will it give us? Why all this whistle-blowing with replacing bits with qubits, replacing logical operations and the final results of calculations? What does it give?

This provides benefits in the whole class of tasks. The most interesting problem for me that a quantum computer solves well is the factorization of discrete logarithms, since it underlies systems with asymmetric cryptography. And every time we buy something on the Internet, our credit card details are encrypted using asymmetric cryptography algorithms, public key cryptography. They, in turn, are based on such problems, in particular, as a discrete logarithm and factorization. And in this sense, the Shore quantum algorithm is the most important and most interesting example of a quantum algorithm, because it solves a practical problem exponentially faster than a classical computer. In this sense, a quantum computer is a threat to the existing information security infrastructure.

As soon as it appears, any open key distribution system that is based on such tasks can be hacked. On the one hand, this is bad, it can lead to a revolution, and often a quantum computer is called the information bomb of the 21st century. But on the other hand, at the moment, there is very little need to worry, because the Shore algorithm requires a universal quantum computer that can solve any algorithmically formulated problem, and this is very difficult. Yes, this gives tremendous advantages, but precisely because of the fact that quantum systems are fragile to external influence, it is very difficult to create a system from a sufficiently large number of qubits to carry out all operations and then measure them.

A quantum computer, in order to ensure, for example, hacking systems with asymmetric cryptography, must have a sufficient number of qubits operating in such a quantum mode. And it requires the creation of effective control methods for these quantum systems.

Today, Evgeny Kiktenko will tell you about a universal quantum computer in the context of algorithms. What algorithms are interesting for a quantum computer in terms of application? And Maxim Anufriev - from the point of view of solving the problem of machine learning on a universal quantum computer.

A universal quantum computer is a difficult task, and it is very important to understand. There is not even a clear time estimate when it appears. This year there is a lot of hype around this topic, even the first issue of Nature magazine has been released, one of the articles is “Quantum computers jump out of the laboratory” with the forecast that in 2017 some kind of commercial quantum computer will appear that can solve really useful tasks. Moreover, the forecast is so optimistic that a full-fledged universal commercial quantum computer will appear to solve practical problems.

Although this is a very controversial issue. Estimates of experts vary from 5 to 25 years. And in this sense, it is very difficult to say when a quantum computer will really arise.

The quantum computer that already exists was built by D-Wave. It is good for solving a very narrow class of problems that are interesting today: machine learning and artificial intelligence. Such a computer is very easy to scale, but it does not work fully in quantum mode and cannot solve any arbitrary task. It gives acceleration only in a certain class of problems due to a very interesting mechanism that Nikolay Pozhar will talk about today , precisely in the context of training not with a universal quantum computer, but with the example of D-Wave.

There is another kind of quantum computer called a quantum simulator. It is designed to solve an even more specific class of problems - namely, to simulate other types of physical systems. There are quite large prospects here, for example, for the search for high-temperature superconductors. These are materials that can conduct electrical current without loss at room temperature. So far, the theory for such systems is known only for very low temperatures. There are experimental studies that suddenly discover some materials that conduct current at different temperatures, for example, at –100 degrees Celsius. However, there is no full-fledged theory of high-temperature superconductors, because it is a computationally difficult task. Quantum simulators are designed to reproduce some properties of such physical systems and give some clue in which direction such materials can be sought. But simulators are also not universal quantum computers.

As I said, IT companies are already investing in quantum computer research. A very cool example is Google, which simply lured John Martinis, one of the leading experts in the field of quantum computing on superconducting qubits. John Martinis simultaneously leads several directions. One of them is the creation of a full-fledged universal quantum computer. Another is the study of the existing D-Wave quantum computer and the search for those tasks in which it gives an advantage.

By the way, John Martinis will be at the conference of the Russian Quantum Center this year . There will be an open lecture, where he can tell just about a quantum computer being developed by Google.

Another big player is IBM. She recently announced her open online platform for working with their five-qubit quantum computer. In this sense, anyone can write programs for a quantum computer, but, of course, its potential is limited by the fact that there are quite few qubits.

Other players in this market are Microsoft and Intel, and they have the longest shot - the creation of an anthropological quantum computer. Due to decoherence, due to the fact that the environment introduces errors into the process of quantum computing, part of the resources of a quantum computer must be spent on correcting them. Topological quantum systems avoid this. At the moment, this is a very fundamentally complex scientific concept, behind which there is a lot of interesting mathematics. This is very far removed at the moment from any practical implementation. In particular, the predicted topological states of matter, which are interesting from the point of view of calculations, have not yet been discovered experimentally. However, in 2016, the Nobel Prize was awarded for basic research in the field of the consequences of topologies for physics.

The following fact is very interesting: we are used to the fact that a classic computer is actually the same system, a solid body, which is responsible for all its functionality. We carry out both memory and calculation, in fact, on the same element base. However, a quantum computer allows us to make the so-called hybrid system, which will take the best from various forms of quantum matter from nature. For example, it is known that processors at the moment seem to be best built using superconducting qubits. All interfaces, all that is why quantum computers and their various elements will communicate with each other, can be built using photons - particles of light. This is the best agent for transmitting information.

Of course, in the process of calculation, sometimes it is necessary to store intermediate results, then carry out further operations with them. The best indicators in terms of storing quantum states show atomic systems. Therefore, a quantum computer is a big and interesting fundamental task that will allow you to combine, take the best from nature and build the most attractive, productive and interesting hybrid system.

At the moment, our main activity is work not on a quantum computer, but on a quantum communication system in the framework of the QRate project. And we will still be happy to talk about quantum communications. Quantum communications is a shield that allows us to defend ourselves against the sword of a quantum computer and create a key distribution system whose strength does not depend on the attacker's computing resources. Thanks for attention.