How can a quantum computer break into modern encryption systems and lower the cost of ammonia production?

    The paradoxes and mysteries of quantum physics excite the minds of scientists for a long time. Today, on the basis of the unusual properties of quantum particles, new instruments and devices are being built that can be many times superior in their characteristics to classical analogues.

    A story about the events in the “Quantum Industry” was addressed to Acronis staff by Alexey Fedorov, Scientific Director of the Quantum Information Technologies Group at the RCC. In this post, we provide a transcript of his lecture on quantum technologies with additions to share useful and interesting data with Acronis subscribers on Habrahabr.

    Large-scale projects are being implemented in the USA, Europe, China and Russia. The greatest interest is a quantum computer - not only universities are involved in the race for its construction, but also large corporations, including Google, IBM, Microsoft and Intel. It is predicted that quantum computers can revolutionize in a number of ways, for example, in protecting information, artificial intelligence, and modeling new materials.

    In the modern context, quantum technologies are methods of controlling individual quantum objects, such as atoms, photons, electrons, ions, and so on. Unlike classical systems, which are always in one of the possible states, quantum systems can be in a state of quantum superposition: to be simultaneously in all admissible states. An example of the difference between the classical world and the quantum one can be a coin. A coin can define two states - an eagle or tails - and encode them as 0 and 1. Then a classic coin can be either in state 0 or in state 1. Two coins - in one of 4 possible states at one time. Four coins are in one of 16 states. Ten coins are in one of 1024 states.

    The principle of superposition allows one “quantum coin” to be not only strictly an eagle or tails, but also to be in one of an infinite number of “intermediate” states between the eagle and tails. It will be more accurate to say that a quantum coin can be in an eagle and tails state at the same time. In this case, two alternatives incompatible from the classical point of view (a coin dropped by an eagle and a coin dropped by a tiling) seem to overlap each other inside a single quantum state. This is what scientists call quantum superposition, and the fact that our brain, which grew up in the classical world, is not even able to imagine - you can only get used to it. Moreover, in order to fully describe such a quantum superposition, two complex numbers corresponding to each of the classically distinguishable alternatives are required. Two “quantum coins" can be in a superposition of 4 states. And 10 “quantum coins" are in a superposition of 1024 states. Such “quantum coins" are called qubits - quantum analogs of bits of information. To describe a system of n qubits, 2 ^ n complex numbers are required.

    The main feature of quantum computing is precisely this: with an increase in the number of qubits, the number of parameters that we operate in the calculations grows exponentially. If there are even 50 qubits, the number of complex numbers necessary to describe their state - 2 ^ 50 - will be so large that it will be impossible to accurately model such a system even on the most powerful supercomputer. Such a threshold is one of the possible explanations for the phenomenon called quantum supremacy (quantum supremacy or quantum advantage): the ability to use a quantum computer to solve those tasks that are not capable of existing classical computers.

    Quantum quest and quantum race

    However, building such a computer is not easy. To do this, you need to solve a whole “quest” for managing quantum matter. Currently, many laboratories in the world are developing new methods for managing quantum objects. A quantum race is taking place both among corporations and in the scientific community. Leading developers are introducing more and more new solutions. But the quantum race is of fundamental importance - beyond the threshold of quantum supremacy, new discoveries await us in completely different fields of physics: from low-temperature physics to high-energy physics. In addition, quantum computers also have great potential for solving practical problems, therefore, corporations have joined in its development.

    What is the quest for managing quantum matter? On the one hand, it is necessary to have a sufficiently large number of qubits to provide a large space of states, but, on the other hand, it is necessary to control each qubit individually. It is clear that the larger the system, the more difficult it is to manage at the level of individual individual components. This is especially important for quantum physics, but, if you think about it, it applies to other areas of human activity. For example, if you want to create a huge and cool company, you will have to hire a lot of talented people. But the more these people are, the more difficult their interactions will be, and the more difficult it will be to control them :-)

    In the quantum world, striking a balance between scale and predictability is the biggest challenge today. But, having overcome it, we will be able to develop powerful quantum computers that can solve interesting problems. For example, IBM uses the term quantum volume - this is the number of qubits per the number of errors in the operation. This is a very obvious measure, it shows that it is not enough just to say how many qubits are in the system, the degree of control over them is also important, which helps to avoid errors. For the growth of the quantum volume, the growth of both the quantity and the “quality” of qubits is necessary.

    It should always be borne in mind that the probability of errors is an integral property of quantum “iron”. Therefore, speaking of qubits, it is necessary to separate physical qubits and logical qubits. Physical qubits are real atoms or superconducting chains, so-called “stamped” elements. Logical qubits are those objects over which there is real control, and they can be accessed with fixed parameters without errors. The computational capabilities of a quantum computer are ultimately determined by the number of logical qubits that work flawlessly. In terms of the quantum volume, this can be understood as follows: if the level of errors is zero, then further computational capabilities (quantum volume) grows due to an increase in the number of logical qubits.

    If we talk about advances in the field of working quantum computers, we cannot but mention the IBM computer at 50 qubits. He became one of the first quantum computers of this magnitude. IBM's “workhorse” of quantum computers is superconducting qubits, which must be cooled to very low temperatures for their work. In the IBM quantum processor, individual control over each qubit is not implemented and the level of errors is quite high, but the chip itself already exists. IBM also has an open 5-qubit and 16-qubit quantum computers that everyone can use over the Internet. In addition, in a few years, the corporation plans to make a 100-qubit system. Recently, IBM announced the integration of the IBM System One integrated quantum computer, which is a complete device that does not require

    Intel is on the verge of the same milestone of 50 qubits, but uses a different technology to create qubits. And this is good, because if one of the corporations encounters problems in implementing its approach, the second will continue to move towards progress.

    The leader of the quantum race today is Google, which demonstrated a 72-qubit quantum computer. Google’s core technology is the same as IBM’s - superconducting qubits. A group of scientists and developers from Google has also published a number of scientific articles describing approaches to achieving quantum excellence. So in the near future, the company can be expected to demonstrate quantum superiority with the help of their developed quantum processor.

    A system of 51 qubits was also created in the academic community - this was possible for the group of Mikhail Lukin (a graduate of Fiztekh and the head of the International Advisory Council of the Russian Quantum Center) based on ultracold neutral atoms, as well as a system of 53 qubits from the group of Christopher Monroe from the University of Maryland, which also He is the founder of IonQ, a company developing a commercial quantum computer based on ions. By the way, IonQ is not the only example of a startup in the field of quantum computing - there are now more than a dozen of them.

    Obviously, China has great potential in the quantum field. “Celestial” bears grandiose plans, planning to construct the largest quantum computer, and the developers already have $ 12 billion for this to create the National Quantum Laboratory.

    Somewhat apart is the company D-Wave. The D-Wave processor has thousands of qubits, but they work in a different mode - the quantum annealing mode. This allows you to solve with the help of such a computer, in fact, only one task. Despite the fact that companies such as Google and Volkswagen are already working with D-Wave, there are heated debates about the advantages of such a quantum computer.

    Applied side of the issue

    Despite all efforts, today quantum computers do not solve many practical problems, but the potential looks impressive. Now the development of quantum computing goes in two directions:

    • Specialized quantum computers that are aimed at solving one specific specific problem, for example, optimization problems. An example of a product is D-Wave quantum computers.
    • Universal quantum computers - which are able to implement arbitrary quantum algorithms. Today, there are only small prototypes of universal quantum computers - Google, IBM and Intel are working in this direction. They lay the foundation, but so far do not allow doing something large-scale and do not know how to cope with errors.

    In any case, quantum computers make it possible to operate with a large space of states, and this can be useful, for example, for solving search problems, optimizing various processes, and modeling complex systems.

    Due to the fact that IBM offers everyone to use a quantum computer, modern quantum programmers are already training in assembling tasks and running them on small quantum computers. For example, to search through an unordered database, the quantum algorithm has a quadratic advantage. In such a task, an unordered database can be represented as a kind of “black box”, to which requests are sent (addresses of elements in this database), and a black box answers them “yes” or “no” (is the element located at given address, request requirements). Imagine that in some database the address of each element consists of n bits, and in this database there is only one element that satisfies certain conditions. To find this element, on average, we need about 2 ^ n queries (more precisely, 2 ^ (n-1)), because due to the disorder of the database, all that remains for us is to sort through all possible addresses (of which 2 ^ n pieces) sequentially until we are finally lucky and get to the right element. If we have a quantum analogue of such a black box (it is also called the “quantum oracle”), in order to get an answer we need about 2 ^ (n / 2) requests. The advantage of the "quantum enumeration algorithm", named after L. Grover, is due to the ability to ask many questions to the quantum box at the same time - to form a superposition of queries. if we have a quantum analogue of such a black box (it is also called the "quantum oracle") in order to get an answer we need about 2 ^ (n / 2) requests. The advantage of the "quantum enumeration algorithm", named after L. Grover, is due to the ability to ask many questions to the quantum box at the same time - to form a superposition of queries. if we have a quantum analogue of such a black box (it is also called the "quantum oracle") in order to get an answer we need about 2 ^ (n / 2) requests. The advantage of the "quantum enumeration algorithm", named after L. Grover, is due to the ability to ask many questions to the quantum box at the same time - to form a superposition of queries.

    It is important to note that the search task in an unordered database is universal in nature - almost any other task (including NP-complete) can be reduced to it. However, to solve it, the number of queries will need to grow exponentially with the complexity of the task (in the example considered, the parameter n corresponded to it). Thus, you should not treat a quantum computer as an omnipotent tool capable of solving arbitrary computational problems with exponential acceleration. In some cases, its capabilities will be much more modest.

    Nevertheless, a great potential is already evident today for problems in the field of quantum chemistry. For example, in industry, the calculation of the parameters of chemical compounds and the modeling of chemical reactions is in demand. When using classic computers, we lack the capabilities and often have to compromise with accuracy. Quantum computers can help to determine in detail reaction chains, process dynamics, find catalysts for the desired reactions - all this is very useful! One of the most discussed problems today is the production of ammonia. This compound is actively used in fertilizers for plants, and 1-2% of all energy on the earth is spent on its production (data from the Quantum Computing Report and BP). If with the help of a quantum computer it would be possible to optimize the process of ammonia production due to accurate knowledge of all parameters,

    Recently, at the junction of quantum physics and machine learning, a new direction has emerged - quantum machine learning or, as they often say, Quantum AI. It is important that the superiority of a quantum computer over classical ones in machine learning problems does not require a full-fledged and multi-qubit quantum computer. Using a quantum computer, for example, it will be possible to speed up individual elements of machine learning algorithms, as well as speed up the process of learning them. In Google in recent years, quantum machine learning is considered one of the top areas in the entire field of quantum technology.

    It's not just about hardware

    For the next breakthrough, however, not only iron is needed, but also new fast quantum algorithms. There is noticeable progress. For example, to study the Fe2S2 compound using quantum chemistry algorithms, it took thirty years earlier when analyzed on a quantum computer. By searching for a more optimal algorithm, this time was reduced to 2 minutes, taking into account the use of the same iron.

    However, quantum algorithms are still not enough. While there are still only a few dozen, and for the full development of the field of quantum computing, there should be much more algorithms.

    Fears and technologies of information security

    A quantum computer has two sides: dark and light. So far, we have talked about the bright side - solving practically demanded tasks that cannot be solved with the help of classical computers. But there is a dark side: a quantum computer solves the factorization problem much better than a classical one. The complexity of this task, as you know, is one of the foundations for ensuring the persistence of common public-key cryptography algorithms. The factorization problem is extremely difficult for a classical computer, and on a quantum one it can be effectively solved using the Shore algorithm. For example, hacking an RSA key consisting of 1024 bits will take millions of years of continuous computing on classical computers, while on a quantum computer this problem will be solved in 10 hours (assuming that each quantum operation is performed 10 ns and that a computer of a sufficient number of logical qubits is available). So far, quantum computers do not allow anything to be hacked - after all, RSA cryptanalysis requires several thousand controlled qubits. And although a potentially dangerous computer does not yet exist, the community is already thinking about protecting it from possible problems in the future.

    One solution is the use of quantum key distribution technology, which allows two parties to exchange cryptographic keys for symmetric encryption. As you know, a single photon cannot be separated, and a quantum state cannot be copied - this is a fundamental limitation of quantum mechanics. On this principle - the protection of transmitted data by fundamental physical laws - new devices are built. In this area, China is leading the world arena. In Russia, the technology of quantum key distribution is being developed by several groups, for example, in the RCC, Moscow State University M.V. Lomonosov and ITMO. The device developed at the RCC has already been tested at Sberbank and Gazprombank.

    By the level of errors in the channel, you can find out if the key was compromised. If the error level is below the critical threshold, then you can correct the errors and exclude information potentially accessible to the attacker using classical algorithms and, thus, generate the final secret key. At the same time, the protected information remains inaccessible to the attacker.

    The central idea is to use quantum-distributed keys in the Vernam cipher - a one-time pad. As far as it is known, such a system is implemented in the most critical systems of China.

    The second principle of protection is post-quantum cryptography. It includes a new class of public key algorithms that are based on tasks that are computationally complex for both a classical computer and a quantum computer.

    Many are interested in the question of whether a quantum computer will harm the blockchain. Yes it is possible. Due to attacks on digital signatures, as well as through the use of the Shore quantum algorithm and the impact on consensus algorithms from the Grover quantum algorithm. However, blockchains can also be protected by quantum key distribution or post-quantum cryptography.

    Waiting for a miracle

    Work on quantum computers continues, and today the issues of creating new iron and developing new algorithms are equally important. This is not so simple to do, because programmers have to deal with completely new entities, and architects have to develop fundamentally new devices for controlling quantum systems. The scientific community and leading corporations are looking towards quantum computers with great optimism - there are reasons for it.

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