Quantum computers: small particles for a big breakthrough
Guest article from Aleksey Fedorov, Researcher at the Russian Quantum Center, co-author of the development of the world's first quantum blockchain
A quantum computer is perhaps the most complex and most intriguing device of the “second quantum revolution”. We can assume that this revolution - a wave of technology based on the use of individual quantum objects - is the idea of ​​a quantum computer, in fact, launched. Indeed, in recent years, technologies such as quantum communications, quantum random number generators, quantum modeling, as well as quantum sensors can be considered a quantum computer as a stimulating factor.
At the moment, a universal quantum computer is a hypothetical device, and its creation is one of the main challenges for science and engineering. The upcoming public lecture by Google Quantum Project Leader John Martinis at the International Conference on Quantum Technologies (to be held in Moscow on July 12-16, 2017) is intended to reveal the most interesting aspects of the race unfolding around the construction of a quantum computer.
What can a quantum computer give us? In addition to the revolutionary implications for existing information security tools, a quantum computer will open the way to new materials, new search methods for databases, pattern recognition, machine learning, and, as predicted, a new era in the development of artificial intelligence.
')
D-Wave quantum computer on Time magazine cover.
The twentieth century gave us computers. Despite the fact that the elementary cell of a computer - a transistor - can also be rightfully considered quantum technologies, classical physics is enough to describe the work of computers that we have at our disposal. Therefore, we will call our familiar computers classic. To describe the process of calculating the concept of a Turing machine, completely imitating the execution of the algorithm on a computer.
The scientific community was led to the idea of ​​a quantum computer by “three mental clouds” [1]. The first “cloud” is the development and generalization of the classical theory of information by Shannon to the quantum case. Despite the fact that at first interest in such a task can be considered purely academic, and consideration is rather abstract (more characteristic for mathematics than for physics), these studies quickly revealed the potential of quantum systems for information theory. Important paradigms for quantum information theory emerged in the works of Yuri Manin, Stephen Wiesner (who proposed conjugate coding and "quantum money"), and also Alexander Holevo (who proved the famous "Theorem Holevo"). Later, the first quantum algorithms for hypothetical quantum computers began to be explored with the help of the quantum Turing machine developed by David Deutsch.
The second “cloud” is an interest in the question of what physical limitations quantum mechanics imposes on the capabilities of computers. This question was raised by Charles Bennet (one of the creators of quantum cryptography), and was addressed by Richard Feynman in one of the first reports on quantum computing. It turned out that to formulate such restrictions (except, perhaps, dimensional, according to which the transistor is unlikely to be less than one atom) is quite difficult. And if you think in terms of dimensional constraints, then you can hypothetically build a very miniature computer in which all classical bits (0 and 1) will be replaced by quantum bits (qubits), implemented using two-level quantum systems (systems that can be in two possible states). Such a miniature computer will be described by the laws of quantum physics, and quantum bits will be located not only in two states, but also in all possible superpositions of these states.
Finally, the third “cloud” is related to the fact that computers have demonstrated their potential for complex design tasks, for example, in atomic or space projects. However, in the problems associated with the calculation of several quantum particles, there was no serious progress. Nevertheless, there are a lot of actual problems for calculations in the field of quantum physics.
All these ideas in aggregate were of great interest to the scientific community, but did not answer the main question: what could a hypothetical quantum computing device provide? The benefits of computing? What is the problem? Calculation of many-particle quantum systems? How?
In the early 1990s, several quantum algorithms were proposed, which gave a noticeable gain compared to the existing classical algorithms. In 1992, David Deutsch and Richard Yozhi (based on the previous work of Deutsch in 1985) showed that a quantum computer gives a gain in a problem in a rather specific problem. Let us imagine that we have a function about which we know for sure that it either always takes the same value (0 or 1) for all arguments, i.e. is constant, or is balanced (for half of the domain of definition, takes the value 0, for the other half, 1). Question: how many times do you need to look at the result of the calculation of this function, to say it is balanced or constant? In this (quite frankly, impractical) task, a quantum computer demonstrates an exponential gain compared to a classical one.
Another (also not painfully practical) important step was the algorithm of Simon. Simon's algorithm calculates the period of the function s in linear time, while any classical algorithm takes exponential time depending on the length of the input argument of the function.
Nevertheless, it was Simon’s algorithm that inspired Peter Shor to create a quantum algorithm for solving the factorization problem (factoring) and discrete logarithms. Despite again present abundance of complex mathematical terms, these tasks are much more practical than they seem at first glance. Such tasks are used in public key cryptography. The idea of ​​public-key cryptography is to use a problem for which direct computation is simple and the inverse problem is complex. In fact, it is quite simple to multiply two primes, but if a large number is given, it is difficult to immediately figure out from which prime factors it consists. It is difficult to figure out not only us, but even the best classic computers.
Thus, if a quantum computer is created, then the existing information infrastructure in terms of information protection methods should be modified. Public key cryptography methods are used in a very wide range of information security products, so a quantum computer is a real threat to data privacy, an information age atomic bomb.
It is interesting to note that the modification method, which guarantees absolute encryption strength even in the presence of a quantum computer, was proposed 8 years before Shore’s algorithm in the work of Charles Bennett and Gilles Brassard, as well as in the work of Arthur Eckert in 1991. However, it was not until the creation of Shor’s algorithm that Bennett and Brassard’s work, which suggested using quantum effects as a way to protect information, received the deserved attention of the scientific community.
The potential of Shor’s quantum algorithm, as well as Grover’s quantum algorithm, which gives acceleration to another practical database search problem, has riveted the attention of the scientific community to the problem of developing a quantum computer. In addition to the “three clouds” mentioned, the fourth has ripened - remarkable experimental progress in creating methods of working with quantum systems at the level of their individual objects (photons, individual atoms, electrons, etc.). This progress was awarded the 2012 Nobel Prize to Serge Arosh and David Weinland with the wording: “for creating breakthrough technologies for manipulating quantum systems that made the measurement of individual quantum systems possible”.
However, the task of building a quantum computer is extremely complex. Build a large system consisting of quantum objects so that it is, on the one hand, well protected from the environment (which can destructively affect its quantum properties), while, on the other hand, allow the objects of this system (qubits) to “talk "With each other for the implementation of calculations, it is really very difficult.
A positive fact is that quantum bits can in principle be created in completely different physical systems. These include ultracold gases of atoms and molecules in optical lattices, superconducting quantum chains, photons, and many other quantum systems. In addition, each of these systems has several advantages and disadvantages.
For example, non-universal quantum computers, often called quantum simulators, can be created with ultracold atoms and molecules in optical lattices. The fact is that the behavior of such particles in optical lattices is very similar to the behavior of electrons in a periodic field created by ions. Having established a certain correspondence between the systems, it is possible with the help of a system of atoms or molecules to reveal new interesting phases, which should under certain conditions arise in solids. The most intriguing here are such tasks as the creation of superalloy alloys or the search for materials that become superconducting at room temperature. The latter, of course, will lead to a revolution in the electrical industry, as it will allow the transfer of energy without loss. Modeling the quantum states of a huge number of atoms on ordinary computers and supercomputers requires enormous resources, and its results are only partially applicable to real physics, and quantum simulators can open up new paths for revolutionary innovations in cellular communications, medicine, and home appliances.
One of the most promising technologies on the way to creating a quantum computer is the use of superconducting qubits. It is on the basis of superconducting quantum bits that D-Wave's quantum processor (calculator) works. D-Wave's product is not a full-fledged and universal quantum computer, so today we can still make purchases on the Internet, encrypting our bank card data with existing means. The product of the D-Wave company, which unites several thousand qubits, is currently designed to a greater extent for solving optimization problems using quantum annealing.
Annealing - a metallurgical term - means a class of methods for solving optimization problems acting on the principle of annealing, i.e. heating to a certain temperature, exposure for a certain time at this temperature and subsequent, usually slow, cooling to room temperature. In the process of cooling, the system “moves” between the states providing the minimum energy until it cools down, choosing the best state for itself. Due to quantum effects, such as tunneling, quantum systems are more “mobile”, therefore they allow to effectively find the best solution. As in the case of quantum simulators, quantum annealing is not a universal method. It can be directed to solving problems of a particular class. However, the potential is quite large. The point is that optimization tasks are closely related to machine learning tasks. Therefore, a quantum computer can potentially be of great benefit to the development of new highly efficient methods for teaching neural networks. In addition, large industrial companies such as NASA and Airbus [2] have expressed great interest in quantum optimization methods.
Perhaps it was this potential that was decisive for Google, which had recently formed research units for the creation and study of quantum computing under the leadership of John Martinis. Moreover, the company explores the potential of an already existing D-Wave quantum computer, and seeks approaches to creating a universal quantum computer based on superconducting qubits.
Other companies, such as IBM, Microsoft, and Intel, are also showing interest in creating quantum computing. For example, a quantum computer of 5 qubits created by IBM is opened [3]. Microsoft and Intel are building close ties with the scientific community. Joint research programs will probably unlock the potential of the most fundamental approach to a quantum computer — topological error-proof quantum computing. The fact is that from errors caused by the environment can be protected using topology. Some system parameters, called invariants, do not change (under certain constraints) when the external conditions change. If we connect qubits with these invariants, then we can protect against errors. However, it is rather difficult to create such states of matter; now, research in the field of topological quantum computing is only beginning from the experimental point of view.
Quantum computer due to the impact of the environment is difficult to create. But if quantum systems react so sensitively to changes in environmental parameters, then why not use it? For example, a quantum sensor in the form of a crystal with a size of the order of several nanometers can be embedded in a cell of a living organism without disrupting its vital activity and then used to measure microscopic fields inside this cell. With this technology, it becomes possible to conduct magnetic resonance imaging of individual cells, their parts and even individual molecules. This opens up completely new horizons for biology and medicine. An enormous amount of knowledge about the vital activity of cell parts, the development of diseases, the mechanisms of functioning of drugs becomes available. Quantum sensors will help to understand the structure of the synaptic connections of the human brain, making possible the treatment of its diseases or allowing understanding of other processes of brain activity.
Do not forget that a quantum computer - not only consists of a processor. It also assumes the presence of memory and interfaces. One of the most promising candidates for building memory for quantum states is ultracold atoms, and for interfaces - photons, because nothing will transfer information faster than particles of light. Therefore, the possible appearance of the future may be a hybrid quantum computer, combining all the best qualities from all the best quantum systems.
It should also be borne in mind that quantum computers (in any form: simulators, “annealing” or universal) do not solve all problems better than classical ones, but only solve special classes. I also do not want to be mistaken in forecasts, as Ken Olsen, who said in 1977, “It is unlikely that anyone would think of installing a computer at home,” but there is reason to believe that quantum computers will enter our daily lives as part of a common and large hybrid information infrastructure XXI century. Such an introduction will truly allow you to unleash the “end-to-end” potential of a quantum computer and quantum technologies in general, opening new doors on the path to progress.
[1] A reference to A. Heim's lecture, where he talked about the "three clouds" that led him to graphene.
[2] www.telegraph.co.uk/finance/newsbysector/industry/12065245/Airbuss-quantum-computing-brings-Silicon-Valley-to-the-Welsh-Valleys.html
[3] phys.org/news/2016-05-ibm-users-quantum.html
A quantum computer is perhaps the most complex and most intriguing device of the “second quantum revolution”. We can assume that this revolution - a wave of technology based on the use of individual quantum objects - is the idea of ​​a quantum computer, in fact, launched. Indeed, in recent years, technologies such as quantum communications, quantum random number generators, quantum modeling, as well as quantum sensors can be considered a quantum computer as a stimulating factor.
At the moment, a universal quantum computer is a hypothetical device, and its creation is one of the main challenges for science and engineering. The upcoming public lecture by Google Quantum Project Leader John Martinis at the International Conference on Quantum Technologies (to be held in Moscow on July 12-16, 2017) is intended to reveal the most interesting aspects of the race unfolding around the construction of a quantum computer.
What can a quantum computer give us? In addition to the revolutionary implications for existing information security tools, a quantum computer will open the way to new materials, new search methods for databases, pattern recognition, machine learning, and, as predicted, a new era in the development of artificial intelligence.
')
D-Wave quantum computer on Time magazine cover.
The twentieth century gave us computers. Despite the fact that the elementary cell of a computer - a transistor - can also be rightfully considered quantum technologies, classical physics is enough to describe the work of computers that we have at our disposal. Therefore, we will call our familiar computers classic. To describe the process of calculating the concept of a Turing machine, completely imitating the execution of the algorithm on a computer.
The scientific community was led to the idea of ​​a quantum computer by “three mental clouds” [1]. The first “cloud” is the development and generalization of the classical theory of information by Shannon to the quantum case. Despite the fact that at first interest in such a task can be considered purely academic, and consideration is rather abstract (more characteristic for mathematics than for physics), these studies quickly revealed the potential of quantum systems for information theory. Important paradigms for quantum information theory emerged in the works of Yuri Manin, Stephen Wiesner (who proposed conjugate coding and "quantum money"), and also Alexander Holevo (who proved the famous "Theorem Holevo"). Later, the first quantum algorithms for hypothetical quantum computers began to be explored with the help of the quantum Turing machine developed by David Deutsch.
The second “cloud” is an interest in the question of what physical limitations quantum mechanics imposes on the capabilities of computers. This question was raised by Charles Bennet (one of the creators of quantum cryptography), and was addressed by Richard Feynman in one of the first reports on quantum computing. It turned out that to formulate such restrictions (except, perhaps, dimensional, according to which the transistor is unlikely to be less than one atom) is quite difficult. And if you think in terms of dimensional constraints, then you can hypothetically build a very miniature computer in which all classical bits (0 and 1) will be replaced by quantum bits (qubits), implemented using two-level quantum systems (systems that can be in two possible states). Such a miniature computer will be described by the laws of quantum physics, and quantum bits will be located not only in two states, but also in all possible superpositions of these states.
Finally, the third “cloud” is related to the fact that computers have demonstrated their potential for complex design tasks, for example, in atomic or space projects. However, in the problems associated with the calculation of several quantum particles, there was no serious progress. Nevertheless, there are a lot of actual problems for calculations in the field of quantum physics.
All these ideas in aggregate were of great interest to the scientific community, but did not answer the main question: what could a hypothetical quantum computing device provide? The benefits of computing? What is the problem? Calculation of many-particle quantum systems? How?
In the early 1990s, several quantum algorithms were proposed, which gave a noticeable gain compared to the existing classical algorithms. In 1992, David Deutsch and Richard Yozhi (based on the previous work of Deutsch in 1985) showed that a quantum computer gives a gain in a problem in a rather specific problem. Let us imagine that we have a function about which we know for sure that it either always takes the same value (0 or 1) for all arguments, i.e. is constant, or is balanced (for half of the domain of definition, takes the value 0, for the other half, 1). Question: how many times do you need to look at the result of the calculation of this function, to say it is balanced or constant? In this (quite frankly, impractical) task, a quantum computer demonstrates an exponential gain compared to a classical one.
Another (also not painfully practical) important step was the algorithm of Simon. Simon's algorithm calculates the period of the function s in linear time, while any classical algorithm takes exponential time depending on the length of the input argument of the function.
Nevertheless, it was Simon’s algorithm that inspired Peter Shor to create a quantum algorithm for solving the factorization problem (factoring) and discrete logarithms. Despite again present abundance of complex mathematical terms, these tasks are much more practical than they seem at first glance. Such tasks are used in public key cryptography. The idea of ​​public-key cryptography is to use a problem for which direct computation is simple and the inverse problem is complex. In fact, it is quite simple to multiply two primes, but if a large number is given, it is difficult to immediately figure out from which prime factors it consists. It is difficult to figure out not only us, but even the best classic computers.
Thus, if a quantum computer is created, then the existing information infrastructure in terms of information protection methods should be modified. Public key cryptography methods are used in a very wide range of information security products, so a quantum computer is a real threat to data privacy, an information age atomic bomb.
It is interesting to note that the modification method, which guarantees absolute encryption strength even in the presence of a quantum computer, was proposed 8 years before Shore’s algorithm in the work of Charles Bennett and Gilles Brassard, as well as in the work of Arthur Eckert in 1991. However, it was not until the creation of Shor’s algorithm that Bennett and Brassard’s work, which suggested using quantum effects as a way to protect information, received the deserved attention of the scientific community.
The potential of Shor’s quantum algorithm, as well as Grover’s quantum algorithm, which gives acceleration to another practical database search problem, has riveted the attention of the scientific community to the problem of developing a quantum computer. In addition to the “three clouds” mentioned, the fourth has ripened - remarkable experimental progress in creating methods of working with quantum systems at the level of their individual objects (photons, individual atoms, electrons, etc.). This progress was awarded the 2012 Nobel Prize to Serge Arosh and David Weinland with the wording: “for creating breakthrough technologies for manipulating quantum systems that made the measurement of individual quantum systems possible”.
However, the task of building a quantum computer is extremely complex. Build a large system consisting of quantum objects so that it is, on the one hand, well protected from the environment (which can destructively affect its quantum properties), while, on the other hand, allow the objects of this system (qubits) to “talk "With each other for the implementation of calculations, it is really very difficult.
A positive fact is that quantum bits can in principle be created in completely different physical systems. These include ultracold gases of atoms and molecules in optical lattices, superconducting quantum chains, photons, and many other quantum systems. In addition, each of these systems has several advantages and disadvantages.
For example, non-universal quantum computers, often called quantum simulators, can be created with ultracold atoms and molecules in optical lattices. The fact is that the behavior of such particles in optical lattices is very similar to the behavior of electrons in a periodic field created by ions. Having established a certain correspondence between the systems, it is possible with the help of a system of atoms or molecules to reveal new interesting phases, which should under certain conditions arise in solids. The most intriguing here are such tasks as the creation of superalloy alloys or the search for materials that become superconducting at room temperature. The latter, of course, will lead to a revolution in the electrical industry, as it will allow the transfer of energy without loss. Modeling the quantum states of a huge number of atoms on ordinary computers and supercomputers requires enormous resources, and its results are only partially applicable to real physics, and quantum simulators can open up new paths for revolutionary innovations in cellular communications, medicine, and home appliances.
One of the most promising technologies on the way to creating a quantum computer is the use of superconducting qubits. It is on the basis of superconducting quantum bits that D-Wave's quantum processor (calculator) works. D-Wave's product is not a full-fledged and universal quantum computer, so today we can still make purchases on the Internet, encrypting our bank card data with existing means. The product of the D-Wave company, which unites several thousand qubits, is currently designed to a greater extent for solving optimization problems using quantum annealing.
Annealing - a metallurgical term - means a class of methods for solving optimization problems acting on the principle of annealing, i.e. heating to a certain temperature, exposure for a certain time at this temperature and subsequent, usually slow, cooling to room temperature. In the process of cooling, the system “moves” between the states providing the minimum energy until it cools down, choosing the best state for itself. Due to quantum effects, such as tunneling, quantum systems are more “mobile”, therefore they allow to effectively find the best solution. As in the case of quantum simulators, quantum annealing is not a universal method. It can be directed to solving problems of a particular class. However, the potential is quite large. The point is that optimization tasks are closely related to machine learning tasks. Therefore, a quantum computer can potentially be of great benefit to the development of new highly efficient methods for teaching neural networks. In addition, large industrial companies such as NASA and Airbus [2] have expressed great interest in quantum optimization methods.
Perhaps it was this potential that was decisive for Google, which had recently formed research units for the creation and study of quantum computing under the leadership of John Martinis. Moreover, the company explores the potential of an already existing D-Wave quantum computer, and seeks approaches to creating a universal quantum computer based on superconducting qubits.
Other companies, such as IBM, Microsoft, and Intel, are also showing interest in creating quantum computing. For example, a quantum computer of 5 qubits created by IBM is opened [3]. Microsoft and Intel are building close ties with the scientific community. Joint research programs will probably unlock the potential of the most fundamental approach to a quantum computer — topological error-proof quantum computing. The fact is that from errors caused by the environment can be protected using topology. Some system parameters, called invariants, do not change (under certain constraints) when the external conditions change. If we connect qubits with these invariants, then we can protect against errors. However, it is rather difficult to create such states of matter; now, research in the field of topological quantum computing is only beginning from the experimental point of view.
Quantum computer due to the impact of the environment is difficult to create. But if quantum systems react so sensitively to changes in environmental parameters, then why not use it? For example, a quantum sensor in the form of a crystal with a size of the order of several nanometers can be embedded in a cell of a living organism without disrupting its vital activity and then used to measure microscopic fields inside this cell. With this technology, it becomes possible to conduct magnetic resonance imaging of individual cells, their parts and even individual molecules. This opens up completely new horizons for biology and medicine. An enormous amount of knowledge about the vital activity of cell parts, the development of diseases, the mechanisms of functioning of drugs becomes available. Quantum sensors will help to understand the structure of the synaptic connections of the human brain, making possible the treatment of its diseases or allowing understanding of other processes of brain activity.
Do not forget that a quantum computer - not only consists of a processor. It also assumes the presence of memory and interfaces. One of the most promising candidates for building memory for quantum states is ultracold atoms, and for interfaces - photons, because nothing will transfer information faster than particles of light. Therefore, the possible appearance of the future may be a hybrid quantum computer, combining all the best qualities from all the best quantum systems.
It should also be borne in mind that quantum computers (in any form: simulators, “annealing” or universal) do not solve all problems better than classical ones, but only solve special classes. I also do not want to be mistaken in forecasts, as Ken Olsen, who said in 1977, “It is unlikely that anyone would think of installing a computer at home,” but there is reason to believe that quantum computers will enter our daily lives as part of a common and large hybrid information infrastructure XXI century. Such an introduction will truly allow you to unleash the “end-to-end” potential of a quantum computer and quantum technologies in general, opening new doors on the path to progress.
[1] A reference to A. Heim's lecture, where he talked about the "three clouds" that led him to graphene.
[2] www.telegraph.co.uk/finance/newsbysector/industry/12065245/Airbuss-quantum-computing-brings-Silicon-Valley-to-the-Welsh-Valleys.html
[3] phys.org/news/2016-05-ibm-users-quantum.html
Source: https://habr.com/ru/post/332790/
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