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American Journal of Engineering and Applied Sciences

Elementary Structure of Matter can be Studied with New Quantum Computers

Nicolae Petrescu, Florian Ion Tiberiu Petrescu

Published Feb 1, 2018• 13 citations
Publisher

Abstract

Much has been talked about quantum computers. Today they are working on difficult simulations, so we can already congratulate the college of researchers at the Oak Ridge National Laboratory as the world's first to successfully simulate an atomic nucleus using a quantum computer. The results that were published in the physical examination letters demonstrate the huge capacity of quantum systems to calculate the problems of nuclear physics and to be able to be successfully used in the future for special and complex simulations. It is already known that quantum calculus, which is based on the quantum principles of matter and which was proposed by American physicist Richard Feynman in the early 1980s, unlike the ordinary bits of normal computers today, uses the qubit units used by quantum computers to store information in two-state systems, such as electrons or photons, considered simultaneously in all possible quantum states (essentially a phenomenon known as overlapping). In October 2017, a multidisciplinary ORNL team began working on codes to perform various simulations on quantum computers such as IBM QX5 and Righetti 19Q within a DOE Quantum Testbed Pathfinder project in an effort to verify and validate various scientific applications on different types of quantum hardware. Today, quantum computers have potential applications in cryptography, artificial intelligence and weather forecasting, as each additional qubit clings in some way inextricably from the others, thus exponentially increasing the number of possible results for the final measured state. Obviously, this huge benefit also has negative effects on the system, because errors can in turn exponentially increase the size of the problem and the final results even. However, it is hoped that in the future on the basis of much-improved hardware, researchers will be able to solve problems that cannot be solved today using current calculation methods. In the present paper the authors propose an original method of rapid theoretical determination with great precision of the dimensions of all elementary particles, the method which, although predicting results similar to those obtained by other theoreticians, still has the advantage of its simplicity, of its general applicability, that is of its universality and especially this new method is a precious tool in the work of scientists worldwide to understand matter at its elementary level. Even though we would have expected that the size of a deuteron would be larger (double) than that of one component particle (of a proton or neutron), at the same velocity, the theory (20-21) demonstrates the opposite. By fusing two free nucleons, a proton and a neutron, a deuterium nucleus is obtained with smaller dimensions than its two components, which makes the energy of rejection between two Deuteron cores much larger than we would have waited. That's why the fusion reaction between two Deuterons is even more difficult than was suspected, even when they are accelerating.

DOI
10.3844/ajeassp.2018.1062.1075

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In the twentieth century, quantum physics is one of the most successful approaches in scientific progress. To theorize the concept of quantum computing Max Planck's idea of the existence of energy in individual units like matter was used. Since then, the idea of manufacturing quantum computers for everyday use is becoming more plausible with technological advances in quantum theory. A classical computer carries out logical operations using a bit which is either 1 or 0. In contrast to a classical computer, a quantum computer works with a quantum bit or qubit, which is not limited to two states only. Qubits can exist in a superposition of the two states creating parallelism. Qubit represents the state of atoms, ions, photons or electrons. These qubits which work together with a control device act as a computer memory.Quantum computers have the potential to become million times more potent than present-day supercomputers due to the presence of these multiple states simultaneously. Concepts and ideas of quantum computing have been demonstrated by different methods like Ion Trap, Quantum Dot methods etc. However, the actual realization of such a superior system is still in the future. A strategy must be formulated to maintain decoherence and other potential sources of error at a permissible level.Astonishingly, quantum computing took a long time to take off, even though the physicists have known about the world of subatomic particles. Even so, it took computer scientists another half-century to consider harnessing quantum effects for computation. Also, it was later discovered that quantum computers could solve quantum mechanical many-body problems that are impractical to solve on a classical computer. The foundations of the subject of quantum computation may have become well-published, but the knowledge is still growing. Hence here is a research paper based on the study of quantum computation.

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Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians.During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability.The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms.These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches.This contribution is an elementary introduction to quantum simulation.We discuss the challenges, define both digital and analog quantum simulators, and list the demanding conditions they require.We also provide a brief account of the contributions gathered in the dossier on Quantum simulation in the Compte rendus Physique of the French Academy of Sciences [1][2][3][4][5][6].The latter completes excellent reviews that appeared previously, see for instance . Universal models and the role of simulations in many-body physicsUnderstanding the behavior of macroscopic quantum systems is a major challenge of modern physics.The basic laws of low-energy physics are by now quite well known at the microscopic, say atomic, scale.Conversely, many fundamental questions remain open, and even debated, about the collective dynamics at the macroscopic scale.By "macroscopic scale", here we mean systems made up of a huge number of constituents, or degrees of freedom, say 10 6 , 10 23 , or even more, as relevant in condensed matter physics or in astrophysics, for instance.Such huge systems cannot be treated exactly, be it a the classical level and, even worse, at the quantum level.Yet, it is the main outcome of the thermodynamic approach that the collective behavior of a macroscopic system can drastically differ from that of its elementary constituents.For instance, the elementary interactions between the H 2 O molecules are fundamentally unchanged when a water bucket turns from the liquid phase to the solid phase at zero degree Celsius.Similarly, the interactions between the microscopic magnetic moments do not show any brutal change when a magnetic material gets magnetized underneath the Curie temperature.Hence, the dramatic effects observed in macroscopic systems are governed by large-scale instabilities, without obvious counterparts at the microscopic level.This observation takes a universal character, summarized in the celebrated motto "More is Different" [15].Such so-called emerging phenomena also appear in quantum systems, where new effects that are impossible in the classical world show up below some critical temperature or at zero temperature when some interaction parameter passes through a critical value.Celebrated examples include the superfluid transition in helium or super-conducting transitions and other metal-insulator transitions in electronic systems.Strikingly enough at first sight, while emerging phenomena only appear in very large scale macroscopic systems, their germs are contained in the mutual interactions of their elementary constituents.Hence, local two-body interactions are sufficient to explain a huge class of phase transitions, such as the liquid-solid and magnetic transitions mentioned above.The Boltzmann statistical approach proved particularly successful in describing this connection between the microscopic and macroscopic scales.To understand emerging phenomena on grounds as fundamental as possible, the programme is now well established: One tries to identify the basic microscopic terms that seem to be relevant and disregards all the other microscopic details.One then elaborates a model, as generic as possible, likely to reproduce the main experimental observations.The most usual examples are the Ising and Heisenberg models for magnetic transitions, or the Hubbard model for metal-insulator transitions [16][17][18].Then all is left to do is to check that the phenomenon of interest indeed emerges from the dynamics of the simplified model.The realization of this programme is nothing but a simulation.It consists in building up a simplified system that mimics the main properties of a real system.

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A happy accident in the laboratory has led to a breakthrough discovery that not only solved a problem that stood for more than half a century, but has major implications for the development of quantum computers and sensors. [55] Significant technical and financial issues remain towards building a large, fault-tolerant quantum computer and one is unlikely to be built within the coming decade. [54] Chemists at Friedrich Schiller University in Jena (Germany) have now synthesised a molecule that can perform the function of a computing unit in a quantum computer. [53] The research team developed the first optical microchip to generate, manipulate and detect a particular state of light called squeezed vacuum, which is essential for HYPERLINK https://phys.org/tags/quantum/ quantum computation. [52] Australian scientists have investigated new directions to scale up qubits-utilising the spin-orbit coupling of atom qubits-adding a new suite of tools to the armory. [51] A team of international researchers led by engineers from the National University of Singapore (NUS) have invented a new magnetic device to manipulate digital information 20 times more efficiently and with 10 times more stability than commercial spintronic digital memories. [50] Working in the lab of Mikhail Lukin, the George Vasmer Leverett Professor of Physics and co-director of the Quantum Science and Engineering Initiative, Evans is lead author of a study, described in the journal Science, that demonstrates a method for engineering an interaction between two qubits using photons. [49] Researchers with the Department of Energy's Oak Ridge National Laboratory have demonstrated a new level of control over photons encoded with quantum information. [48] Researchers from Intel Corp. and the University of California, Berkeley, are looking beyond current transistor technology and preparing the way for a new type of memory and logic circuit that could someday be in every computer on the planet. [47]

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R. Blatt, Immanuel Bloch, J. I. Cirac +1 more

Quantum many-body systems, as they appear in different branches of physics and chemistry, are very hard to simulate. The number of parameters defining their quantum states grows exponentially with the number of constituents. This prevents us from exploring and investigating relevant problems involving relatively small numbers of subsystems even with the help of the most powerful supercomputers. Richard Feynman already noticed this difficulty back in 1981 when he wrote his visionary paper “Simulating Physics with Computers” [Int. J. Theor. Phys. 21:6/7, 467 (1982)]. There, he proposed to use quantum systems (as opposed to classical computers) to perform the simulation and in this way to circumvent the need to store and compute a colossal number of parameters, necessary to describe the pertaining superpositions. What was a visionary idea at that time has become a very active field of research in the last few years. The extraordinary progress of both theoretical and experimental research in quantum physics allows us now to tame, control, and manipulate various quantum systems with unprecedented precision. Laser, magnetic, electronic and other technologies enable us to arrange quantum subsystems in different geometries, modify their interactions, and detect them. This allows us to engineer Hamiltonians and emulate systems displaying some of the most intriguing quantum phenomena. This tremendous progress is, to a large extent, due to the pioneering work of many researchers during the last twenty to thirty years. Here, the investigations of basic phenomena with one or few atoms or photons were of particular impact. The degree of control achieved in the experiments has enabled the observation of mind-boggling quantum effects, related to the superposition principle or to entangled states, and their disappearance due to decoherence. In fact, the 2012 Nobel Prize has been awarded to two scientists, S. Haroche and D. Wineland, for such ground-breaking experiments. Such experiments, often in combination with laser cooling of atoms or ions and Bose-Einstein condensation, have formed one of the pillars on which the field of quantum simulations is being established. Quantum simulations with cold atoms, either in magnetic traps or in optical lattices, with trapped ions, with photons, with superconducting devices, with quantum dots, etc., have been theoretically proposed and experimentally considered by many researchers. Most of the proposals so far deal with problems in condensed matter physics that are either difficult to tackle with modern supercomputers or are difficult to observe in solid state systems. This has established a very close link between different disciplines, like atomic, molecular, and optical (AMO) physics, and condensed matter physics. Although some of the experiments are still in their infancy, and a lot of research is still needed, the extraordinary progress made in all these research areas during the last few years makes us feel confident that in the not too distant future quantum simulators will provide a key tool to investigate many-body quantum systems. Furthermore, we also expect that quantum simulators will help quantum physicists to establish new and fruitful links to other scientific communities, like high-energy physics or quantum chemistry. The present special issue contains various review papers as well as research papers on quantum simulations. It starts out with two papers written by last year's Nobel Prize winners describing their foundational work (Wineland, p. 739 and Haroche, p. 763). The issue continues with three thorough, invited review papers covering different topics on quantum simulations. The first one reviews recent theoretical proposals to use cold atoms in optical lattices to simulate lattice gauge theories of the sort that appear in high-energy physics (U.-J. Wiese, p. 783). The second covers both theoretical proposals and experimental demonstrations of cold-atom systems to simulate the physics of matter in the presence of gauge fields, displaying so-called topological phenomena, which so far have only been observed in solid-state systems (I. Spielman, p. 794). The third one contains an extensive overview and new proposals to perform a broad range of quantum simulations using quantum dot systems (P. Barthelmy et al., p. 813). The issue also includes six original papers with a variety of theoretical proposals as well as the introduction of novel theoretical techniques related to the field of quantum simulation. The field of quantum simulations is just starting, but we are confident that it will soon generate an even larger plethora of new ideas and discoveries, trigger interdisciplinary research, and lead us to the adventure of describing and understanding the quantum world. We hope that this special issue will help future researchers in such an exciting adventure. Rainer Blatt received his PhD degree in physics from the University of Mainz in 1981. As a postdoctoral fellow he worked on atomic beam cooling in Boulder, CO and later as a research assistant in Hamburg with single trapped ions. In 1995 he accepted a chair in experimental physics at the University of Innsbruck working on quantum information processing with trapped ions. Since 2003 he is also scientific director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences. Immanuel Bloch received his PhD degree in physics from the Ludwig Maximilians University of Munich in 2000. As a junior group leader, he continued in Munich starting his work on ultracold quantum gases in optical lattices. In 2008 he was appointed scientific director of the newly founded division on Quantum Many-Body Systems at the Max Planck Institute of Quantum Optics. Since 2009 he also holds a chair in quantum optics at the Ludwig-Maximilians University of Munich. Ignacio Cirac received his PhD degree in physics from the Universidad Complutense de Madrid in 1991. He was professor at the Universities of Castilla-La Mancha and Innsbruck from 1991–1996 and 1996–2001, respectively. In 2001 he joined the Max-Planck Institute of Quantum Optics, where he leads the Theory Division. His current research interests include quantum information theory and quantum optics. Peter Zoller obtained his doctorate from the University of Innsbruck in 1977. He was Max Kade Fellow at the University of Southern California from 1978/79, and was JILA visiting Fellow 1981/82 and 1988. In 1990 he became JILA Fellow and professor of physics at the University of Colorado. At the end of 1994, he accepted a chair at the University of Innsbruck, where he has worked ever since. Since 2003, he has also held the position of Scientific Director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences.

Annalen der Physik•Nov 1, 2013•3 citations
Much has been talked about quantum computers. Today they are working on difficult simulations, so we can already congratulate the college of researchers at the Oak Ridge National Laboratory as the world's first to successfully simulate an atomic nucleus using a quantum computer. The results that were published in the physical examination letters demonstrate the huge capacity of quantum systems to calculate the problems of nuclear physics and to be able to be successfully used in the future for special and complex simulations. It is already known that quantum calculus, which is based on the quantum principles of matter and which was proposed by American physicist Richard Feynman in the early 1980s, unlike the ordinary bits of normal computers today, uses the qubit units used by quantum computers to store information in two-state systems, such as electrons or photons, considered simultaneously in all possible quantum states (essentially a phenomenon known as overlapping). In October 2017, a multidisciplinary ORNL team began working on codes to perform various simulations on quantum computers such as IBM QX5 and Righetti 19Q within a DOE Quantum Testbed Pathfinder project in an effort to verify and validate various scientific applications on different types of quantum hardware. Today, quantum computers have potential applications in cryptography, artificial intelligence and weather forecasting, as each additional qubit clings in some way inextricably from the others, thus exponentially increasing the number of possible results for the final measured state. Obviously, this huge benefit also has negative effects on the system, because errors can in turn exponentially increase the size of the problem and the final results even. However, it is hoped that in the future on the basis of much-improved hardware, researchers will be able to solve problems that cannot be solved today using current calculation methods. In the present paper the authors propose an original method of rapid theoretical determination with great precision of the dimensions of all elementary particles, the method which, although predicting results similar to those obtained by other theoreticians, still has the advantage of its simplicity, of its general applicability, that is of its universality and especially this new method is a precious tool in the work of scientists worldwide to understand matter at its elementary level. Even though we would have expected that the size of a deuteron would be larger (double) than that of one component particle (of a proton or neutron), at the same velocity, the theory (20-21) demonstrates the opposite. By fusing two free nucleons, a proton and a neutron, a deuterium nucleus is obtained with smaller dimensions than its two components, which makes the energy of rejection between two Deuteron cores much larger than we would have waited. That's why the fusion reaction between two Deuterons is even more difficult than was suspected, even when they are accelerating.
In the twentieth century, quantum physics is one of the most successful approaches in scientific progress. To theorize the concept of quantum computing Max Planck's idea of the existence of energy in individual units like matter was used. Since then, the idea of manufacturing quantum computers for everyday use is becoming more plausible with technological advances in quantum theory. A classical computer carries out logical operations using a bit which is either 1 or 0. In contrast to a classical computer, a quantum computer works with a quantum bit or qubit, which is not limited to two states only. Qubits can exist in a superposition of the two states creating parallelism. Qubit represents the state of atoms, ions, photons or electrons. These qubits which work together with a control device act as a computer memory.Quantum computers have the potential to become million times more potent than present-day supercomputers due to the presence of these multiple states simultaneously. Concepts and ideas of quantum computing have been demonstrated by different methods like Ion Trap, Quantum Dot methods etc. However, the actual realization of such a superior system is still in the future. A strategy must be formulated to maintain decoherence and other potential sources of error at a permissible level.Astonishingly, quantum computing took a long time to take off, even though the physicists have known about the world of subatomic particles. Even so, it took computer scientists another half-century to consider harnessing quantum effects for computation. Also, it was later discovered that quantum computers could solve quantum mechanical many-body problems that are impractical to solve on a classical computer. The foundations of the subject of quantum computation may have become well-published, but the knowledge is still growing. Hence here is a research paper based on the study of quantum computation.
Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Due to technical obstacles, till date, a quantum computer has not yet been realized. But the concepts and ideas of quantum computing has been demonstrated using various methods like NMR, Ion Trap, Quantum Dot, Optical Methods, etc. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. Research must devise a way to maintain decoherence and other potential sources of error at an acceptable level. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. Thereby, quantum computers will emerge as the superior computational devices and perhaps one day make today's modern computer obsolete.
Abstract: Quantum computing is a new type of computing that uses the principles of quantum physics to perform calculations in ways that are not possible with traditional computers. Unlike classical computers, which process information using bits that are either 0 or 1, quantum computers use quantum bits (qubits) that can exist in multiple states at the same time. This ability allows quantum systems to solve certain complex problems much faster than classical machines. This paper presents a simple and human-centered explanation of quantum computing, focusing on how it works, why it matters, and how it can be applied in real-world situations. The study discusses key concepts such as superposition, entanglement, and quantum gates using easy-to-understand language. It also explores practical applications including cryptography, optimization, drug discovery, and material simulation. In addition, this paper examines the current challenges in quantum computing, such as hardware instability, error correction, limited qubit scalability, and high implementation cost. A conceptual hybrid classical–quantum system model is proposed to show how quantum and classical computers can work together to solve complex problems more efficiently. The goal of this research is to make quantum computing more understandable to students, educators, and decision-makers, and to encourage early awareness and responsible development of this powerful technology. Keywords — quantum computing, qubit, superposition, entanglement, quantum gate, error correction, hybrid computing
Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians.During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability.The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms.These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches.This contribution is an elementary introduction to quantum simulation.We discuss the challenges, define both digital and analog quantum simulators, and list the demanding conditions they require.We also provide a brief account of the contributions gathered in the dossier on Quantum simulation in the Compte rendus Physique of the French Academy of Sciences [1][2][3][4][5][6].The latter completes excellent reviews that appeared previously, see for instance . Universal models and the role of simulations in many-body physicsUnderstanding the behavior of macroscopic quantum systems is a major challenge of modern physics.The basic laws of low-energy physics are by now quite well known at the microscopic, say atomic, scale.Conversely, many fundamental questions remain open, and even debated, about the collective dynamics at the macroscopic scale.By "macroscopic scale", here we mean systems made up of a huge number of constituents, or degrees of freedom, say 10 6 , 10 23 , or even more, as relevant in condensed matter physics or in astrophysics, for instance.Such huge systems cannot be treated exactly, be it a the classical level and, even worse, at the quantum level.Yet, it is the main outcome of the thermodynamic approach that the collective behavior of a macroscopic system can drastically differ from that of its elementary constituents.For instance, the elementary interactions between the H 2 O molecules are fundamentally unchanged when a water bucket turns from the liquid phase to the solid phase at zero degree Celsius.Similarly, the interactions between the microscopic magnetic moments do not show any brutal change when a magnetic material gets magnetized underneath the Curie temperature.Hence, the dramatic effects observed in macroscopic systems are governed by large-scale instabilities, without obvious counterparts at the microscopic level.This observation takes a universal character, summarized in the celebrated motto "More is Different" [15].Such so-called emerging phenomena also appear in quantum systems, where new effects that are impossible in the classical world show up below some critical temperature or at zero temperature when some interaction parameter passes through a critical value.Celebrated examples include the superfluid transition in helium or super-conducting transitions and other metal-insulator transitions in electronic systems.Strikingly enough at first sight, while emerging phenomena only appear in very large scale macroscopic systems, their germs are contained in the mutual interactions of their elementary constituents.Hence, local two-body interactions are sufficient to explain a huge class of phase transitions, such as the liquid-solid and magnetic transitions mentioned above.The Boltzmann statistical approach proved particularly successful in describing this connection between the microscopic and macroscopic scales.To understand emerging phenomena on grounds as fundamental as possible, the programme is now well established: One tries to identify the basic microscopic terms that seem to be relevant and disregards all the other microscopic details.One then elaborates a model, as generic as possible, likely to reproduce the main experimental observations.The most usual examples are the Ising and Heisenberg models for magnetic transitions, or the Hubbard model for metal-insulator transitions [16][17][18].Then all is left to do is to check that the phenomenon of interest indeed emerges from the dynamics of the simplified model.The realization of this programme is nothing but a simulation.It consists in building up a simplified system that mimics the main properties of a real system.
A happy accident in the laboratory has led to a breakthrough discovery that not only solved a problem that stood for more than half a century, but has major implications for the development of quantum computers and sensors. [55] Significant technical and financial issues remain towards building a large, fault-tolerant quantum computer and one is unlikely to be built within the coming decade. [54] Chemists at Friedrich Schiller University in Jena (Germany) have now synthesised a molecule that can perform the function of a computing unit in a quantum computer. [53] The research team developed the first optical microchip to generate, manipulate and detect a particular state of light called squeezed vacuum, which is essential for HYPERLINK https://phys.org/tags/quantum/ quantum computation. [52] Australian scientists have investigated new directions to scale up qubits-utilising the spin-orbit coupling of atom qubits-adding a new suite of tools to the armory. [51] A team of international researchers led by engineers from the National University of Singapore (NUS) have invented a new magnetic device to manipulate digital information 20 times more efficiently and with 10 times more stability than commercial spintronic digital memories. [50] Working in the lab of Mikhail Lukin, the George Vasmer Leverett Professor of Physics and co-director of the Quantum Science and Engineering Initiative, Evans is lead author of a study, described in the journal Science, that demonstrates a method for engineering an interaction between two qubits using photons. [49] Researchers with the Department of Energy's Oak Ridge National Laboratory have demonstrated a new level of control over photons encoded with quantum information. [48] Researchers from Intel Corp. and the University of California, Berkeley, are looking beyond current transistor technology and preparing the way for a new type of memory and logic circuit that could someday be in every computer on the planet. [47]
Quantum many-body systems, as they appear in different branches of physics and chemistry, are very hard to simulate. The number of parameters defining their quantum states grows exponentially with the number of constituents. This prevents us from exploring and investigating relevant problems involving relatively small numbers of subsystems even with the help of the most powerful supercomputers. Richard Feynman already noticed this difficulty back in 1981 when he wrote his visionary paper “Simulating Physics with Computers” [Int. J. Theor. Phys. 21:6/7, 467 (1982)]. There, he proposed to use quantum systems (as opposed to classical computers) to perform the simulation and in this way to circumvent the need to store and compute a colossal number of parameters, necessary to describe the pertaining superpositions. What was a visionary idea at that time has become a very active field of research in the last few years. The extraordinary progress of both theoretical and experimental research in quantum physics allows us now to tame, control, and manipulate various quantum systems with unprecedented precision. Laser, magnetic, electronic and other technologies enable us to arrange quantum subsystems in different geometries, modify their interactions, and detect them. This allows us to engineer Hamiltonians and emulate systems displaying some of the most intriguing quantum phenomena. This tremendous progress is, to a large extent, due to the pioneering work of many researchers during the last twenty to thirty years. Here, the investigations of basic phenomena with one or few atoms or photons were of particular impact. The degree of control achieved in the experiments has enabled the observation of mind-boggling quantum effects, related to the superposition principle or to entangled states, and their disappearance due to decoherence. In fact, the 2012 Nobel Prize has been awarded to two scientists, S. Haroche and D. Wineland, for such ground-breaking experiments. Such experiments, often in combination with laser cooling of atoms or ions and Bose-Einstein condensation, have formed one of the pillars on which the field of quantum simulations is being established. Quantum simulations with cold atoms, either in magnetic traps or in optical lattices, with trapped ions, with photons, with superconducting devices, with quantum dots, etc., have been theoretically proposed and experimentally considered by many researchers. Most of the proposals so far deal with problems in condensed matter physics that are either difficult to tackle with modern supercomputers or are difficult to observe in solid state systems. This has established a very close link between different disciplines, like atomic, molecular, and optical (AMO) physics, and condensed matter physics. Although some of the experiments are still in their infancy, and a lot of research is still needed, the extraordinary progress made in all these research areas during the last few years makes us feel confident that in the not too distant future quantum simulators will provide a key tool to investigate many-body quantum systems. Furthermore, we also expect that quantum simulators will help quantum physicists to establish new and fruitful links to other scientific communities, like high-energy physics or quantum chemistry. The present special issue contains various review papers as well as research papers on quantum simulations. It starts out with two papers written by last year's Nobel Prize winners describing their foundational work (Wineland, p. 739 and Haroche, p. 763). The issue continues with three thorough, invited review papers covering different topics on quantum simulations. The first one reviews recent theoretical proposals to use cold atoms in optical lattices to simulate lattice gauge theories of the sort that appear in high-energy physics (U.-J. Wiese, p. 783). The second covers both theoretical proposals and experimental demonstrations of cold-atom systems to simulate the physics of matter in the presence of gauge fields, displaying so-called topological phenomena, which so far have only been observed in solid-state systems (I. Spielman, p. 794). The third one contains an extensive overview and new proposals to perform a broad range of quantum simulations using quantum dot systems (P. Barthelmy et al., p. 813). The issue also includes six original papers with a variety of theoretical proposals as well as the introduction of novel theoretical techniques related to the field of quantum simulation. The field of quantum simulations is just starting, but we are confident that it will soon generate an even larger plethora of new ideas and discoveries, trigger interdisciplinary research, and lead us to the adventure of describing and understanding the quantum world. We hope that this special issue will help future researchers in such an exciting adventure. Rainer Blatt received his PhD degree in physics from the University of Mainz in 1981. As a postdoctoral fellow he worked on atomic beam cooling in Boulder, CO and later as a research assistant in Hamburg with single trapped ions. In 1995 he accepted a chair in experimental physics at the University of Innsbruck working on quantum information processing with trapped ions. Since 2003 he is also scientific director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences. Immanuel Bloch received his PhD degree in physics from the Ludwig Maximilians University of Munich in 2000. As a junior group leader, he continued in Munich starting his work on ultracold quantum gases in optical lattices. In 2008 he was appointed scientific director of the newly founded division on Quantum Many-Body Systems at the Max Planck Institute of Quantum Optics. Since 2009 he also holds a chair in quantum optics at the Ludwig-Maximilians University of Munich. Ignacio Cirac received his PhD degree in physics from the Universidad Complutense de Madrid in 1991. He was professor at the Universities of Castilla-La Mancha and Innsbruck from 1991–1996 and 1996–2001, respectively. In 2001 he joined the Max-Planck Institute of Quantum Optics, where he leads the Theory Division. His current research interests include quantum information theory and quantum optics. Peter Zoller obtained his doctorate from the University of Innsbruck in 1977. He was Max Kade Fellow at the University of Southern California from 1978/79, and was JILA visiting Fellow 1981/82 and 1988. In 1990 he became JILA Fellow and professor of physics at the University of Colorado. At the end of 1994, he accepted a chair at the University of Innsbruck, where he has worked ever since. Since 2003, he has also held the position of Scientific Director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences.