Quantum mini-toc
In a world overwhelmed by increasing amounts of data, finding new ways to store and process information has become a necessity. Conventional silicon-based electronics has experienced rapid and steady growth, thanks to the progressive miniaturization of its basic component, the transistor, but that trend cannot continue indefinitely.
![Figure][1]
CREDIT: PHOTO: CURT SUPLEE AND EMILY EDWARDS, JOINT QUANTUM INSTITUTE AND UNIVERSITY OF MARYLAND; CHIP FABRICATION: SANDIA NATIONAL LABORATORIES WITH SUPPORT FROM THE INTELLIGENCE ADVANCED RESEARCH PROJECTS ACTIVITY
In conventional devices, information is stored and manipulated in binary form: The elementary components of these devices—the so-called bits—have two states, each of which encodes the binary 0 or 1. To move beyond the binary system, one can exploit the laws of quantum mechanics. A quantum-mechanical object with two energy levels at its disposal can occupy either of those two levels, but also an arbitrary combination (superposition) of the two, much like an electron in a two-slit experiment can go through both slits at once. This results in infinitely many quantum states that a single quantum bit, or qubit, can take; together with another strange property of quantum mechanics—entanglement—it allows for a much more powerful information platform than is possible with conventional components.
Quantum information processing (QIP) uses qubits as its basic information units. QIP has many facets, from quantum simulation, to cryptography, to quantum computation, which is expected to solve problems more complex than those within the capabilities of conventional computers. To be useful for QIP, a qubit needs to be both isolated from its environment and tightly controllable, which places stringent requirements on its physical realization. But this is only the first step; to build a quantum computer, for example, we must also have a scalable architecture and error correction that can be performed in parallel with computation; in addition, efficient quantum algorithms must exist for solving the problem at hand—a considerable theoretical challenge.
A number of qubit types have been proposed and experimentally realized that satisfy at least some of these criteria, and tremendous progress has been made over the past decade in improving the figures of merit, such as the coherence time. In this special section, four Reviews look into the future of QIP in some of its most promising physical realizations. On p. [1164][2], Monroe and Kim discuss the challenges of scaling trapped ion architectures to hundreds and thousands of qubits and beyond. Devoret and Schoelkopf (p. [1169][3]) speculate on the future of superconducting circuits, whereas Awschalom et al. (p. [1174][4]) focus on the many promising qubit flavors based on spins in semiconductors. Finally, Stern and Lindner (p. [1179][5]) lay out the prospects for quantum computation using the entirely different approach of topologically protected states.
The future of QIP appears bright in spite of the many remaining challenges. As a bonus, overcoming these challenges will probably also advance basic research.
[1]: pending:yes
[2]: /lookup/volpage/339/1164?iss=6124
[3]: /lookup/volpage/339/1169?iss=6124
[4]: /lookup/volpage/339/1174?iss=6124
[5]: /lookup/volpage/339/1179?iss=6124
In a world overwhelmed by increasing amounts of data, finding new ways to store and process information has become a necessity. Conventional silicon-based electronics has experienced rapid and steady growth, thanks to the progressive miniaturization of its basic component, the transistor, but that trend cannot continue indefinitely.
CREDIT: PHOTO: CURT SUPLEE AND EMILY EDWARDS, JOINT QUANTUM INSTITUTE AND UNIVERSITY OF MARYLAND; CHIP FABRICATION: SANDIA NATIONAL LABORATORIES WITH SUPPORT FROM THE INTELLIGENCE ADVANCED RESEARCH PROJECTS ACTIVITY
In conventional devices, information is stored and manipulated in binary form: The elementary components of these devices—the so-called bits—have two states, each of which encodes the binary 0 or 1. To move beyond the binary system, one can exploit the laws of quantum mechanics. A quantum-mechanical object with two energy levels at its disposal can occupy either of those two levels, but also an arbitrary combination (superposition) of the two, much like an electron in a two-slit experiment can go through both slits at once. This results in infinitely many quantum states that a single quantum bit, or qubit, can take; together with another strange property of quantum mechanics—entanglement—it allows for a much more powerful information platform than is possible with conventional components.
Quantum information processing (QIP) uses qubits as its basic information units. QIP has many facets, from quantum simulation, to cryptography, to quantum computation, which is expected to solve problems more complex than those within the capabilities of conventional computers. To be useful for QIP, a qubit needs to be both isolated from its environment and tightly controllable, which places stringent requirements on its physical realization. But this is only the first step; to build a quantum computer, for example, we must also have a scalable architecture and error correction that can be performed in parallel with computation; in addition, efficient quantum algorithms must exist for solving the problem at hand—a considerable theoretical challenge.
A number of qubit types have been proposed and experimentally realized that satisfy at least some of these criteria, and tremendous progress has been made over the past decade in improving the figures of merit, such as the coherence time. In this special section, four Reviews look into the future of QIP in some of its most promising physical realizations. On p. 1164, Monroe and Kim discuss the challenges of scaling trapped ion architectures to hundreds and thousands of qubits and beyond. Devoret and Schoelkopf (p. 1169) speculate on the future of superconducting circuits, whereas Awschalom et al. (p. 1174) focus on the many promising qubit flavors based on spins in semiconductors. Finally, Stern and Lindner (p. 1179) lay out the prospects for quantum computation using the entirely different approach of topologically protected states.
The future of QIP appears bright in spite of the many remaining challenges. As a bonus, overcoming these challenges will probably also advance basic research.
Quantum Information Science is a cross-disciplinary subject that has arisen in the last twenty years. It concerns itself with the consequences of our most complete description of the physical world (that is, quantum mechanics) for the reliable, secure, private, and rapid processing of information, both in communication and computation. While its invention is often ascribed to the famous theoretical physicist Richard Feynman in the 1980s, his contributions were only one of many that initiated the field around that time. While he perceived that new types of physical devices, in which the quantum laws of superposition and entanglement function at the logical level, could give new power in the simulation of quantum physics, it was others (Bennett, Brassard) who showed that the uncertainty principle led to fundamentally more secure ways of communicating secret messages. It was yet others (Deutsch, Vazirani) who understood that quantum theory defined a new kind of Turing machine, and that not only quantum physics simulations, but potentially many other computational problems, are sped up in this machine. And it was yet another (Shor) who found a simple, very fast algorithm for prime factorization. The word "qubit" was coined only in 1995. Its introduction is indicative of a new mindset that has developed in recent years for studying and using quantum systems. "Qubit" now stands for a durable paradigm that spans a very wide variety of fields. It thus has many sub-meanings: first, it is the basic abstract unit of information for workers ranging from optical communication engineers to NMR spectroscopists to black-hole theorists. Second, it is the name we now routinely give to physical two level systems, as they are realized by photons, atomic and ionic eigenlevels, electronic and nuclear spin, structural defects in solids, and circulating-current states of superconducting devices. Physics has long dealt with some of these two-level systems, but calling them qubits implies a whole suite of interrelated ideas and capabilities that we ascribe to these systems: the ability to precisely set, and to precisely measure, the quantum state of one unique specimen, to avoid its coupling with the environment while at the same time strongly and controllably coupling the qubits together, to exploit the resulting quantum entanglement as a resource for metrological, cryptographic, and computational tasks. Quantum Information is a very diverse subject pursued today in many different directions, by many hundreds of researchers internationally: In theoretical physics, it has enlivened and sharpened the understanding of efficient representations of entangled many-particle wavefunctions, and has provided the prospect of applications for new concepts such as anyons and majorana fermions. Information theorists has benefitted from having a rigorous extension of the basis of their field, in which classical information theory is subsumed into a greatly broader subject. Theoretical computer scientists continue the search for new quantum algorithms, and have used quantum concepts to prove new results about the classification of computational complexity. Coding theorists have had the new and subtle problem of quantum error correction to analyse and conquer. Most strikingly, the program of experimental physics has been influenced in many directions by Quantum Information Science. State-of-the-art optics experiments transmit quantum states over long distances and perform precision manipulations in single quanta (atomic ions, impurity spins, quantum dots) in the quest to have working quantum cyptography and quantum computing. Quantum Hall systems, and topological insulators, are being assiduously examined for new elementary excitations for use as qubits. In the course of ten years, superconducting devices have improved by over four orders of magnitude in their quantum coherence, a metric made precise by the ideas of quantum computing. [...] DiVincenzo, David
Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics. Present technology is mainly based upon classical physics such as mechanics and electromagnetism. We now face a similar paradigm shift as was experienced two hundred years ago, at the time of the industrial revolution. Engineered construction of systems is currently increasingly based on quantum physics instead of classical physics, and quantum information is replacing much of classical communication. Quantum computing is one of the most exciting sub-fields of this revolution. Individual quantum systems can be used to store and process information. They are called quantum bits, or qubits for short. A quantum computer could eventually be constructed by combining a number of qubits that act coherently. Important computations can be performed much more quickly than by classical computers. However, while we control and measure a qubit, it must be sufficiently isolated from its environment to avoid noise that causes decoherence at the same time. Currently, low temperature is generally needed to obtain sufficiently long decoherence times. Single qubits of many different kinds can be built and manipulated; some research groups have managed to successfully couple qubits and perform rudimentary logic operations. However, the fundamental problems, such as decoherence, entanglement, quantum measurements and error correction, have yet to be solved. It has been predicted that quantum computers will be able to perform certain complicated computations or simulations in minutes or hours instead of years as with present computers. So far there exist very few useful quantum algorithms; however there is hope that the development of these will be stimulated once there is a breakthrough in hardware. Remarkable progress has been made in quantum engineering and quantum measurements, but a large scale quantum computer is still far off. Quantum communication and cryptography are much closer to the market than a quantum computer. The development of quantum information has meant a large push in the field of quantum physics, that previously could only be studied in the microscopic world. Artificial atoms, realized by circuit technology and mimicking the properties of 'natural' atoms, are one example of the new possibilities opened up by quantum engineering. Several different types of qubits have been suggested. Some are based upon microscopic entities, like atoms and ions in traps, or nuclear spins in molecules. They can have long coherence times (i.e. a long period allowing many operations, of the order of 10 000, to be performed before the state needs to be refreshed) but they are difficult to integrate into large systems. Other qubits are based upon solid state components that facilitate integration and coupling between qubits, but they suffer from interactions with the environment and their coherent states have a limited lifetime. Advanced experiments have been performed with superconducting Josephson junctions and many breakthroughs have been reported in the last few years. They have an advantage in the inherent coherence of superconducting Cooper pairs over macroscopic distances. We chose to focus the Nobel Symposium on Qubits for Future Quantum Information on superconducting qubits to allow for depth in discussions, but at the same time to allow comparison with other types of qubits that may prevail in the long run. The purpose of the symposium was to bring together leading researchers in adjoining fields. Often, microscopic qubits are considered at conferences within atomic, molecular and optical physics, while macroscopic ones belong to the solid state community. At the symposium, we experienced objective comparisons between different types of qubits—pros and cons as well as prospects. One example was the topic of quantum electrodynamics of superconducting circuits where qubits are coupled to a high- Q microwave resonator. This breakthrough technology was covered in several talks and was compared, in detail, with the corresponding case of light coupled to atoms in a cavity. A highlight was the presentation of how arbitrary photon states can be created in a cavity and the measurement of the corresponding Wigner functions. A Nobel Symposium provides an excellent opportunity to bring together a group of outstanding scientists for a stimulating exchange of ideas and results. The present symposium took place in Gothenburg, 25–28 May 2009. In order to allow local researchers and students to get a feeling of what is happening in the field, the first day of the symposium was held at the Chalmers campus. The remaining three days were spent at the mansion built by William Chalmers, the benefactor behind Chalmers University of Technology. Thirty-three speakers gave popular lectures open to the general public, overviews of different types of qubits, quantum phenomena, and quantum computing requirements, as well as specialized contributions in six sessions, and ten posters were displayed. The list of participants, program, abstracts and summaries of presentations is given at www.chalmers.se/mc2/EN/nobel-symposium-2009 . In order to encourage constructive interactions and discussions, ample time was given to extensive critical discussions and to individual meetings in relaxing and stimulating environments. Questions and discussions followed all talks but longer, more extensive, discussions of about one hour ended each session. These discussions were initiated by a special questioner (a kind of 'devil's advocate'). Receptions were given by the President of Chalmers and by the City of Gothenburg. The participants also sailed with SS Bohuslän in the archipelago outside the city. The symposium was sponsored by the Nobel Foundation through its Nobel Symposium Committee and was organized by Thilo Bauch, Tord Claeson, Per Delsing, Ann-Marie Frykestig, Eva Hellberg, Göran Johansson, Göoran Wendin, and Chris Wilson. Special thanks are given to the program committee: John Clarke, Daniel Estève, Steve Girvin, Anne l'Huillier, Anthony Leggett, and Mikko Paalanen. The editor of the proceedings is Göran Johansson.
The field of quantum computing has emerged as a promising frontier in information technology, harnessing the counterintuitive principles of quantum mechanics to revolutionize the way we process and manipulate information. This paper delves into the fundamentals of quantum computing, exploring its theoretical underpinnings, physical realizations, and potential applications. By examining the principles of quantum superposition, entanglement, and quantum parallelism, we shed light on the remarkable capabilities of quantum computers and their ability to tackle complex computational problems that are intractable for classical computers. The paper also investigates the various physical platforms being explored for the realization of quantum computing, including superconducting circuits, trapped ions, and topological systems. Additionally, we discuss the current state of quantum computing hardware, highlighting the challenges and progress in areas such as qubit scalability, error correction, and quantum supremacy. Finally, we explore the potential applications of quantum computing across diverse fields, ranging from cryptography and optimization to quantum simulation and machine learning. Through a comprehensive analysis of theoretical frameworks, experimental findings, and technological developments, this paper aims to provide a comprehensive understanding of the quantum computing landscape and its vast implications for the future of information processing. Keywords: Quantum Computing, Information Processing, Quantum Mechanics, Superposition, Entanglement, Computation, Theoretical Foundations, Qubit, Quantum Gates, Quantum Computing Models, Circuit Model, Adiabatic Model, Quantum Error Correction, Decoherence.
A new quantum information technology (QIT) could emerge in the future, based on current research in the fields of quantum information processing and communication1, 2, 3 (QIPC). In contrast to conventional IT, where quantum mechanics plays a support role in improving the building blocks, fundamental quantum phenomena play a central role in QIPC — information is stored, processed, and communicated according to the laws of quantum physics. This additional freedom could enable future QIT to perform tasks we will never achieve with ordinary IT. Today many people are familiar with at least the consequences of Moore’s Law — the fastest computer in the shops doubles in speed about every 18 months to two years. This exponential progress, first noted4 by Gordon Moore — cofounder and former CEO of Intel — in 1965, has continued ever since. But it cannot go on forever. Hurdles exist, for example: silicon will hit problems, with oxide thinness or track width5; new materials or even new paradigms, such as self-assembled nano-devices or molecular electronics, will be needed; lots of dollars will be required as Moore’s second law tells us that fabrication costs are also growing exponentially. However, even if the hurdles can be overcome, we will eventually run into nature.
Q uantum mechanics has had an enormous technological and societal impact.To grasp this point, it is sufficient to cite the invention of the transistor, perhaps the most remarkable among the countless other applications of quantum mechanics.It is also easy to see the enormous impact of computers on everyday life.The importance of computers is such that it is appropriate to say that we are now living in the information age.This information revolution became possible thanks to the invention of the tran sistor, that is, thanks to the synergy between computer science and quantum physics.Today this synergy offers completely new opportunities and promises exciting advances in both funda mental science and technological application.We are referring here to the fact that quantum mechanics can be used to process and transmit information [1,2].Miniaturization provides us with an intuitive way of under standing why, in the near future, quantum laws will become important for computation.The electronics industry for com puters grows hand-in-hand with the decrease in size of integrated circuits.This miniaturization is necessary to increase computa tional power, that is, the number of floating-point operations per second (flops) a computer can perform.In the 1950's, electronic computers based on vacuum-tube technology were capable of performing approximately 103 floating-point operations per second, while nowadays there exist supercomputers whose power is greater than lOteraflops (1013 flops).As we have remarked, this enormous growth of computational power has been made possi ble owing to progress in m in ia tu riz a tio n , w hich m ay be quantified empirically in Moore's law.This law is the result of a remarkable observation made by Gordon Moore in 1965: the number of transistors on a single integrated-circuit chip doubles approximately every 18 24 months.This exponential growth has not yet saturated and Moore's law is still valid.At the present time the limit is approximately 108 transistors per chip and the typical size of circuit components is of the order of 100 nanometres.Extrapolating Moore's law, one would estimate that around the year 2020 we shall reach the atomic size for storing a single bit of inform atio n .At th a t p o in t, q u a n tu m effects will becom e unavoidably dominant.One should be aware that, besides quantum effects, other fac tors could bring Moore's law to an end.In the first place, there are economic considerations.Indeed, the cost of building fabri cation facilities to m an u factu re chips has also increased exponentially with time.Nevertheless, it is important to under stand the ultimate limitations set by quantum mechanics.Even though we might overcome economic barriers by means of tech nological breakthroughs, quantum physics sets fundamental limitations on the size of the circuit components.The first ques tion under debate is whether it would be more convenient to push References
Silicon has raised an increasing interest in the development of future devices for quantum information processing. Quantum computing consists of the implementation of quantum algorithms on a physical substrate made of interacting qubits, the quantum version of digital bits. Quantum algorithms are those algorithms conceived to solve hard computational problems, such as prime factorization of large integers and minimization of multidimensional functionals based on the encoding of the information by quantum states. Quantum information processing involves all the techniques to process quantum information stored in a physical system from the physical to the virtual layer, the quantum error correction, the logical, and finally the application layer. The power of quantum information processing currently relies mainly on two different quantum computing models. On the one hand, there is universal digital quantum computing, also called circuital quantum computing, based on a set of time-reversible quantum logic ports required to cover the spectrum of all possible unitary operations on the qubits.