Quantum computation is not an imminent achievement . We will not wake up tomorrow and find quantum computers on our desks. At the time of this writing, IBM has just unveiled the Condor – a chip containing 1,121 superconducting qubits. This number will likely increase (perhaps spectacularly) in the near future. However, the qubits have a relatively large error rate and, in the absence of a breakthrough advance that significantly lowers this rate, one would need hundreds of physical qubits to realize an error-corrected logical qubit. Predicting how long it will take to achieve the controlled manipulation of thousands of (logical) qubits (i.e., a number of qubits consistent with the “useful” implementation of known quantum algorithms) is probably not a rational undertaking, at least for a scientist. The most pessimistic experts regard the lively research activity in quantum computation as a waste of time and resources. But the pervading mood in this field is one of cautious optimism, particularly considering the possibility of achieving useful tasks (e.g., simulating quantum systems) with a sufficiently large number of “imperfect” qubits. Expediency may be responsible for some of this optimism; a good feeling about the prospects for quantum computation certainly helps when it comes to publishing papers and getting funded. Ultimately, however, the responsibility for the wise distribution of resources rests with the funding agencies; scientists, on the other hand, are called to explore every aspect of real and possible worlds that looks fascinating and worthy of their curiosity. From this perspective, quantum computation (defined broadly) offers plenty of opportunities for producing “good science.” The problems brought to the fore by the development of this field range from basic questions regarding the foundations of quantum mechanics and unsolved problems in computational complexity, to the investigation of new phases of matter (e.g., topological quantum phases), the quest for “complete” control over quantum systems, and the critical need for significant advances in materials science and device fabrication (e.g., engineering nanoscale heterostructures with atomic precision). Progress in these areas will naturally open new possibilities for interesting applications. Precisely identifying these applications is premature, but building a (general purpose) quantum computer will not necessarily be among the first of them.
Quantum computation is not an imminent achievement . We will not wake up tomorrow and find quantum computers on our desks. At the time of this writing, IBM has just unveiled the Condor – a chip containing 1,121 superconducting qubits. This number will likely increase (perhaps spectacularly) in the near future. However, the qubits have a relatively large error rate and, in the absence of a breakthrough advance that significantly lowers this rate, one would need hundreds of physical qubits to realize an error-corrected logical qubit. Predicting how long it will take to achieve the controlled manipulation of thousands of (logical) qubits (i.e., a number of qubits consistent with the “useful” implementation of known quantum algorithms) is probably not a rational undertaking, at least for a scientist. The most pessimistic experts regard the lively research activity in quantum computation as a waste of time and resources. But the pervading mood in this field is one of cautious optimism, particularly considering the possibility of achieving useful tasks (e.g., simulating quantum systems) with a sufficiently large number of “imperfect” qubits. Expediency may be responsible for some of this optimism; a good feeling about the prospects for quantum computation certainly helps when it comes to publishing papers and getting funded. Ultimately, however, the responsibility for the wise distribution of resources rests with the funding agencies; scientists, on the other hand, are called to explore every aspect of real and possible worlds that looks fascinating and worthy of their curiosity. From this perspective, quantum computation (defined broadly) offers plenty of opportunities for producing “good science.” The problems brought to the fore by the development of this field range from basic questions regarding the foundations of quantum mechanics and unsolved problems in computational complexity, to the investigation of new phases of matter (e.g., topological quantum phases), the quest for “complete” control over quantum systems, and the critical need for significant advances in materials science and device fabrication (e.g., engineering nanoscale heterostructures with atomic precision). Progress in these areas will naturally open new possibilities for interesting applications. Precisely identifying these applications is premature, but building a (general purpose) quantum computer will not necessarily be among the first of them.
Quantum computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. \n \nQuantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. \n \nThis thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. \n \nThree techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.
In this research notebook on quantum computation and applications for quantum engineers, researchers, and scientists, we will discuss and summarized the core principles and practical application areas of quantum computation. We first discuss the historical prospect from which quantum computing emerged from the early days of computing before the dominance of modern microprocessors. And the re-emergence of that quest with the sunset of Moore's law in the current decade. The mapping of computation onto the behavior of physical systems is a historical challenge vividly illustrate by considering how quantum bits may be realized with a wide variety of physical systems, spanning from atoms to photons, using semiconductors and superconductors. The computing algorithms also change with the underline variety of physical systems and the possibility of encoding the information in the quantum systems compared to the ordinary classical computers because of these new abilities afforded by quantum systems. We will also consider the emerging engineering, science, technology, business, and social implications of these advancements. We will describe a substantial difference between quantum and classical computation paradigm. After we will discuss and understand engineering challenges currently faced by developers of the real quantum computation system. We will evaluate the essential technology required for quantum computers to be able to function correctly. Later on, discuss the potential business application, which can be touch by these new computation capabilities. We utilize the IBM Quantum Experience to run the real-world problem, although on a small scale.
Few technological ideas in recent memory have stirred as much excitement—or skepticism—as quantum computing. The promise is genuine: for certain computational tasks, a quantum machine can do in seconds what would take a classical supercomputer longer than the age of the universe. At the heart of realising that promise is the qubit, the quantum analogue of a classical bit, and among the many physical systems that can host a qubit, superconducting circuits have quietly become the frontrunner. They can be fabricated in the same cleanrooms used to make conventional chips, controlled with ordinary microwave electronics, and scaled up in ways that other approaches cannot yet match. This thesis traces the full arc from first principles to working code. We start with the quantum mechanics a reader needs—superposition, entanglement, measurement—and build from therethrough the physics of superconductivity to the engineering of real qubit circuits. A key character in that story is the Josephson junction: a thin sandwich of metal and insulator whose quirky nonlinear behaviour is what makes the whole enterprise of superconducting qubits possible. A major focus of this work is the surface code, a topological quantum error-correcting code widely regarded as the most promising approach for achieving fault-tolerant quantum computation. We provide a rigorous analysis of the surface code’s lattice structure, stabilizer formalism, syndrome extraction, and decoding algorithms—in particular the minimum-weight perfect matching (MWPM) algorithm. A full Python/Qiskit implementation of a distance-3 surface code is presented, including qubit initialization, syndrome measurement circuits, error simulation, and decoding logic. We close by looking ahead. Modular processors, 3D circuit integration, and the long road to fault-tolerant machines are all on the horizon, and we try to give an honest assessment of where things stand and what the real obstacles are. Throughout, the goal has been to bridge theory and practice—to be precise enough to be useful, but grounded enough to stay connected to what is actually happening in laboratories today.
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.
In the preceding chapter we established that a suitable set of quantum gates, complemented by quantum error correction, allows us to produce a desired multiqubit unitary transformation. This transformation is one of the three steps in a quantum computation; the others, of course, are the preparation of the qubits in their initial state and the measurement of them after the transformation has been implemented. A quantum computation is designed to solve a problem or class of problems. The power of quantum computers is that they can do this, at least for some problems, very much more efficiently and quickly than any conventional computer based on classical logic operations. If we can build a quantum computer then a number of important problems which are currently intractable will become solvable. The potential for greatly enhanced computational power is, in itself, reason enough to study quantum computers, but there is another. Moore’s law is the observation that the number of transistors on a chip doubles roughly every eighteen months. A simple corollary is that computer performance also doubles on the same timescale. Associated with this exponential improvement is a dramatic reduction in the size of individual components. If the pace is to be kept up then it is inevitable that quantum effects will become increasingly important and ultimately will limit the operation of the computer. In these circumstances it is sensible to consider the possibility of harnessing quantum effects to realize quantum information processors and computers. We start with a brief introduction to the theory of computer science, the principles of which underlie the operation of what we shall refer to as classical computers. These include all existing machines and any based on the manipulation of classical bits. The development of computer science owes much to Turing, who devised a simple but powerful model of a computing device: the Turing machine. It its most elementary form, this consists of four elements. (i) A tape for data storage, which acts as a memory. This tape has a sequence of spaces, each of which has on it one of a finite set of symbols. (ii) A processor, which controls the operations of the machine.
Physics is living an era of unprecedented cross-fertilization among the different areas of science. In this perspective review, we discuss the manifold impact that state-of-the-art cold and ultracold-atomic platforms can have in fundamental and applied science through the development of platforms for quantum simulation, computation, metrology and sensing. We illustrate how the engineering of table-top experiments with atom technologies is engendering applications to understand problems in condensed matter and fundamental physics, cosmology and astrophysics, unveil foundational aspects of quantum mechanics, and advance quantum chemistry and the emerging field of quantum biology. In this journey, we take the perspective of two main approaches, i.e., creating quantum analogues and building quantum simulators, highlighting that independently of the ultimate goal of a universal quantum computer to be met, the remarkable transformative effects of these achievements remain unchanged. We wish to convey three main messages. First, this atom-based quantum technology enterprise is signing a new era in the way quantum technologies are used for fundamental science, even beyond the advancement of knowledge, which is characterised by truly cross-disciplinary research, extended interplay between theoretical and experimental thinking, and intersectoral approach. Second, quantum many-body physics is unavoidably taking center stage in frontier’s science. Third, quantum science and technology progress will have capillary impact on society, meaning this effect is not confined to isolated or highly specialized areas of knowledge, but is expected to reach and have a pervasive influence on a broad range of society aspects: while this happens, the adoption of a responsible research and innovation approach to quantum technologies is mandatory, to accompany citizens in building awareness and future scaffolding. Following on all the above reflections, this perspective review is thus aimed at scientists active or interested in interdisciplinary research, providing the reader with an overview of the current status of these wide fields of research where cold and ultracold-atomic platforms play a vital role in their description and simulation.