Download or read book Control Gates and Error Suppression with Hamiltonians in Quantum Computation written by Adam Darryl Bookatz and published by . This book was released on 2016 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we are primarily interested in studying how to suppress errors, perform simulation, and implement logic gates in quantum computation within the context of using Hamiltonian controls. We also study the complexity class QMA-complete. We first investigate a method (introduced by Jordan, Farhi, and Shor) for suppressing environmentally induced errors in Hamiltonian-based quantum computation, involving encoding the system with a quantum error-detecting code and enforcing energy penalties against leaving the codespace. We prove that this method does work in principle: in the limit of infinitely large penalties, local errors are completely suppressed. We further derive bounds for the finite-penalty case and present numerical simulations suggesting that the method achieves even greater protection than these bounds indicate. We next consider the task of Hamiltonian simulation, i.e. effectively changing a system Hamiltonian to some other desired Hamiltonian by applying external time-dependent controls. We propose protocols for this task that rely solely on realistic bounded-strength control Hamiltonians. For systems coupled to an uncontrollable environment, our approach may be used to perform simulation while simultaneously suppressing unwanted decoherence. We also consider the scenario of removing unwanted couplings in many-body quantum systems obeying local system Hamiltonians and local environmental interactions. We present protocols for efficiently switching off the Hamiltonian of a system, i.e. simulating the zero Hamiltonian, using bounded-strength controls. To this end, we introduce the combinatorial concept of balanced-cycle orthogonal arrays, show how to construct them from classical error-correcting codes, and show how to use them to decouple n-qudit l-local Hamiltonians using protocols of length at most O(l-1 log n). We then present a scheme for implementing high-fidelity quantum gates using a few interacting bosons obeying a Bose-Hubbard Hamiltonian on a line. We find high-fidelity logic operations for a gate set (including the CNOT gate) that is universal for quantum information processing. Lastly, we discuss the quantum complexity class QMA-complete, surveying all known such problems, and we introduce the "quantum non-expander" problem, proving that it is QMA-complete. A quantum expander is a type of rapidly-mixing quantum channel; we show that estimating its mixing time is a co-QMA-complete problem.
Download or read book Quantum Computing written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2019-04-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.
Download or read book Large scale Simulations of Error Prone Quantum Computation Devices written by Doan Binh Trieu and published by Forschungszentrum Jülich. This book was released on 2010 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Decoherence Suppression in Quantum Systems 2008 written by Mikio Nakahara and published by World Scientific. This book was released on 2010 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: While innovative ideas and creative works increasingly drive economic success, the historic approach to encouraging innovation and creativity by granting property rights has come under attack by a growing number of legal theorists and technologists. In Laws of Creation, Ronald Cass and Keith Hylton take on these critics with a vigorous defense of intellectual property law. The authors look closely at the IP doctrines that have been developed over many years in patent, copyright, trademark, and trade secret law. In each area, legislatures and courts have weighed the benefits that come from preserving incentives to innovate against the costs of granting innovators a degree of control over specific markets. Over time, the authors show, a set of rules has emerged that supports wealth-creating innovation while generally avoiding overly expansive, growth-retarding licensing regimes. These rules are now under pressure from detractors who claim that changing technology undermines the case for intellectual property rights. But Cass and Hylton explain how technological advances only strengthen that case. In their view, the easier it becomes to copy innovations, the harder to detect copies and to stop copying, the greater the disincentive to invest time and money in inventions and creative works. The authors argue convincingly that intellectual property laws help create a society that is wealthier and inspires more innovation than those of alternative legal systems. Ignoring the social value of intellectual property rights and making what others create and nurture âeoefreeâe would be a costly mistake indeed.
Download or read book The Complexity of Noise written by Amit Hagar and published by Morgan & Claypool Publishers. This book was released on 2010 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart (5). Physical objects as they are, QIP devices are subject to the laws of physics. No doubt, the application of these laws is error-free, but noise - be it external influences or hardware imprecisions - can sometimes cause a mismatch between what the QIP device is supposed to do and what it actually does. In recent years the elimination of noise that result from external disturbances or from imperfect gates has become the "holy grail" within the quantum computing community, and a worldwide quest for a large scale, fault-tolerant, and computationally superior QIP device is currently taking place. Whether such machines are possible is an exciting open question, yet the debate on their feasibility has been so far rather ideological in character (45) (66)(110) (162). Remarkably, philosophers of science have been mostly silent about it: common wisdom has it that philosophy should not intervene in what appears to be (and is also presented as) an engineering problem, and besides, the mathematics employed in the theory of fault-tolerant quantum error correction (FTQEC henceforth) is rather daunting. It turns out, however, that behind this technical veil the central issues at the heart of the debate are worthy of philosophical analysis and, moreover, bear strong similarities to the conceptual problems that have been saturating a field quite familiar to philosophers, namely the foundations of statistical mechanics (SM henceforth). Reconstructing the debate on FTQEC with statistical mechanical analogies, this book aims to introduce it to readership outside the quantum computing community, and to take preliminary steps towards making it less ideological and mor
Download or read book Quantum Atom Optics written by Tim Byrnes and published by Cambridge University Press. This book was released on 2021-08-05 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapid development of quantum technologies has driven a revolution in related research areas such as quantum computation and communication, and quantum materials. The first prototypes of functional quantum devices are beginning to appear, frequently created using ensembles of atoms, which allow the observation of sensitive, quantum effects, and have important applications in quantum simulation and matter wave interferometry. This modern text offers a self-contained introduction to the fundamentals of quantum atom optics and atomic many-body matter wave systems. Assuming a familiarity with undergraduate quantum mechanics, this book will be accessible for graduate students and early career researchers moving into this important new field. A detailed description of the underlying theory of quantum atom optics is given, before development of the key, quantum, technological applications, such as atom interferometry, quantum simulation, quantum metrology, and quantum computing.
Download or read book Quantum Computing and Supply Chain Management A New Era of Optimization written by Hassan, Ahdi and published by IGI Global. This book was released on 2024-07-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today's supply chains are becoming more complex and interconnected. As a result, traditional optimization engines struggle to cope with the increasing demands for real-time order fulfillment and inventory management. With the expansion and diversification of supply chain networks, these engines require additional support to handle the growing complexity effectively. This poses a significant challenge for supply chain professionals who must find efficient and cost-effective solutions to streamline their operations and promptly meet customer demands. Quantum Computing and Supply Chain Management: A New Era of Optimization offers a transformative solution to these challenges. By harnessing the power of quantum computing, this book explores how supply chain planners can overcome the limitations of traditional optimization engines. Quantum computing's ability to process vast amounts of data from IoT sensors in real time can revolutionize inventory management, resource allocation, and logistics within the supply chain. It provides a theoretical framework and practical examples to illustrate how quantum algorithms can enhance transparency, optimize dynamic inventory allocation, and improve supply chain resilience.
Download or read book Handbook of Research on Quantum Computing for Smart Environments written by Tyagi, Amit Kumar and published by IGI Global. This book was released on 2023-03-03 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today, computation is an essential component of every technology. However, there has not been much research on quantum computing, even though it has the capability to solve complex problems in an efficient way. Further study is required to fully understand the uses and benefits of this technology. The Handbook of Research on Quantum Computing for Smart Environments presents investigating physical realizations of quantum computers, encoders, and decoders, including photonic quantum realization, cavity quantum electrodynamics, and many more topics on Bits to Qubits. Covering key topics such as machine learning, software, quantum algorithms, and neural networks, this major reference work is ideal for engineers, computer scientists, physicists, mathematicians, researchers, academicians, scholars, practitioners, instructors, and students.
Download or read book Quantum Error Correction written by Daniel A. Lidar and published by Cambridge University Press. This book was released on 2013-09-12 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on methods for quantum error correction, this book is invaluable for graduate students and experts in quantum information science.
Download or read book Classical and Quantum Computation written by Alexei Yu. Kitaev and published by American Mathematical Soc.. This book was released on 2002 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to a rapidly developing topic: the theory of quantum computing. Following the basics of classical theory of computation, the book provides an exposition of quantum computation theory. In concluding sections, related topics, including parallel quantum computation, are discussed.
Download or read book Semiconductor Spintronics and Quantum Computation written by D.D. Awschalom and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past few decades of research and development in solid-state semicon ductor physics and electronics have witnessed a rapid growth in the drive to exploit quantum mechanics in the design and function of semiconductor devices. This has been fueled for instance by the remarkable advances in our ability to fabricate nanostructures such as quantum wells, quantum wires and quantum dots. Despite this contemporary focus on semiconductor "quantum devices," a principal quantum mechanical aspect of the electron - its spin has it accounts for an added quan largely been ignored (except in as much as tum mechanical degeneracy). In recent years, however, a new paradigm of electronics based on the spin degree of freedom of the electron has begun to emerge. This field of semiconductor "spintronics" (spin transport electron ics or spin-based electronics) places electron spin rather than charge at the very center of interest. The underlying basis for this new electronics is the intimate connection between the charge and spin degrees of freedom of the electron via the Pauli principle. A crucial implication of this relationship is that spin effects can often be accessed through the orbital properties of the electron in the solid state. Examples for this are optical measurements of the spin state based on the Faraday effect and spin-dependent transport measure ments such as giant magneto-resistance (GMR). In this manner, information can be encoded in not only the electron's charge but also in its spin state, i. e.
Download or read book Quantum Coherence Correlation and Control in Finite Quantum Systems written by Hui Yan and published by Frontiers Media SA. This book was released on 2022-10-21 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Methods in Quantum Error Correction and Fault tolerant Quantum Computing written by Christopher Chamberland and published by . This book was released on 2018 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers have the potential to solve several interesting problems in polynomial time for which no polynomial time classical algorithms have been found. However, one of the major challenges in building quantum devices is that quantum systems are very sensitive to noise arising from undesired interactions with the environment. Noise can lead to errors which can corrupt the results of the computation. Quantum error correction is one way to mitigate the effects of noise arising in quantum devices. With a plethora of quantum error correcting codes that can be used in various settings, one of the main challenges of quantum error correction is understanding how well various codes perform under more realistic noise models that can be observed in experiments. This thesis proposes a new decoding algorithm which can optimize threshold values of error correcting codes under different noise models. The algorithm can be applied to any Markovian noise model. Further, it is shown that for certain noise models, logical Clifford corrections can further improve a code's threshold value if the code obeys certain symmetries. Since gates and measurements cannot in general be performed with perfect precision, the operations required to perform quantum error correction can introduce more errors into the system thus negating the benefits of error correction. Fault-tolerant quantum computing is a way to perform quantum error correction with imperfect operations while retaining the ability to suppress errors as long as the noise is below a code's threshold. One of the main challenges in performing fault-tolerant error correction is the high resource requirements that are needed to obtain very low logical noise rates. With the use of flag qubits, this thesis develops new fault-tolerant error correction protocols that are applicable to arbitrary distance codes. Various code families are shown to satisfy the requirements of flag fault-tolerant error correction. We also provide circuits using a constant number of qubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer qubits than previous fault-tolerant error correction protocols. It is often the case that the noise afflicting a quantum device cannot be fully characterized. Further, even with some knowledge of the noise, it can be very challenging to use analytic decoding methods to improve the performance of a fault-tolerant scheme. This thesis presents decoding schemes using several state of the art machine learning techniques with a focus on fault-tolerant quantum error correction in regimes that are relevant to near term experiments. It is shown that even in low noise rate regimes and with no knowledge of the noise, noise can be further suppressed for small distance codes. Limitations of machine learning decoders as well as the classical resources required to perform active error correction are discussed. In many cases, gate times can be much shorter than typical measurement times of quantum states. Further, classical decoding of the syndrome information used in quantum error correction to compute recovery operators can also be much slower than gate times. For these reasons, schemes where error correction can be implemented in a frame (known as the Pauli frame) have been developed to avoid active error correction. In this thesis, we generalize previous Pauli frame schemes and show how Clifford frame error correction can be implemented with minimal overhead. Clifford frame error correction is necessary if the logical component of recovery operators were chosen from the Clifford group, but could also be used in randomized benchmarking schemes.
Download or read book Unconventional Computing 2007 written by Andrew Adamatzky and published by Luniver Press. This book was released on 2007 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unconventional computing is the quest for groundbreaking new algorithms and computing architectures based on and inspired by the principles of information processing in physical, chemical and biological systems. The timely scientific contributions in this book include cutting-edge theoretical work on quantum and kinematic Turing machines, computational complexity of physical systems, molecular and chemical computation, processing incomplete information, physical hypercomputation, automata networks and swarms. They are nicely complemented by recent results on experimental implementations of logical and arithmetical circuits in a domino substrate, DNA computers, and self-assembly. The book supports interdisciplinary research in the field of future computing and contributes toward developing a common interface between computer science, biology, mathematics, chemistry, electronics engineering, and physics.
Download or read book Quantum Computing An Applied Approach written by Jack D. Hidary and published by Springer Nature. This book was released on 2021-09-29 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training. The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition. This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates. Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X.
Download or read book Thermodynamics and Control of Open Quantum Systems written by Gershon Kurizki and published by Cambridge University Press. This book was released on 2022-01-13 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The control of open quantum systems and their associated quantum thermodynamic properties is a topic of growing importance in modern quantum physics and quantum chemistry research. This unique and self-contained book presents a unifying perspective of such open quantum systems, first describing the fundamental theory behind these formidably complex systems, before introducing the models and techniques that are employed to control their quantum thermodynamics processes. A detailed discussion of real quantum devices is also covered, including quantum heat engines and quantum refrigerators. The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.
Download or read book Quantum Computation and Quantum Information written by Michael A. Nielsen and published by Cambridge University Press. This book was released on 2010-12-09 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.
