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Approximate Quantum Markov Chains
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Book Synopsis Approximate Quantum Markov Chains by : David Sutter
Download or read book Approximate Quantum Markov Chains written by David Sutter and published by Springer. This book was released on 2018-04-20 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple matrix inequality can be extended to more than three matrices. Finally, we carefully discuss the properties of approximate quantum Markov chains and their implications. The book is aimed to graduate students who want to learn about approximate quantum Markov chains as well as more experienced scientists who want to enter this field. Mathematical majority is necessary, but no prior knowledge of quantum mechanics is required.
Book Synopsis Approximating Countable Markov Chains by : David Freedman
Download or read book Approximating Countable Markov Chains written by David Freedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains, you're in. The first two books are quite independent of one another, and completely independent of this one, which is a monograph explaining one way to think about chains with instantaneous states. The results here are supposed to be new, except when there are specific disclaimers. It's written in the framework of Markov chains; we wanted to reprint in this volume the MC chapters needed for reference. but this proved impossible. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Book Synopsis Advances in Cryptology – CRYPTO 2024 by : Leonid Reyzin
Download or read book Advances in Cryptology – CRYPTO 2024 written by Leonid Reyzin and published by Springer Nature. This book was released on with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Markov Chain Monte Carlo Methods in Quantum Field Theories by : Anosh Joseph
Download or read book Markov Chain Monte Carlo Methods in Quantum Field Theories written by Anosh Joseph and published by Springer Nature. This book was released on 2020-04-16 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.
Book Synopsis Computer Aided Verification by : Arie Gurfinkel
Download or read book Computer Aided Verification written by Arie Gurfinkel and published by Springer Nature. This book was released on with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Markov Chains written by David Freedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are specific disclaim ers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will VB1 PREFACE argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Book Synopsis Quantum Markov Chains and Position Distributions for States of Boson Systems by : Katrin Schubert
Download or read book Quantum Markov Chains and Position Distributions for States of Boson Systems written by Katrin Schubert and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reinforcement Learning with Hybrid Quantum Approximation in the NISQ Context by : Leonhard Kunczik
Download or read book Reinforcement Learning with Hybrid Quantum Approximation in the NISQ Context written by Leonhard Kunczik and published by Springer Nature. This book was released on 2022-05-31 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the combination of Reinforcement Learning and Quantum Computing in the light of complex attacker-defender scenarios. Reinforcement Learning has proven its capabilities in different challenging optimization problems and is now an established method in Operations Research. However, complex attacker-defender scenarios have several characteristics that challenge Reinforcement Learning algorithms, requiring enormous computational power to obtain the optimal solution. The upcoming field of Quantum Computing is a promising path for solving computationally complex problems. Therefore, this work explores a hybrid quantum approach to policy gradient methods in Reinforcement Learning. It proposes a novel quantum REINFORCE algorithm that enhances its classical counterpart by Quantum Variational Circuits. The new algorithm is compared to classical algorithms regarding the convergence speed and memory usage on several attacker-defender scenarios with increasing complexity. In addition, to study its applicability on today's NISQ hardware, the algorithm is evaluated on IBM's quantum computers, which is accompanied by an in-depth analysis of the advantages of Quantum Reinforcement Learning.
Book Synopsis Quantum Robotics by : Prateek Tandon
Download or read book Quantum Robotics written by Prateek Tandon and published by Springer Nature. This book was released on 2022-05-31 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum robotics is an emerging engineering and scientific research discipline that explores the application of quantum mechanics, quantum computing, quantum algorithms, and related fields to robotics. This work broadly surveys advances in our scientific understanding and engineering of quantum mechanisms and how these developments are expected to impact the technical capability for robots to sense, plan, learn, and act in a dynamic environment. It also discusses the new technological potential that quantum approaches may unlock for sensing and control, especially for exploring and manipulating quantum-scale environments. Finally, the work surveys the state of the art in current implementations, along with their benefits and limitations, and provides a roadmap for the future.
Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Sanjeev Arora
Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Sanjeev Arora and published by Springer. This book was released on 2003-12-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.
Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Leslie Ann Goldberg
Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Leslie Ann Goldberg and published by Springer Science & Business Media. This book was released on 2011-08-05 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011, and the 15th International Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, USA, in August 2011. The volume presents 29 revised full papers of the APPROX 2011 workshop, selected from 66 submissions, and 29 revised full papers of the RANDOM 2011 workshop, selected from 64 submissions. They were carefully reviewed and selected for inclusion in the book. In addition two abstracts of invited talks are included. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
Book Synopsis Quantum Markov Chains and the Process of Recognition by : Karl-Heinz Fichtner
Download or read book Quantum Markov Chains and the Process of Recognition written by Karl-Heinz Fichtner and published by . This book was released on 2007 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Model Checking Quantum Systems by : Mingsheng Ying
Download or read book Model Checking Quantum Systems written by Mingsheng Ying and published by Cambridge University Press. This book was released on 2021-02-04 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model checking is one of the most successful verification techniques and has been widely adopted in traditional computing and communication hardware and software industries. This book provides the first systematic introduction to model checking techniques applicable to quantum systems, with broad potential applications in the emerging industry of quantum computing and quantum communication as well as quantum physics. Suitable for use as a course textbook and for self-study, graduate and senior undergraduate students will appreciate the step-by-step explanations and the exercises included. Researchers and engineers in the related fields can further develop these techniques in their own work, with the final chapter outlining potential future applications.
Book Synopsis Supervised Learning with Quantum Computers by : Maria Schuld
Download or read book Supervised Learning with Quantum Computers written by Maria Schuld and published by Springer. This book was released on 2018-08-30 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum machine learning investigates how quantum computers can be used for data-driven prediction and decision making. The books summarises and conceptualises ideas of this relatively young discipline for an audience of computer scientists and physicists from a graduate level upwards. It aims at providing a starting point for those new to the field, showcasing a toy example of a quantum machine learning algorithm and providing a detailed introduction of the two parent disciplines. For more advanced readers, the book discusses topics such as data encoding into quantum states, quantum algorithms and routines for inference and optimisation, as well as the construction and analysis of genuine ``quantum learning models''. A special focus lies on supervised learning, and applications for near-term quantum devices.
Book Synopsis Spectral Methods for Quantum Markov Chains by : Oleg Szehr
Download or read book Spectral Methods for Quantum Markov Chains written by Oleg Szehr and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Markov Chains written by D. Revuz and published by Elsevier. This book was released on 2008-07-15 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.
Book Synopsis Optimal Transport on Quantum Structures by : Jan Maas
Download or read book Optimal Transport on Quantum Structures written by Jan Maas and published by Springer Nature. This book was released on with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt:
