Quantum Proofs
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Quantum Proofs
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Author : Thomas Vidick
language : en
Publisher: Foundations and Trends (R) in Theoretical Computer Science
Release Date : 2016-03-30
Quantum Proofs written by Thomas Vidick and has been published by Foundations and Trends (R) in Theoretical Computer Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with categories.
Quantum Proofs provides an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, it discusses non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class QSZK, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*. Quantum Proofs is mainly intended for non-specialists having a basic background in complexity theory and quantum information. A typical reader may be a student or researcher in either area desiring to learn about the fundamentals of the (actively developing) theory of quantum interactive proofs.
Quantum Computing Physics Blockchains And Deep Learning Smart Networks
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Author : Melanie Swan
language : en
Publisher: World Scientific
Release Date : 2020-03-20
Quantum Computing Physics Blockchains And Deep Learning Smart Networks written by Melanie Swan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-20 with Science categories.
Quantum information and contemporary smart network domains are so large and complex as to be beyond the reach of current research approaches. Hence, new theories are needed for their understanding and control. Physics is implicated as smart networks are physical systems comprised of particle-many items interacting and reaching criticality and emergence across volumes of macroscopic and microscopic states. Methods are integrated from statistical physics, information theory, and computer science. Statistical neural field theory and the AdS/CFT correspondence are employed to derive a smart network field theory (SNFT) and a smart network quantum field theory (SNQFT) for the orchestration of smart network systems. Specifically, a smart network field theory (conventional or quantum) is a field theory for the organization of particle-many systems from a characterization, control, criticality, and novelty emergence perspective.This book provides insight as to how quantum information science as a paradigm shift in computing may influence other high-impact digital transformation technologies, such as blockchain and machine learning. Smart networks refer to the idea that the internet is no longer simply a communications network, but rather a computing platform. The trajectory is that of communications networks becoming computing networks (with self-executing code), and perhaps ultimately quantum computing networks. Smart network technologies are conceived as autonomous self-operating computing networks. This includes blockchain economies, deep learning neural networks, autonomous supply chains, self-piloting driving fleets, unmanned aerial vehicles, industrial robotics cloudminds, real-time bidding for advertising, high-frequency trading networks, smart city IoT sensors, and the quantum internet.
Quantum Proofs The Local Hamiltonian Problem And Applications
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Author : Alex Bredariol Grilo
language : en
Publisher:
Release Date : 2018
Quantum Proofs The Local Hamiltonian Problem And Applications written by Alex Bredariol Grilo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
In QMA, the quantum generalization of the complexity class NP, a quantum state is provided as a proof of a mathematical statement, and this quantum proof can be verified by a quantum algorithm. This complexity class has a very natural complete problem, the Local Hamiltonian problem. Inspired by Condensed Matters Physics, this problem concerns the groundstate energy of quantum systems. In this thesis, we study some problems related to QMA and to the Local Hamiltonian problem. First, we study the difference of power when classical or quantum proofs are provided to quantum verification algorithms. We propose an intermediate setting where the proof is a “simpler” quantum state, and we manage to prove that these simpler states are enough to solve all problems in QMA. From this result, we are able to present a new QMA-complete problem and we also study the one-sided error version of our new complexity class. Secondly, we propose the first relativistic verifiable delegation scheme for quantum computation. In this setting, a classical client delegates her quantumcomputation to two entangled servers who are allowed to communicate, but respecting the assumption that information cannot be propagated faster than speed of light. This protocol is achieved through a one-round two-prover game for the Local Hamiltonian problem where provers only need polynomial time quantum computation and access to copies of the groundstate of the Hamiltonian. Finally, we study the quantumPCP conjecture, which asks if all problems in QMA accept aproof systemwhere only a fewqubits of the proof are checked. Our result consists in proposing an extension of QPCP proof systems where the verifier is also provided an auxiliary classical proof. Based on this proof system, we propose a weaker version of QPCP conjecture. We then show that this new conjecture can be formulated as a Local Hamiltonian problem and also as a problem involving the maximum acceptance probability of multi-prover games. This is the first equivalence of a multi-prover game and some QPCP statement.
Algorithms And Computation
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Author : Toshihide Ibaraki
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-03
Algorithms And Computation written by Toshihide Ibaraki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-03 with Computers categories.
This book constitutes the refereed proceedings of the 14th International Symposium on Algorithms and Computation, ISAAC 2003, held in Kyoto, Japan, in December 2003. The 73 revised full papers presented were carefully reviewed and selected from 207 submissions. The papers are organized in topical sections on computational geometry, graph and combinatorial algorithms, computational complexity, quantum computing, combinatorial optimization, scheduling, computational biology, distributed and parallel algorithms, data structures, combinatorial and network optimization, computational complexity and cryptography, game theory and randomized algorithms, and algebraic and arithmetic computation.
Statistical Structure Of Quantum Theory
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Author : Alexander S. Holevo
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-20
Statistical Structure Of Quantum Theory written by Alexander S. Holevo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-20 with Language Arts & Disciplines categories.
New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.
Introduction To Quantum Cryptography
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Author : Thomas Vidick
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Introduction To Quantum Cryptography written by Thomas Vidick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Science categories.
This book offers an accessible and engaging introduction to quantum cryptography, assuming no prior knowledge in quantum computing. Essential background theory and mathematical techniques are introduced and applied in the analysis and design of quantum cryptographic protocols. The title explores several important applications such as quantum key distribution, quantum money, and delegated quantum computation, while also serving as a self-contained introduction to the field of quantum computing. With frequent illustrations and simple examples relevant to quantum cryptography, this title focuses on building intuition and challenges readers to understand the basis of cryptographic security. Frequent worked examples and mid-chapter exercises allow readers to extend their understanding, and in-text quizzes, end-of-chapter homework problems, and recommended further reading reinforce and broaden understanding. Online resources available to instructors include interactive computational problems in Julia, videos, lecture slides, and a fully worked solutions manual.
Mastering Zero Knowledge Proofs
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Author : Dr. Amit Dua
language : en
Publisher: BPB Publications
Release Date : 2024-08-03
Mastering Zero Knowledge Proofs written by Dr. Amit Dua and has been published by BPB Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-03 with Computers categories.
DESCRIPTION "Mastering Zero-knowledge Proofs" is your ultimate guide to blockchain and ZKPs. It connects blockchain's core elements, like distributed ledgers and smart contracts, to ZKPs' advanced privacy solutions, emphasizing their significance in today's digital world, and provides a robust understanding of how these cryptographic techniques can revolutionize security and privacy in various applications. In this book, you will explore the basics of blockchain and ZKPs. You will gain technical skills like group theory and elliptic curve cryptography. Each chapter covers practical applications of ZKPs in blockchain systems, addressing challenges, ongoing research, and real-world use cases across industries like healthcare and finance. You will find detailed explanations of SNARKs, STARKs, and PLONK, along with practical guidance on constructing and implementing these non-interactive proofs. You will learn about innovative solutions, zero-knowledge virtual machines, ZK-Rollups, and ZK-EVM, along with a step-by-step guide for building and deploying these technologies. By the end of this book, you will have a solid understanding of Zero-knowledge Proofs and their applications in blockchain development. You will be equipped to implement privacy-preserving solutions, enhancing security and efficiency in your projects, making you a competent contributor in the evolving blockchain space. KEY FEATURES ● In-depth exploration of Zero-knowledge Proof concepts and applications. ● Practical insights into implementing ZKP in real-world systems. ● Comprehensive coverage from blockchain basics to advanced cryptography. WHAT YOU WILL LEARN ● Understand the fundamentals of Zero-knowledge Proofs and blockchain. ● Construct and implement SNARKs, STARKs, and PLONK proofs. ● Apply Zero-knowledge Proofs to enhance security and privacy in applications. ● Utilize zero-knowledge virtual machines and ZK-Rollups. ● Integrate ZK-EVM into Ethereum for scalable solutions. ● Identify and overcome challenges in Zero-knowledge Proofs. WHO THIS BOOK IS FOR This book is ideal for blockchain developers, security professionals, and researchers with a foundational understanding of cryptography and blockchain technology. TABLE OF CONTENTS 1. Introduction to Blockchain Technology 2. Introduction to Zero-knowledge Proofs 3. Introduction to SNARKS 4. SNARK Construction: Non-interactive Proof Building 5. Advanced SNARK Paradigms and Techniques 6. SNARK versus STARK 7. SNARKs In-depth and PLONK 8. Zero-Knowledge Virtual Machines 9. ZK-Rollups: Scalability Meets Privacy 10. Conceptualizing ZK-EVM in Ethereum 11. ZK Swaps: Revolutionizing Decentralized Exchanges 12. Zero-Knowledge Identity 13. Challenges and Limitations of Zero-knowledge Proofs 14. Ongoing Research and Development in Zero-knowledge Proofs 15. Real-world Applications of Zero-knowledge Proofs
Verifying Quantum Proofs With Entangled Games
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Author : Anand Venkat Natarajan
language : en
Publisher:
Release Date : 2018
Verifying Quantum Proofs With Entangled Games written by Anand Venkat Natarajan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
A team of students has been given a challenging physics exam: find the ground energy of a complicated, n-spin system. Even if they succeed, how can the examiners be sure that their answer is correct without physically measuring all n spins of the ground state, or worse, having to read a description of the 2n components of its wavefunction? The main result of this thesis is a protocol such that, if the examiners are allowed to separately interrogate multiple students, they can be confident that the students possess the n-spin ground state as well as learn its energy to high precision, after exchanging just O(log(n)) bits of classical communication with the students! The protocol and its analysis combine classical computer science techniques for efficiently checking proofs with Bell inequalities. Stated more formally, the main result of this thesis is a multi-prover interactive proof protocol, in which a classical verifier exchanging only O(log(n)) bits of classical communication with 7 untrusted, entangled provers can certify that they share between them an encoding of an n-qubit quantum state Ib), and estimate its energy under a local Hamiltonian H to high (1/ poly(n)) precision. As a consequence, we show that, under poly-time randomized reductions, it is QMA-hard to estimate the entangled value of a nonlocal game up to constant error, proving the quantum entangled games PCP conjecture of Fitzsimons and Vidick. Our main technical innovations are two constructions of robust self-tests for entanglement: two-player nonlocal games where to succeed with probability E-close to 1, the players must share a state that is [delta] = poly([epsilon])-close in trace distance to n EPR pairs. These tests are robust in that [delta] is independent of the number n of EPR pairs being tested. Our techniques draw heavily on the original, "algebraic" proof of the PCP theorem in classical complexity theory, and in particular, each of our robust self-tests is based on a classical locally-testable error correcting code: the first on the Hadamard code and the associated linearity test of Blum, Luby, and Rubinfeld, and the second on Reed-Muller code and the associated low-degree test of Raz and Safra.
People Problems And Proofs
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Author : Richard J. Lipton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
People Problems And Proofs written by Richard J. Lipton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Computers categories.
People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck. The authors' style is characterize d by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.
Simple Theorems Proofs And Derivations In Quantum Chemistry
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Author : Istvan Mayer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Simple Theorems Proofs And Derivations In Quantum Chemistry written by Istvan Mayer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chem istry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibly in prepara tion of a master's or Ph.D. thesis in theoretical chemistry. In such a situation, I have the freedom to discuss, in detail, a limited number of topics which I feel are important for one reason or another. The exact coverage may vary from year to year, but I usually concentrate on the general principles and theorems and other basic theoretical results which I foresee will retain their importance despite the rapid development of quantum chemistry. I commonly organize my lectures by treating the subject from the begin ning, without referring explicitly to any actual previous knowledge in quantum chemistry-only some familiarity with its goals, approaches and, to a lesser ex tent, techniques is supposed. I concentrate on the formulae and their derivation, assuming the audience essentially understands the reasons for deriving these results. This book is basically derived from the material of my lectures. The spe cial feature, distinguishing it from most other textbooks, is that all results are explicitly proved or derived, and the derivations are presented completely, step by step. True understanding of a theoretical result can be achieved only if one has gone through its derivation.