Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium: American Mathematical Challenge Society, Short Course, January 17-18, 2000, Washington, DC
An invitation to quantum computation: A Rosetta stone for quantum mechanics with an introduction to quantum computation by S. J. Lomonaco, Jr. Qubit devices by H. E. Brandt Quantum algorithms and quantum complexity theory: Introduction to quantum algorithms by P. W. Shor Shor's quantum factoring algorithm by S. J. Lomonaco, Jr. Grover's quantum search algorithm by S. J. Lomonaco, Jr. A survey of quantum complexity theory by U. V. Vazirani Quantum error correcting codes and quantum cryptography: An introduction to quantum error correction by D. Gottesman A talk on quantum cryptography or how Alice outwits Eve by S. J. Lomonaco, Jr. More mathematical connections: Topological quantum codes and anyons by A. Kitaev Quantum topology and quantum computing by L. H. Kauffman An entangled tale of quantum entanglement by S. J. Lomonaco, Jr. Index.
An invitation to quantum computation: A Rosetta stone for quantum mechanics with an introduction to quantum computation by S. J. Lomonaco, Jr. Qubit devices by H. E. Brandt Quantum algorithms and quantum complexity theory: Introduction to quantum algorithms by P. W. Shor Shor's quantum factoring algorithm by S. J. Lomonaco, Jr. Grover's quantum search algorithm by S. J. Lomonaco, Jr. A survey of quantum complexity theory by U. V. Vazirani Quantum error correcting codes and quantum cryptography: An introduction to quantum error correction by D. Gottesman A talk on quantum cryptography or how Alice outwits Eve by S. J. Lomonaco, Jr. More mathematical connections: Topological quantum codes and anyons by A. Kitaev Quantum topology and quantum computing by L. H. Kauffman An entangled tale of quantum entanglement by S. J. Lomonaco, Jr. Index.
Space searches with a quantum robot by P. Benioff Perturbation theory and numerical modeling of quantum logic operations with a large number of qubits by G. P. Berman, G. D. Doolen, D. I. Kamenev, G. V. Lopez, and V. I. Tsifrinovich Inconclusive rate with a positive operator valued measure by H. E. Brandt Quantum amplitude amplification and estimation by G. Brassard, P. Hoyer, M. Mosca, and A. Tapp Manipulating the entanglement of one copy of a two-particle pure entangled state by L. Hardy Geometric algebra in quantum information processing by T. F. Havel and C. J. L. Doran Quantum computing and the Jones polynomial by L. H. Kauffman Quantum hidden subgroup algorithms: A mathematical perspective by S. J. Lomonaco, Jr. and L. H. Kauffman Improved two-party and multi-party purification protocols by E. N. Maneva and J. A. Smolin Quantum games and quantum algorithms by D. A. Meyer A proof that measured data and equations of quantum mechanics can be linked only by guesswork by J. M. Myers and F. H. Madjid Quantum computation by geometrical means by J. Pachos Pauli exchange and quantum error correction by M. B. Ruskai Relative entropy in quantum information theory by B. Schumacher and M. D. Westmoreland An unentangled Gleason's theorem by N. R. Wallach Entangled chains by W. K. Wootters.
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Many examples are given. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced.
Coding theory: Grobner bases, Pade approximation, and decoding of linear codes by J. B. Farr and S. Gao Some computational tools for estimating the parameters of algebraic geometry codes by G. L. Matthews An introduction to algebraic coding theory by H. N. Ward Recent results on p-ranks and Smith normal forms of some 2−(v,k,λ) designs by Q. Xiang Quantum computing: Quantum walks on graphs and quantum scattering theory by E. Feldman and M. Hillery A continuous variable Shor algorithm by S. J. Lomonaco, Jr. and L. H. Kauffman Entangled states of light by S. J. van Enk Entanglement beyond subsystems by L. Viola, H. Barnum, E. Knill, G. Ortiz, and R. Somma Generalized GHZ states and distributed quantum computing by A. Yimsiriwattana and S. J. Lomonaco, Jr.
The goal of this talk is to present an introduction to quantum computing for non-specialists. I will first present the quantum computing model in order to have a first feel of what we can and cannot do with a quantum computer. Then I will present a few iconic quantum algorithms such as Grover’s algorithm and Shor’s algorithm. Finally, I will talk about perspectives relative to quantum-secure cryptography. During the talk, I will also briefly talk about error correction for quantum computation and quantum cryptography.
In the 1990's it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics. It begins with an introduction to the quantum theory from a computer-science perspective. It illustrates the quantum-computational approach with several elementary examples of quantum speed-up, before moving to the major applications: Shor's factoring algorithm, Grover's search algorithm, and quantum error correction. The book is intended primarily for computer scientists who know nothing about quantum theory, but will also be of interest to physicists who want to learn the theory of quantum computation, and philosophers of science interested in quantum foundational issues. It evolved during six years of teaching the subject to undergraduates and graduate students in computer science, mathematics, engineering, and physics, at Cornell University.
Quantum Computing represents a paradigm shift in computation, leveraging the principles of quantum mechanics to solve problems intractable for classical computers. This book provides a comprehensive exploration of quantum computing, encompassing its foundational concepts, architecture, algorithms, programming techniques, and real-world applications. Beginning with an overview and historical evolution, it delves into the fundamental differences between classical and quantum computing, highlighting key quantum mechanical phenomena such as superposition, entanglement, and interference. The book further examines quantum states, qubits, and gates, elucidating their roles in quantum computation. The architecture of quantum systems, including superconducting qubits, trapped ions, and photonic qubits, is analyzed alongside quantum circuits, hardware challenges, and error correction mechanisms. Core quantum algorithms, including Shor’s algorithm for factorization and Grover’s algorithm for search, are discussed with practical examples. The book also emphasizes quantum programming, featuring tools like Qiskit, Cirq, and PyQuil, and explores challenges in quantum simulation and circuit development. Applications in cryptography, artificial intelligence, drug discovery, and optimization are detailed, underscoring quantum computing’s transformative potential. The book concludes with an examination of challenges such as scalability, noise, and ethical concerns, while providing insights into future directions, including hardware advancements, emerging algorithms, and integration with classical systems. It serves as an essential resource for students, researchers, and professionals aiming to understand and contribute to the quantum revolution. Keywords: Quantum computing, classical computing, quantum mechanics, qubits, quantum gates, superposition, entanglement, quantum algorithms, Shor’s algorithm, Grover’s algorithm, quantum programming, Qiskit, Cirq, quantum circuits, quantum hardware, error correction, cryptography, artificial intelligence, drug discovery, optimization, scalability, quantum noise, ethical implications, future directions