This monograph provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. It provides a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field.

This book constitutes the refereed proceedings of the 24th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2004, held in Chennai, India, in December 2004. The 35 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 176 submissions. The papers address a broad variety of current issues in software science, programming theory, systems design and analysis, formal methods, mathematical logic, mathematical foundations, discrete mathematics, combinatorial mathematics, complexity theory, automata theory, and theoretical computer science in general.

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.

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

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 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

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.• Requires no preliminary knowledge of graduate and advanced mathematics • Discusses the fundamental results of last 15 years in this theory• Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

This volume provides a fascinating snapshot of the future of physics, covering fundamental physics, at the frontiers of research. It comprises a wide variety of contributions from leading thinkers in the field, inspired by the pioneering work of John A. Wheeler. Quantum theory represents a unifying theme within the book, along with topics such as the nature of physical reality, the arrow of time, models of the universe, superstrings, gravitational radiation, quantum gravity and cosmic inflation. Attempts to formulate a final unification of physics are discussed, along with the existence of hidden dimensions of space, space-time singularities, hidden cosmic matter, and the strange world of quantum technology.