We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem structure as used by classical backtrack methods to avoid unproductive search choices. This quantum algorithm is much more likely to find solutions than the simple direct use of quantum parallelism. Furthermore, empirical evaluation on small problems shows this quantum algorithm displays the same phase transition behavior, and at the same location, as seen in many previously studied classical search methods. Specifically, difficult problem instances are concentrated near the abrupt change from underconstrained to overconstrained problems. August

This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.

It has been shown that non-determinism, both angelic and demonic, can be encoded in a functional language in di#erent representation of sets. In this paper we see quantum programming as a special kind of non-deterministic programming where negative probabilities are allowed.

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms. 1. Introduction Quantum computers (Benioff, 1982; Bernstein & Vazirani, 1993; Deutsch, 1985, 1989; DiVincenzo, 1995; Feynman, 1986; Lloyd, 1993) offer a new approach to combinatorial search problems (Garey & Johnson, 1979) with quantum parallelism, i.e., the abilit...

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A confining gauge theory violates the completeness of asymptotic states held as foundation points of the S-matrix. Spin-dependent experiments can yield results that appear to violate quantum mechanics. The point is illustrated by violation of the Soffer bound in QCD. Experimental confirmation that the bound is violated would be a discovery of immense importance, sweeping away fundamental assumptions of strong interaction physics held for the past 50 years. 1 A Completeness Paradox of Confinement Confinement was not anticipated in early days formulating the S-matrix. Let |p, s 〉 be a set of asymptotic hadron in-states. The S-matrix elements Sp ′ p are defined by S p ′ s ′;ps = limt→∞ p

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PACS 03.65.Fd – First pacs description PACS 03.65.Ca – Second pacs description PACS 02.10.Ox – Third pacs description Abstract.- We consider algebraic structure of Quantum Theory and provide its combinatorial representation. It is shown that by lifting to the richer algebra of graphs operator calculus gains simple interpretation as the shadow of natural operations on graphs. This provides insights into the algebraic structure of the theory and sheds light on the combinatorial nature and philosophy hidden behind its formalism. Introduction. – Quantum Theory seen in action is an interplay of mathematical ideas and physical concepts. From the present-day perspective its formalism and structure is founded on theory of Hilbert spaces [1]. According to a few basic postulates physical notions of a system and

formalism in quantum mechanics 1