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22
Quantum Computing and Phase Transitions in Combinatorial Search
 J. of Artificial Intelligence Research
, 1996
"... 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 un ..."
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Cited by 21 (7 self)
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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
Interpreting the Quantum
, 1997
"... This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of informa ..."
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Cited by 16 (1 self)
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This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic 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 informationtheoretic 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 informationtheoretic 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.
Functional Quantum Programming
 In Proceedings of the 2nd Asian Workshop on Programming Languages and Systems
, 2001
"... It has been shown that nondeterminism, 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 nondeterministic programming where negative probabilities are allowed. ..."
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Cited by 9 (0 self)
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It has been shown that nondeterminism, 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 nondeterministic programming where negative probabilities are allowed.
Solving Highly Constrained Search Problems with Quantum Computers
 Journal of Artificial Intelligence Research
, 1999
"... A previously developed quantum search algorithm for solving 1SAT problems in a single step is generalized to apply to a range of highly constrained kSAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a co ..."
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Cited by 8 (0 self)
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A previously developed quantum search algorithm for solving 1SAT problems in a single step is generalized to apply to a range of highly constrained kSAT 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...
Mathematical Models of Contemporary Elementary Quantum Computing Devices
, 2003
"... Abstract. Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1bit and 2bit quantum gates are universal for quantum computation, i.e., any nbit unitary operation can be carried out by conca ..."
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Cited by 1 (0 self)
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Abstract. Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1bit and 2bit quantum gates are universal for quantum computation, i.e., any nbit unitary operation can be carried out by concatenations of 1bit and 2bit elementary quantum gates. Three contemporary quantum devices–cavity QED, ion traps and quantum dots–have been widely regarded as perhaps the most promising candidates for the construction of elementary quantum gates. In this paper, we describe the physical properties of these devices, and show the mathematical derivations based on the interaction of the laser field as control with atoms, ions or electron spins, leading to the following: (i) the 1bit unitary rotation gates; and (ii) the 2bit quantum phase gates and the controllednot gate. This paper is aimed at providing a sufficiently selfcontained survey account of analytical nature for mathematicians, physicists and computer scientists to aid interdisciplinary understanding in the research of quantum computation. 1.
Exploring Confinement with Spin
, 810
"... A confining gauge theory violates the completeness of asymptotic states held as foundation points of the Smatrix. Spindependent 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 t ..."
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A confining gauge theory violates the completeness of asymptotic states held as foundation points of the Smatrix. Spindependent 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 Smatrix. Let p, s 〉 be a set of asymptotic hadron instates. The Smatrix elements Sp ′ p are defined by S p ′ s ′;ps = limt→∞ p
epl draft Graph Algebras for Quantum Theory
, 710
"... 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 calcul ..."
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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 presentday 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