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471
Efficient simulation of quantum systems by quantum computers. Online preprint quantph/9603026
, 1996
"... We show that the time evolution of the wave function of a quantummechanical manyparticle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a per ..."
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Cited by 58 (0 self)
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We show that the time evolution of the wave function of a quantummechanical manyparticle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a performance which can’t be expected from any classical simulation of a quantum system. We then show how quantities of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum computers.
Density theorems for sampling and interpolation in the BargmannFock space
 II, J. Reine Angew. Math
"... Abstract. We give a complete description of sampling and interpolation in the BargmannFock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von Neumann latti ..."
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Cited by 41 (1 self)
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Abstract. We give a complete description of sampling and interpolation in the BargmannFock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von Neumann lattice, and similarly, a discrete set is a set of interpolation if and only if its density in every part of the plane is strictly smaller than that of the von Neumann lattice. 1. Introduction and
Differentiation And The BalianLow Theorem
 J. Fourier Anal. Appl
, 1995
"... . The BalianLow theorem (BLT) is a key result in timefrequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system fe 2ßimbt g(t \Gamma na)g m;n2Z with ab = 1 forms an orthonormal basis for L 2 (R), then `Z 1 \Gamma1 jt g(t)j 2 dt ' `Z 1 \Gamma1 ..."
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Cited by 37 (18 self)
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. The BalianLow theorem (BLT) is a key result in timefrequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system fe 2ßimbt g(t \Gamma na)g m;n2Z with ab = 1 forms an orthonormal basis for L 2 (R), then `Z 1 \Gamma1 jt g(t)j 2 dt ' `Z 1 \Gamma1 jfl g(fl)j 2 dfl ' = +1: The BLT was later extended from orthonormal bases to exact frames. This paper presents a tutorial on Gabor systems, the BLT, and related topics, such as the Zak transform and Wilson bases. Because of the fact that (g 0 ) (fl) = 2ßifl g(fl), the role of differentiation in the proof of the BLT is examined carefully. The major new contributions of this paper are the construction of a complete Gabor system of the form fe 2ßibm t g(t \Gamma an )g such that f(an ; bm )g has density strictly less than 1, an Amalgam BLT that provides distinct restrictions on Gabor systems fe 2ßimbt g(t \Gamma na)g that form exact frames, and a new proof of the BLT for exact frame...
Evolving SelfReference: Matter, Symbols, And Semantic Closure
 Communication and Cognition  Artificial Intelligence
, 1995
"... A theory of emergent or openended evolution that is consistent with the epistemological foundations of physical theory and the logic of selfreference requires complementary descriptions of the material and symbolic aspects of events. The mattersymbol complementarity is explained in terms of the l ..."
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Cited by 36 (2 self)
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A theory of emergent or openended evolution that is consistent with the epistemological foundations of physical theory and the logic of selfreference requires complementary descriptions of the material and symbolic aspects of events. The mattersymbol complementarity is explained in terms of the logic of selfreplication, and physical distinction of laws and initial conditions. Physical laws and natural selection are complementary models of events. Physical laws describe those invariant events over which organisms have no control. Evolution by natural selection is a theory of how organisms increase their control over events. A necessary semantic closure relation is defined relating the material and symbolic aspects of organisms capable of openended evolution.
Linear representations of probabilistic transformations induced by context transitions
 PROC. OF CONF. ”QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS, SERIES MATH. MODELING, 2 , VÄXJÖ UNIV
, 2001
"... By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonom ..."
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Cited by 26 (2 self)
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By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonometric; (b) hyperbolic; (c) hypertrigonometric. Each class is characterized by a perturbation of the ‘classical probabilistic rule’: (a) cos θ, (b) cosh θ, (c) both cos θ and cosh θ. Trigonometric transformations correspond to contexttransitions that induce statistical deviations of relatively small magnitudes (in classical physics negligibly small); hyperbolic relatively large magnitudes. We found that not only preparation procedures described by conventional quantum formalism can have trigonometric probabilistic behaviour. We propose generalizations of Clinear space probabilistic calculus to describe non quantum (trigonometric and hyperbolic) probabilistic transformations.
Applications of Cut Polyhedra
, 1992
"... We group in this paper, within a unified framework, many applications of the following polyhedra: cut, boolean quadric, hypermetric and metric polyhedra. We treat, in particular, the following applications: ffl ` 1  and L 1 metrics in functional analysis, ffl the maxcut problem, the Boole probl ..."
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Cited by 25 (2 self)
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We group in this paper, within a unified framework, many applications of the following polyhedra: cut, boolean quadric, hypermetric and metric polyhedra. We treat, in particular, the following applications: ffl ` 1  and L 1 metrics in functional analysis, ffl the maxcut problem, the Boole problem and multicommodity flow problems in combinatorial optimization, ffl lattice holes in geometry of numbers, ffl density matrices of manyfermions systems in quantum mechanics. We present some other applications, in probability theory, statistical data analysis and design theory.
The causal set approach to quantum gravity. To be published in ’Approaches to Quantum Gravity  Towards a new understanding of space and time
, 2006
"... The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The causal set is a discrete structure which avoids this problem a ..."
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Cited by 22 (0 self)
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The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The causal set is a discrete structure which avoids this problem and provides a possible history space on which to build a “path integral ” type quantum gravity theory. Motivation, results and open problems are discussed and some comparisons to other approaches are made. Some recent progress on recovering locality in causal sets is recounted. How can we reach a theory of quantum gravity? Many answers to this question have been proposed, motivated by different experiences and views of current theories [1]. A more specific set of questions might be: what demands should we put on our framework, so that it is best able to meet all the challenges involved in creating a theory of quantum gravity? What choices are most likely to give the correct theory, according to the clues we have from known physics? Are there any problems with our initial assumptions that may lead to trouble further down the road? The latter seems to be one of the most important
Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
 Am. J. Phys
, 2001
"... This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these cor ..."
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Cited by 22 (1 self)
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This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible
A Rosetta stone for quantum mechanics with an introduction to quantum computation
, 2002
"... Abstract. 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 ..."
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Cited by 21 (9 self)
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Abstract. 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
Quantum dynamics of human decisionmaking
, 2006
"... A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics descri ..."
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Cited by 18 (6 self)
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A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics describe the evolution of complex valued probability amplitudes over time, whereas Markov models describe the evolution of real valued probabilities over time. Quantum dynamics generate interference effects, which are not possible with Markov models. An interference effect occurs when the probability of the union of two possible paths is smaller than each individual path alone. The choice probabilities and distribution of choice response time for the quantum model are derived, and the predictions are contrasted with the Markov model.