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Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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be implemented and introduce some new, purely quantum mechanical primitives, such as changing the computational basis and carrying out an arbitrary unitary transformation of polynomially bounded dimension. We also consider the precision to which the transition amplitudes of a quantum Turing machine need
Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 584 (8 self)
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in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers.
LLVM: A compilation framework for lifelong program analysis & transformation
, 2004
"... ... a compiler framework designed to support transparent, lifelong program analysis and transformation for arbitrary programs, by providing highlevel information to compiler transformations at compiletime, linktime, runtime, and in idle time between runs. LLVM defines a common, lowlevel code re ..."
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Cited by 852 (20 self)
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... a compiler framework designed to support transparent, lifelong program analysis and transformation for arbitrary programs, by providing highlevel information to compiler transformations at compiletime, linktime, runtime, and in idle time between runs. LLVM defines a common, lowlevel code
View Interpolation for Image Synthesis
"... Imagespace simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry t ..."
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Cited by 603 (0 self)
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this concept to its logical extreme by using interpolated images to portray threedimensional scenes. The specialeffects technique of morphing, which combines interpolation of texture maps and their shape, is applied to computing arbitrary intermediate frames from an array of prestored images. If the images
An Algorithm for Planning CollisionFree Paths Among Polyhedral Obstacles
, 1979
"... This paper describes a collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects. The algorithm transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object. A traject ..."
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Cited by 404 (3 self)
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This paper describes a collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects. The algorithm transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object. A
Good quantum error correcting codes exist
 REV. A
, 1996
"... A quantum errorcorrecting code is defined to be a unitary mapping (encoding) of k qubits (2state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used ..."
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Cited by 349 (9 self)
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A quantum errorcorrecting code is defined to be a unitary mapping (encoding) of k qubits (2state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can
On sparse representations in arbitrary redundant bases
 IEEE Trans. Inf. Th
, 2004
"... Abstract—The purpose of this contribution is to generalize some recent results on sparse representations of signals in redundant bases. The question that is considered is the following: given a matrix of dimension ( ) with and a vector = , find a sufficient condition for to have a unique sparsest re ..."
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Cited by 253 (0 self)
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representation as a linear combination of columns of. Answers to this question are known when is the concatenation of two unitary matrices and either an extensive combinatorial search is performed or a linear program is solved. We consider arbitrary matrices and give a sufficient condition for the unique
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D
Reliable Feature Matching Across Widely Separated Views
, 2000
"... In this paper we present a robust method for automatically matching features in images corresponding to the same physical point on an object seen from two arbitrary viewpoints. Unlike conventional stereo matching approaches we assume no prior knowledge about the relative camera positions and orienta ..."
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Cited by 308 (0 self)
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In this paper we present a robust method for automatically matching features in images corresponding to the same physical point on an object seen from two arbitrary viewpoints. Unlike conventional stereo matching approaches we assume no prior knowledge about the relative camera positions
Elementary Gates for Quantum Computation
, 1995
"... We show that a set of gates that consists of all onebit quantum gates (U(2)) and the twobit exclusiveor gate (that maps Boolean values (x, y)to(x, x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We in ..."
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