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380
An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
, 2009
"... ..."
Transgression and the calculation of cocyclic matrices
 Australas. J. Combin
, 1995
"... It is conjectured that binary cocyclic matrices are a uniform source of Hadamard matrices. In testing this conjecture, it is useful to have a general method of calculating cocyclic matrices. We present such a method in this paper. The method draws on standard cohomology theory of finite groups. In p ..."
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Cited by 4 (0 self)
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It is conjectured that binary cocyclic matrices are a uniform source of Hadamard matrices. In testing this conjecture, it is useful to have a general method of calculating cocyclic matrices. We present such a method in this paper. The method draws on standard cohomology theory of finite groups
Quantum algorithms for weighing matrices and quadratic residues
 Algorithmica
, 2002
"... In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is signific ..."
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Cited by 18 (2 self)
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In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity
Graphs of unitary matrices
 Ars Combinatoria
"... Abstract. The support of a matrix M is the (0,1)matrix with ijth entry equal to 1 if the ijth entry of M is nonzero, and equal to 0, otherwise. The digraph whose adjacency matrix is the support of M is said to be the digraph of M. This paper observes some structural properties of digraphs and Ca ..."
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Cited by 3 (1 self)
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and Cayley digraphs, of unitary matrices. (MSC2000: Primary 05C50; Secondary 05C25.) 1.
www.ui.ac.ir PARAUNITARY MATRICES AND GROUP RINGS
"... Abstract. Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing nonseparable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Parauni ..."
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Abstract. Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing nonseparable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given
An Algorithm for Computing Cocyclic Matrices Developed Over Some Semidirect Products
"... An algorithm for calculating a set of generators of representative 2cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1] ..."
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Cited by 1 (1 self)
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An algorithm for calculating a set of generators of representative 2cocycles on semidirect product of finite abelian groups is constructed, in light of the theory over cocyclic matrices developed by Horadam and de Launey in [7, 8]. The method involves some homological perturbation techniques [3, 1
Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
, 1996
"... We address the question: How should N ndimensional subspaces of mdimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N; n; m are described, as well as a reformulation of the problem that was suggested by th ..."
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Cited by 126 (11 self)
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We address the question: How should N ndimensional subspaces of mdimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N; n; m are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe n dimensional subspaces of mspace as points on a sphere in dimension (m \Gamma 1)(m+2), which provides a (usually) lowerdimensional representation than the Pl ucker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multidimensional data via Asimov's grand tour method.
On quantum algorithms for noncommutative hidden subgroups
, 2000
"... Quantum algorithms for factoring and finding discrete logarithms have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum ..."
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Cited by 83 (3 self)
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algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear number of calls to the input function. We also explore the difficulties of developing an algorithm to process the data to explicitly calculate a generating set for the subgroup. A general framework
Results 11  20
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380