Quantum Algorithms for Weighing Matrices and Quadratic Residues
نویسندگان
چکیده
منابع مشابه
Weighing matrices and optical quantum computing
Abstract. Quantum computation in the one-way model requires the preparation of certain resource states known as cluster states. We describe how the construction of continuous-variable cluster states for optical quantum computing relate to the existence of certain families of matrices. The relevant matrices are known as weighing matrices, with a few additional constraints. We prove some results ...
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We present a class of superfast quantum algorithms that retrieve the entire contents of a quantum database Y in a single query. The class includes binary search problems and coin-weighing problems. Our methods far exceed the efficiency of classical algorithms which are bounded by the classical information-theoretic bound. We show the connection between classical algorithms based on linear hashi...
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In this paper we establish a fundamental link between the search for weighing matrices constructed from two circulants and the operation of sorting strings, an operation that has been studied extensively in computer science. In particular, we demonstrate that the search for weighing matrices constructed from two circulants using the power spectral density criterion and exploiting structural pat...
متن کاملOn circulant weighing matrices
Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 8 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.
متن کاملWeighing matrices and spherical codes
Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In this paper, we clarify the relation between MUWM and the spherical codes, and determine the maximum size of a set of MUWM with weight 4 for any order. Moreover, we define mutually quasi-unbiased weighing matrices (MQUWM) as a natural generalization of MUWM from the viewpoint of spheri...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2002
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-002-0975-4