相关论文: A new algorithm to search for small nonzero |x^3 -…
In this paper we consider the problem of locating a nonzero entry in a high-dimensional vector from possibly adaptive linear measurements. We consider a recursive bisection method which we dub the compressive binary search and show that it…
The $\texttt{IntegerHull}$ function is part of Maple's $\texttt{PolyhedralSets}$ library, which calculates the integer hull of a given polyhedral set. This algorithm works by translating the supporting hyperplanes of the facets of the input…
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
We introduce a randomized Hall-Littlewood RSK algorithm and study its combinatorial and probabilistic properties. On the probabilistic side, a new model --- the Hall-Littlewood RSK field --- is introduced. Its various degenerations contain…
It is questionable that Grover algorithm may be more valuable than a classical one, when a partial information is given in a unstructured database. In this letter, to consider quantum search when a partial information is given, we replace…
We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly…
We computationally investigate the complete polytope of Bell inequalities for 2 particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection of this problem to the computationally hard…
New numerical algorithms based on rational functions are introduced that can solve certain Laplace and Helmholtz problems on two-dimensional domains with corners faster and more accurately than the standard methods of finite elements and…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well known quantum mechanical tunneling property which enables small bodies to penetrate…
We propose a new cross-conv algorithm for approximate computation of convolution in different low-rank tensor formats (tensor train, Tucker, Hierarchical Tucker). It has better complexity with respect to the tensor rank than previous…
A new, "quantum mechanical" algorithm is proposed for automatic photopeak location in gamma-ray spectra from semiconductor and scintillator detectors.
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
This paper explores Quantum Search on the two dimensional spatial grid. Recent exploration into the topic has devised a solution that runs in O(sqrt(n*ln(n))). This paper explores a new algorithm that gives promise for the O(sqrt(n)) result…
We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…
We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…
This work focuses on the definition and study of the n-dimensional k-vector, an algorithm devised to perform orthogonal range searching in static databases with multiple dimensions. The methodology first finds the order in which to search…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…
A new search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing depth-first search combined with some methods which reduce the search space. Using the proposed…