127,781 research outputs found
The domain matrix method: a new calculation scheme for diffraction profiles
A new calculation scheme for diffraction profiles is presented that combines the matrix method with domain approaches. Based on a generalized Markov chain, the method allows the exact solution of the diffraction problem from any one-dimensionally disordered domain structure. The main advantage of this model is that a domain statistic is used instead of a cell statistic and that the domain-length distribution can be chosen independently from the domain-type stacking. A recursive relation is derived for the correlations between the domains and a double recursive algorithm, not reducible to a simpler one, is obtained as solution. The algorithm developed here is referred to as the domain matrix method. Results and applications of the new approach are discussed
A Quantum-Quantum Metropolis Algorithm
Recently, the idea of classical Metropolis sampling through Markov chains has
been generalized for quantum Hamiltonians. However, the underlying Markov chain
of this algorithm is still classical in nature. Due to Szegedy's method, the
Markov chains of classical Hamiltonians can achieve a quadratic quantum speedup
in the eigenvalue gap of the corresponding transition matrix. A natural
question to ask is whether Szegedy's quantum speedup is merely a consequence of
employing classical Hamiltonians, where the eigenstates simply coincide with
the computational basis, making cloning of the classical information possible.
We solve this problem by introducing a quantum version of the method of
Markov-chain quantization combined with the quantum simulated annealing (QSA)
procedure, and describe explicitly a novel quantum Metropolis algorithm, which
exhibits a quadratic quantum speedup in the eigenvalue gap of the corresponding
Metropolis Markov chain for any quantum Hamiltonian. This result provides a
complete generalization of the classical Metropolis method to the quantum
domain.Comment: 7 page
Generalized Finite Algorithms for Constructing Hermitian Matrices with Prescribed Diagonal and Spectrum
In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix. They perform this feat by applying a sequence of (N-1) or fewer plane rotations, where N is the dimension of the matrix. Both the Bendel-Mickey and the Chan-Li algorithms are special cases of the proposed procedures. Using the fact that a positive semidefinite matrix can always be factored as \mtx{X^\adj X}, we also provide more efficient versions of the algorithms that can directly construct factors with specified singular values and column norms. We conclude with some open problems related to the construction of Hermitian matrices with joint diagonal and spectral properties
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