A time-dependent periodic Hamiltonian admitting exact solutions is applied to construct a set of universal gates for quantum computer. The time evolution matrices are obtained in an explicit form and used to construct logic gates for computation. A way of obtaining entanglement operator is discussed, too. The method is based on transformation of soluble time-independent equations into time-depe...

The paper is concerned with a generalization of concepts introduced in [13], i.e. introduced are matrices of linear transformations over a finitedimensional vector space. Introduced are linear transformations over a finitedimensional vector space depending on a given matrix of the transformation. Finally, I prove that the rank of linear transformations over a finite-dimensional vector space is ...

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the ...

The paper demonstrates a simple optimization of the color transformation stage in software video decoding. Calculation of RGB color components from YCRCB components consumes up to 40% of the processing power in highly optimized decoder. A significant reduction of the number of calculations may be achieved through a rearrangement of arithmetic operations that is possible due to linearity of the ...

Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and eecient. Both algorithms are based on transforming the problem to one over the cone of positive semideenite matrices. One of the algorithms does this transformation through an intermediat...

This paper presents three new systematic approaches for computing coefficient matrices of the Heffron-Phillips multi-machine model (K1, …, K6). The amount of computations needed for conventional and three new approaches are compared by counting number of multiplications and divisions. The advantages of new approaches are: (1) their computation burdens are less than 73 percent of that of convent...

The notion of Bezout matrix is an essential tool in studying broad variety of subjects: zeroes of polynomials, stability of differential equations, rational transformations of algebraic curves, systems of commuting nonselfadjoint operators, boundaries of quadrature domains etc. We present a survey of several properties of Bezout matrices and their applications in all mentioned topics. We use th...

a method for solving the descriptor discrete-time linear system is focused. for easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. in partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

A class of transformations of Rq-matrices is introduced such that the q → 1 limit gives explicit nonstandard Rh-matrices. The transformation matrix is singular itself at q → 1 limit. For the transformed matrix, the singularities, however, cancel yielding a well-defined construction. Our method can be implemented systematically for R-matrices of all dimensions and not only for sl(2) but also for...