To advance our understanding of Quantum Cellular Automata in problem solving through parallel and distributed computing, this research quantized the density classification problem and adopted the Quantum Particle Automata (QPA) [12] to solve the quantized problem. In order to solve this problem, the QPA needed a unitary operator to carry out the QPA evolution and a boundary partition to make th...

The physical meaning of the concepts underlying the density operator formalism are analyzed from different points of view. In particular, the diversity of ways of expressing the density operator of the simplest NMR sample is exploited to show that there are many molecular-scale physical pictures compatible with each macroscopic state, some of them being more useful than others for specific aims...

2 Quantum Error Correction 3 2.1 Quantum operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Density matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 System-environment model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.3 Quantum operations definition . . . . . . . . . . . ....

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

We are interested in solutions Ψt of the Schrödinger equation of N interacting bosons under the influence of a time dependent external field, where the range and the coupling constant of the interaction scale with N in such a way, that the interaction energy per particle stays more or less constant. Let N0 be the particle number operator with respect to some φ0 ∈ L (R → C). Assume that the rela...

We present a quantitative estimate of the confusion of cluster radio halos and galaxies in the measurement of the angular power spectrum of the thermal Sunyaev-Zel’dovich (SZ) effect. To achieve the goal, we use a purely analytic approach to both radio sources and dark matter of clusters by incorporating empirical models and observational facts together with some theoretical considerations. It ...

We consider an elliptic self-adjoint first-order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact three-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squares of Euclidean norms of eigenfunctions evaluated at a given point of the...

A general real-time formalism is developed to resum the self-energy operator of broken symmetry scalar field theories in form of self-consistent gap equations for the spectral function. The solution of the equations is approximated with finite lifetime quasi-particles. In the Landau damping rates viscosity terms, analogous to gauge theories, appear, what leads to a finite damping rate for the l...

We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential μ for a given gauge configuration on the finite-volume lattice. We make use of the Banks-Casher relations to relate the eigenvalue spectral density to the physical obser...

I study the leading effects of discretization errors on the low-energy part of the spectrum of the Hermitian Wilson-Dirac operator in infinite volume. The method generalizes that used to study the spectrum of the Dirac operator in the continuum, and uses partially quenched chiral perturbation theory for Wilson fermions. The leading-order corrections are proportional to a2 (a being the lattice s...