In this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. We have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. We have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

Discrimination of unitary operations is fundamental in quantum computation and information. A lot algorithms including the well-known Deutsch-Jozsa algorithm, Simon Grover algorithm can essentially be regarded as discriminating among individual, or sets (oracle operators). The problem between two $U$ $V$ described as: Given $X\in\{U, V\}$, determine which one $X$ is. If given with multiple copi...

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/epsilon)] for accuracy epsilon} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our cir...

Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so their coefficients are as $\epsilon \rightarrow 0$. I propose definition renormalized $\epsilon$-finite integrals, which incorporate ultraviolet divergence subtractions specific way. A key advantage this cho...

The asymmetric quantum Rabi model (AQRM) exhibits level crossings in the eigenspectrum for values $\epsilon\in\frac{1}{2}\mathbb{Z}$ of bias parameter $\epsilon$. Such are expected to be associated with some hidden symmetry model. origin this is established by finding operators which commute AQRM hamiltonian at these special values. construction given explicitly first several cases and can appl...