The discrete logarithm problem in Jacobians of curves of high genus g over finite fields Fq is known to be computable with subexponential complexity Lqg (1/2, O(1)). We present an algorithm for a family of plane curves whose degrees in X and Y are low with respect to the curve genus, and suitably unbalanced. The finite base fields are arbitrary, but their sizes should not grow too fast compared...

A rigorous implementation of the Wheeler–Dewitt equations was derived in context Loop Quantum Gravity (LQG) and coined Spin Dynamics (QSD). The Hamiltonian constraint QSD criticised as being too local to prevent “propagation” canonical LQG. That criticism based on an algorithm developed for generating solutions Wheeler–DeWitt equations. fine details that could not be worked out because makes cr...

One of remarkable features loop quantum gravity (LQG) is that it can provide resolutions to both the black hole and big bang singularities. In mini-superspace approach based on polymerization procedure in LQG, a corrected metric constructed. This also known as self-dual spacetime since form invariant under exchange $r \to a_0/r$ with $a_0$ being proportional minimum area LQG $r$ standard radial...

The Barbero-Immirzi parameter ($\gamma$) is introduced in loop quantum gravity (LQG) whose physical significance still a biggest open question; because of its profound traits. In some cases, it real-valued; while, complex-valued other cases. This emerges out the process denoting Lorentz connection with non compact group $SO(3,1)$ form complex values rotations, either $SO(3)$ or $SU(2)$. Initial...

The problem of simulating complex quantum processes on classical computers gave rise to the field simulations. Quantum simulators solve problems, such as Boson sampling, where counterparts fail. In another physics, unification general relativity and theory is one greatest challenges our time. One leading approach Loop Gravity (LQG). Here, we connect these two fields design a linear-optical simu...

The discrete-time optimal projection equations, which constitute necessary conditions for optimal reducedorder LQG compensation, are strengthened. For the class of minimal stabilizing compensators the strengthened discrete-time optimal projection equations are proved to be equivalent tofirst-order necessary optimality conditionsfor optimal reduced-order LQG compensation. The conventional discre...