Information processing with lossless cellular neural networks

Summary form only given. The eigenvalues of a symmetric tridiagonal matrix can be computed via an iterative diagonalization with the aid of the QR-algorithm. Interpolating the matrices of subsequent iteration steps with continuous (time) trajectories leads to the concept of matrix flows on manifolds. This can be viewed as the transients of a nonlinear dynamical system. In the fixed point of the dynamical system, the desired eigenvalues are found. Mapping the nonlinear ODE's onto physical structures, lossless nonlinear dynamical circuits are obtained. These circuits can be interpreted as CNN's with nonlinear templates. While these lossless CNNs are interesting by themselves, the important question arises, whether a robust implementation without any power supply and, therefore, without dissipation is practically feasible indeed. Conventional realizations would necessitate (nonlinear) inductors and would not be well suited for solid state silicon implementations. Any simulation of the inductors with the aid of transistors will not alleviate the problem, because the resulting circuits will not be truly lossless any more. Future nanoscale quantum devices open up new possibilities of low loss nanoelectronic computing structures.