In a recent paper [7], Shor and Laflamme define two “weight enumerators” for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We extend their work by introducing another enumerator, based on the classical theory of shadow codes, that tightens their bounds significantly. In particular, nearly all of the codes...

In this paper, we propose a novel computational method for solving non-linear optimal control problems. The is based on the use of Fourier–Hermite series approximating action-value function arising in dynamic programming instead conventional Taylor-series expansion used differential (DDP). coefficients can be numerically computed by using sigma-point methods, which leads to class methods. We al...