We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string–genus “joint relation,” involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the C* Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation.

We find the shock wave solutions in a class of cosmological backgrounds with a null singularity, each of these backgrounds admits a matrix description. A shock wave solution breaks all supersymmetry meanwhile indicates that the interaction between two static D0-branes cancel, thus provides basic evidence for the matrix description. The probe action of a D0-brane in the background of another suggests that the usual perturbative expansion of matrix model breaks down.

We compute the one-loop effective action of two D0-branes in the matrix model for a cosmological background, and find vanishing static potential. However, there is a non-vanishing v2 term not predicted in a supergravity calculation. This term is complex and signals an instability of the two D0-brane system, it may also indicate that the matrix model is incorrect.

We discuss a few examples in 2+1 dimensions and 1+1 dimensions supporting a recent conjecture concerning the relation between the Planck scale and the coupling strength of a non-gravitional interaction, unlike those examples in 3+1 dimensions, we do not have to resort to exotic physics such as small black holes. However, the result concerning these low dimensional examples is a direct consequence of the 3+1 dimensional conjecture.

The cosmological observations provide a strong evidence that there is a positive cosmological constant in our universe and thus the spacetime is asymptotical de Sitter space. The conjecture of gravity as the weakest force in the asymptotical dS space leads to a lower bound on the U(1) gauge coupling $g$, or equivalently, the positive cosmological constant gets an upper bound $\rho_V \leq g^2 M_p^4$ in order that the U(1) gauge theory can survive in four dimensions. This result has a simple explanation in string theory, i.e. the string scale $\sqrt{\alpha '}$ should not be greater than the size of the cosmic horizon. Our proposal in string theory can be generalized to U(N) gauge theory and gives a guideline to the microscopic explanation of the de Sitter entropy. The similar results are also obtained in the asymptotical anti-de Sitter space.