Theoretical knock-outs on biological networks.

In this work we redefine the concept of biological importance and how to compute it, based on a model of complex networks and random walk. We call this new procedure, theoretical knock-out (KO). The proposed method generalizes the procedure presented in a recent study about Oral Tolerance. To devise this method, we make two approaches: algebraically and algorithmically. In both cases we compute a vector on an asymptotic state, called flux vector. The flux is given by a random walk on a directed graph that represents a biological phenomenon. This vector gives us the information about the relative flux of walkers on a vertex which represents a biological agent. With two vector of this kind, we can calculate the relative mean error between them by averaging over its coefficients. This quantity allows us to assess the degree of importance of each vertex of a complex network that evolves in time and has experimental background. We find out that this procedure can be applied in any sort of biological phenomena in which we can know the role and interrelationships of its agents. These results also provide experimental biologists to predict the order of importance of biological agents on a mounted complex network.

Stabilizer codes for open quantum systems.

The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method for constructing a decoherence-free subspace. In this paper, we develop tools for constructing decoherence-free stabilizer codes for open quantum systems governed by the Lindblad master equation. This is done by pursuing an extension of the stabilizer formalism beyond the celebrated group structure of Pauli error operators. We then show how to utilize decoherence-free stabilizer codes in quantum metrology in order to attain the Heisenberg limit scaling with low computational complexity.