We use one photon to simulate an n-qubit quantum system for the first time. We propose a new scheme to realize universal quantum computation in polynomial time O(n^5). A generating set of gates can be realized with high accuracy in the lab. We conclude that photonic quantum computation is one of the promising approaches to universal quantum computation.

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In Chu (Syst Control Lett 56:303314, 2007), the pole assignment problem was considered for the control system \dot{x} = Ax + Bu with linear state-feedback \dot{x} = Ax + Bu An algorithm using the Schur form has been proposed, producing good suboptimal solutions which can be refined further using optimization. In this paper, the algorithm is improved, incorporating the minimization of the feedback gain \dot{x} = Ax + Bu It is also extended for the pole assignment of the descriptor system \dot{x} = Ax + Bu with linear state- and derivative-feedback \dot{x} = Ax + Bu Newton refinement for the solutions is discussed and several illustrative numerical examples are presented.

The SimpleMatrix encryption scheme as proposed by Tao et al. \cite{TD13} is one of the very few existing approaches to create a secure and efficient encryption scheme on the basis of multivariate polynomials. However, in its basic version, decryption failures occur with non-negligible probability. Although this problem has been addressed in several papers \cite{DP14,TX15}, a general solution to it is still missing. In this paper we propose an improved version of the SimpleMatrix scheme, which eliminates decryption failures completely and therefore solves the biggest problem of the SimpleMatrix encryption scheme. Additionally, we propose a second version of the scheme, which reduces the blow-up factor between plain and ciphertext size to a value arbitrary close to 1.