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.

In this paper, we continues to investigate the properties of symmetric inequalities. We study the necessary condition for the extremum to be attained in a semi-algebraic system. From which, we partly solve the problem of the further generalization of Jensen inequality which the author brought up in the previous article. Namely, by using the sign of the (n+1)^th derivative while xing the value of the sum of power of n variables, we get a dimension-descending method. Further, we prove that the necessary and sucient condition for the symmetric inequality of degree m with n variables to hold on R+n is that it holds when the number of nonzero variables does not exceed max&{1, frac{m}{2}}&.

We study the rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature-like quantities for polyhedral surfaces are introduced and are shown to determine the polyhedral metric up to isometry. The action functionals in the variational approaches are derived from the cosine law. They can be considered as 2-dimensional counterparts of the Schlaefli formula.

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