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.

We propose and analyze a multivariate encryption scheme that uses odd characteristic and an embedding in its construction. This system has a very simple core map F(X) = X^2, allowing for efficient decryption. We also discuss ways to make this decryption faster with specific parameter choices. We give heuristic arguments along with experimental data to show that this scheme resists all known attacks.

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We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called ST-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independent parameters for given ranks of two connection matrices, or in calculating the scattering matrix when both matrices are singular. The new form of boundary conditions, called the P Q R S-form, also gives a natural scheme to design generalized low and high pass quantum filters.

Short integer solution (SIS) and learning with errors (LWE) are two hard lattice problems. These two problems are believed having huge potential in application of cryptography. In 2012, Ding et al. [5] introduced the first provably secure key exchange based on LWE problem. On the other hand, we believe that it is very difficult to do key exchange on SIS problem only. In 2014, Wang et al. [6] did an attempt, but it was not successful. Mao et al. [7] broke the protocol by an attack based on CBi-SIS problem in 2016. However, their attack is not efficient. In this paper, we present a extremely straightforward and simple attack to Wang’s key exchange and then we will construct a key exchange based on SIS and LWE problems.