Based on the matrix of the time-dependent quantum transformation theory,we derive the analytic expression of the evolution operator for the time-dependent oscillators by using the time-dependent quantum transformation theory.

On the general properties of time-dependent invariants;

Theory of linear quantum transformation and its application;

By the aid of the linear quantum transformation theory, we derive the analytic expression of the partition function for the quadratic systems.

By the aid of the linear quantum transformation (LQT) theory, we give a concise diagonalization for n-mode boson and fermion of quadratic Hamiltonian.

By means of time-dependent gauge transformation, we do a thorough study on undynamic phase which emerge in the quantum system.

The time-dependent gauge transformation can be applyed to the J-C model which is a full quantumized model to describe a two-level atom interact with single model elecromagnetic field.

A decomposition of quantum Fourier transformation;

Simulation of the multi-qubit quantum Fourier transform;

By using the circuit model which is the most representative in the study of quantum computing,the quantum computing process was simulated and two of the important quantum algorithms—the Deutsch s algorithm and the quantum Fourier transform were implemented.

An exact three-dimensional time-dependent quantum wave packet was used to calculate the He+H2+ reaction using the potential energy function of HeH2+ [1].

Full three-dimension time-dependent quantum wave packet calculations have been carried out for H+HBr reaction on the latest analytical ab initio potential energy surface.