Computational procedure to determine quantum state evolution in Fock space

A new algorithm to solve the quantum state evolution of a system described by a general quadratic Hamiltonian form in creation and the annihilation operators of Fock space is presented. The nonlinear equation for the dynamic operators are obtained in the matrix representation, and by a recursive relation the time evolution operator in the Fock basis is constructed. The method permits to obtain the evolution of entangled quantum states of interacting subsystems when the Hamiltonian of the whole system is in the above mentioned form. Numerical solution with the method is sufficiently accurate to safely analyze the important question of quantum state transfer between the interacting subsystems. A qubits transfer is discussed as an illustrative example when the method is applied to a system described by a particular quadratic Hamiltonian form.