Dynamical invariants for quantum control of four-level systems

We present a Lie-algebraic classification and detailed construction of the dynamical invariants, also known as Lewis-Riesenfeld invariants, of the four-level systems including two-qubit systems which are most relevant and sufficiently general for quantum control and computation. These invariants not only solve the time-dependent Schr\"odinger equation of four-level systems exactly but also enable the control, and hence quantum computation based on which, of four-level systems fast and beyond adiabatic regimes.Comment: 11 pages, 5 table

Generalized Grassmannian Coherent States For Pseudo-Hermitian nn Level Systems

The purpose of this paper is to generalize fermionic coherent states for two-level systems described by pseudo-Hermitian Hamiltonian \cite{Trifonov}, to n-level systems. Central to this task is the expression of the coherent states in terms of generalized Grassmann variables. These kind of Grassmann coherent states satisfy bi-overcompleteness condition instead of over-completeness one, as it is reasonably expected because of the biorthonormality of the system. Choosing an appropriate Grassmann weight function resolution of identity is examined. Moreover Grassmannian coherent and squeezed states of deformed group $SU_{q}(2)$ for three level pseudo-Hermitian system are presented.Comment: 17 page