Photon echo quantum RAM integration in quantum computer

We have analyzed an efficient integration of the multi-qubit echo quantum memory into the quantum computer scheme on the atomic resonant ensembles in quantum electrodynamics cavity. Here, one atomic ensemble with controllable inhomogeneous broadening is used for the quantum memory node and other atomic ensembles characterized by the homogeneous broadening of the resonant line are used as processing nodes. We have found optimal conditions for efficient integration of multi-qubit quantum memory modified for this analyzed physical scheme and we have determined a specified shape of the self temporal modes providing a perfect reversible transfer of the photon qubits between the quantum memory node and arbitrary processing nodes. The obtained results open the way for realization of full-scale solid state quantum computing based on using the efficient multi-qubit quantum memory.Comment: 13 pages, 5 figure

Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics

A class of integrable 2-dim classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With similar technique a new class of potentials connected with Lax method is found which provides the integrability of corresponding 2-dim hamiltonian systems. In addition, some integrable 2-dim systems with potentials expressed in elliptic functions are explored.Comment: 19 pages, LaTeX, final version to be published in J.Phys.

Intertwining relations of non-stationary Schr\"odinger operators

General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in a $R$-separation of variables. The Fokker-Planck and diffusion equation are briefly considered. Second-order intertwining operators are also discussed within a general approach. However, due to its complicated structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20