grape_liouv.m

Gradient Ascent Pulse Engineering (GRAPE) objective function, gradient, and Hessian. Propagates the system through a user-supplied shaped pulse from a given initial state and projects the result onto the given final state. The fidelity is returned, along with its gradient and Hessian with respect to amplitudes of all control operators in every time step of the shaped pulse.

Syntax

    [traj_data,fidelity,grad,hess]=grape_liouv(spin_system,drifts,controls,...
                                               waveform,rho_init,rho_targ,...
                                               fidelity_type)

Parameters

  spin_system         - Spinach data object that has been through 
                        the optimcon.m problem setup function.

  drifts              - the drift Liouvillians: a cell array containing
                        one matrix for time-independent drift, or multiple
                        matrices for time-dependent drift.

  controls            - control operators in Liouville space (cell 
                       array of matrices).

  waveform            - control coefficients for each control ope-
                        rator in the vertical dimension, at each time
                        slice in the horizontal dimension, rad/s

  rho_init            - initial state of the system as a vector in
                        Liouville space, ignored in stroboscopic
                        steady state optimisations.

  rho_targ            - target state of the system as a vector in
                        Liouville space.

  fidelity_type       - 'real'   (real part of the overlap)
                        'imag'   (imaginary part of the overlap)
                        'square' (absolute square of the overlap)

Returns

  fidelity            - fidelity of the control sequence

  grad                - gradient of the fidelity with respect to
                        the control sequence

  hess                - Hessian of the fidelity with respect to the 
                        control sequence, not available for piecewise-linear
                        and stroboscopic steady state optimisations

  traj_data.forward   - forward trajectory from the initial condition
                        or stroboscopic steady state; this is returned
                        only when requested by the control settings

Notes

This is a low level function that is not designed to be called directly. Use grape_xy.m, grape_phase.m, or other wrapper functions instead.

See also

dirdiff.m, step.m, optimcon.m, grape_xy.m, grape_phase.m, penalty.m, grape_coop.m, grape_curv.m, grape_hilb.m, tgrape.m, Optimal_control_module

Version 2.2, authors: Ilya Kuprov, David Goodwin