Grape liouv.m

Gradient Ascent Pulse Engineering (GRAPE) fidelity, gradient and Hessian.

Syntax

    [traj_data,fidelity,grad,hess]=grape(spin_system,drift,controls,...
                                             waveform,dt,rho_init,rho_targ,...
                                             fidelity_type)

Description

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 operators in every time step of the shaped pulse.

Arguments

  drift               - The drift Liouvillian (matrix).

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

  waveform            - Control coefficients for each control operator,
                        rad/s (vector array)

  dt                  - Size of time steps in the piecewise constant
                        approximation used within grape, seconds.

  rho_init            - Initial state of the system as a vector in
                        Liouville space.

  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
                        repect to the control sequence

  hess                - Hessian of the fidelity with respect to the 
                        control sequence

  traj_data.forward   - Forward trajectory of the grape simulation of 
                        control amplitudes from the initial state.

  traj_data.backward  - Backward trajectory of the grape simulation of
                        control amplitudes from the desired target state.

Notes

This is a low level function that is not designed to be called directly. Use grape_xy.m and grape_phase.m instead.

See also

dirdiff.m, step.m, optimcon.m

Version 2.0, authors: Ilya Kuprov, David Goodwin