grape_hilb.m

Gradient Ascent Pulse Engineering objective function and gradient for Hilbert space. Propagates a system through a shaped pulse from an initial state to a target state and returns fidelity and its gradient.

Syntax

[traj_data,fidelity,grad] = grape_hilb(spin_system,drifts,controls,waveform,rho_init,rho_targ,fidelity_type) %#ok<*PFBNS>

Arguments

spin_system - Spinach data object that has been

                         through the optimcon.m problem 
                         setup function

   drifts              - the drift Hamiltonians: a cell array 
                         containing one matrix (for time-inde-
                         pendent drift) or multiple matrices 
                         (for time-dependent drift)

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

   waveform            - control coefficients for each control 
                         operator (in rows of a matrix), rad/s

   rho_init            - initial state of the system as a density 
                         matrix in Hilbert space

   rho_targ            - target state of the system as a density 
                         matrix in Hilbert space

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

Outputs

fidelity - fidelity of the control sequence

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

   traj_data.forward   - forward trajectory from the initial con-
                         dition (a stack of state vectors)

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

Optimal control module

Version 2.11, authors: Ilya Kuprov, Maxi Keitel