# grape.m

## 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,

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

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.