Difference between revisions of "Grape liouv.m"
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{{DISPLAYTITLE:grape_liouv.m}} __NOTOC__ | {{DISPLAYTITLE:grape_liouv.m}} __NOTOC__ | ||
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Gradient Ascent Pulse Engineering (GRAPE) fidelity, 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 operators in every time step of the shaped pulse. | Gradient Ascent Pulse Engineering (GRAPE) fidelity, 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 operators in every time step of the shaped pulse. | ||
==Syntax== | ==Syntax== | ||
| − | [traj_data,fidelity,grad,hess]=grape_liouv(spin_system, | + | [traj_data,fidelity,grad,hess]=grape_liouv(spin_system,drift,controls,... |
| + | waveform,dt,rho_init,rho_targ,... | ||
| + | fidelity_type) | ||
==Arguments== | ==Arguments== | ||
| − | spin_system - Spinach data object that has been through | + | spin_system - Spinach data object that has been through |
| − | the optimcon.m problem setup function. | + | the [[optimcon.m]] problem setup function. |
| − | + | ||
| − | + | drift - the drift Liouvillian (matrix). | |
| − | + | ||
| − | + | controls - control operators in Liouville space (cell | |
| − | + | array of matrices). | |
| − | + | ||
| − | controls - control operators in Liouville space (cell | ||
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waveform - control coefficients for each control ope- | waveform - control coefficients for each control ope- | ||
| − | rator (in | + | rator (in rows of a matrix), rad/s |
| − | + | ||
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rho_init - initial state of the system as a vector in | rho_init - initial state of the system as a vector in | ||
Liouville space. | Liouville space. | ||
| − | + | ||
rho_targ - target state of the system as a vector in | rho_targ - target state of the system as a vector in | ||
Liouville space. | Liouville space. | ||
| − | + | ||
fidelity_type - 'real' (real part of the overlap) | fidelity_type - 'real' (real part of the overlap) | ||
'imag' (imaginary part of the overlap) | 'imag' (imaginary part of the overlap) | ||
'square' (absolute square of the overlap) | 'square' (absolute square of the overlap) | ||
| − | == | + | ==Returns== |
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| + | fidelity - fidelity of the control sequence | ||
| + | |||
grad - gradient of the fidelity with respect to | grad - gradient of the fidelity with respect to | ||
the control sequence | the control sequence | ||
| − | + | ||
| − | hess - Hessian of the fidelity with respect to the | + | hess - Hessian of the fidelity with respect to the |
control sequence | control sequence | ||
| − | + | ||
traj_data.forward - forward trajectory from the initial condi- | traj_data.forward - forward trajectory from the initial condi- | ||
tion(a stack of state vectors) | tion(a stack of state vectors) | ||
| − | + | ||
| − | + | traj_data.backward - backward trajectory from the target state | |
| − | + | (a stack of state vectors) | |
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==Notes== | ==Notes== | ||
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This is a low level function that is not designed to be called directly. Use [[grape_xy.m]] and [[grape_phase.m]] instead. | 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== | ==See also== | ||
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[[dirdiff.m]], [[step.m]], [[optimcon.m]], [[grape_xy.m]], [[grape_phase.m]], [[penalty.m]] | [[dirdiff.m]], [[step.m]], [[optimcon.m]], [[grape_xy.m]], [[grape_phase.m]], [[penalty.m]] | ||
''Version 2.2, authors: [[Ilya Kuprov]], [[David Goodwin]]'' | ''Version 2.2, authors: [[Ilya Kuprov]], [[David Goodwin]]'' | ||
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Revision as of 15:48, 5 April 2026
Gradient Ascent Pulse Engineering (GRAPE) fidelity, 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 operators in every time step of the shaped pulse.
Syntax
[traj_data,fidelity,grad,hess]=grape_liouv(spin_system,drift,controls,...
waveform,dt,rho_init,rho_targ,...
fidelity_type)
Arguments
spin_system - Spinach data object that has been through
the optimcon.m problem setup function.
drift - the drift Liouvillian (matrix).
controls - control operators in Liouville space (cell
array of matrices).
waveform - control coefficients for each control ope-
rator (in rows of a matrix), rad/s
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 respect to
the control sequence
hess - Hessian of the fidelity with respect to the
control sequence
traj_data.forward - forward trajectory from the initial condi-
tion(a stack of state vectors)
traj_data.backward - backward trajectory from the target state
(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
dirdiff.m, step.m, optimcon.m, grape_xy.m, grape_phase.m, penalty.m
Version 2.2, authors: Ilya Kuprov, David Goodwin
