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Use QuantumPropagators in standalone examples
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README.md

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@@ -33,7 +33,7 @@ A minimal working example optimizing a state-to-state transition `|0⟩ → |1
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```julia
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using GRAPE
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using QuantumControl: hamiltonian # data structure for `H = H₀ + ϵ(t) H₁`
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using QuantumPropagators: hamiltonian # data structure for `H = H₀ + ϵ(t) H₁`
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using QuantumControl.Functionals: J_T_sm # square-modulus functional
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using QuantumPropagators: ExpProp # propagation method: matrix exponentiation
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docs/src/tutorial.md

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We may also want to place some _physical_ constraints onto ``Ω(t)``. For example, we may want ``Ω(t)`` to smoothly switch on from zero and off to zero at the beginning and end of the time grid. One way of achieving this is to define ``Ω(t) = S(t) ϵ(t)`` where ``S(t)`` is a static shape that has the smooth switch-on and off, and ``ϵ(t)`` is an arbitrary function that we can optimize freely.
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The `QuantumControl` framework provides a [`ShapedAmplitude`](@extref `QuantumPropagators.Amplitudes.ShapedAmplitude`) object to implement this:
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The `QuantumPropagators` framework provides a [`ShapedAmplitude`](@extref `QuantumPropagators.Amplitudes.ShapedAmplitude`) object to implement this:
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```@example
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using QuantumControl.Amplitudes: ShapedAmplitude
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using QuantumPropagators.Amplitudes: ShapedAmplitude
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```
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For a fixed time grid ending at
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we can define the function ``S(t)`` as
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```@example
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using QuantumControl.Shapes: flattop
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using QuantumPropagators.Shapes: flattop
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shape(t) = flattop(t, T = T, t_rise = 15ns);
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nothing # hide
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```
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```@example
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using QuantumControl.Controls: get_controls
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using QuantumPropagators.Controls: get_controls
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get_controls(trajectories)
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```

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