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Copy file name to clipboardExpand all lines: docs/src/examples/index.md
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## Krotov-specific examples
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*[Optimization of a State-to-State Transfer in a Two-Level-System](https://juliaquantumcontrol.github.io/Krotov.jl/stable/examples/simple_state_to_state/)
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*[Optimization of a Dissipative Quantum Gate](https://juliaquantumcontrol.github.io/Krotov.jl/stable/examples/rho_3states/)
*[Optimization for a perfect entangler](https://juliaquantumcontrol.github.io/Krotov.jl/stable/examples/perfect_entanglers/)
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*[Optimization of a State-to-State Transfer in a Two-Level-System](https://juliaquantumcontrol.github.io/QuantumControlExamples.jl/stable/examples/simple_state_to_state/#Optimization-of-a-State-to-State-Transfer-in-a-Two-Level-System)
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*[Optimization of a Dissipative Quantum Gate](https://juliaquantumcontrol.github.io/QuantumControlExamples.jl/stable/examples/rho_3states/#Optimization-of-a-Dissipative-Quantum-Gate)
*[Optimization for a perfect entangler](https://juliaquantumcontrol.github.io/QuantumControlExamples.jl/stable/examples/perfect_entanglers/#Optimizing-for-a-general-perfect-entangler)
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## GRAPE-specific examples
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*[Optimization of a State-to-State Transfer in a Two-Level-System](https://juliaquantumcontrol.github.io/GRAPE.jl/stable/examples/simple_state_to_state/)
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*[Optimization for a perfect entangler](https://juliaquantumcontrol.github.io/GRAPE.jl/stable/examples/perfect_entanglers/)
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*[Optimization of a State-to-State Transfer in a Two-Level-System](https://juliaquantumcontrol.github.io/QuantumControlExamples.jl/stable/examples/simple_state_to_state/#Optimization-of-a-State-to-State-Transfer-in-a-Two-Level-System)
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*[Optimization for a perfect entangler](https://juliaquantumcontrol.github.io/QuantumControlExamples.jl/stable/examples/perfect_entanglers/#Optimizing-for-a-general-perfect-entangler)
Copy file name to clipboardExpand all lines: docs/src/glossary.md
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The time-dependent coefficient ``a_l(t)`` for the [Control Operator](@ref) in Eq. (G2). A control amplitude may depend on on or more control functions, as well as have an explicit time dependency. Some conceptual examples for control amplitudes and how they may depend on a [Control Function](@ref) are the following:
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* Non-linear coupling of a control field to the operator, e.g., the quadratic coupling of the laser field to a Stark shift operator
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*[Pulse Parametrization](@ref) as a way to enforce bounds on a [Control Field](@ref)
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*[Pulse Parameterization](@ref) as a way to enforce bounds on a [Control Field](@ref)
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* Transfer functions, e.g., to model the response of an electronic device to the optimal control field ``ϵ(t)``.
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* Noise in the amplitude of the control function
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* Non-controllable aspects of the control amplitude, e.g. a "guided" control amplitude ``a_l(t) = R(t) + ϵ_l(t)`` or a non-controllable envelope ``S(t)`` in ``a_l(t) = S(t) ϵ(t)`` that ensures switch-on- and switch-off in a CRAB pulse `ϵ(t)`.
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##### Control Parameters
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Non-time-dependent parameters that a [Control Function](@ref) depends on, ``ϵ(t) = ϵ(\{u_n\}, t)``. One common parametrization of a control field is as a [Pulse](@ref), where the control parameters are the amplitude of the field at discrete points of a time grid. Parametrization as a "pulse" is implicit in Krotov's method and standard GRAPE.
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Non-time-dependent parameters that a [Control Function](@ref) depends on, ``ϵ(t) = ϵ(\{u_n\}, t)``. One common parameterization of a control field is as a [Pulse](@ref), where the control parameters are the amplitude of the field at discrete points of a time grid. Parameterization as a "pulse" is implicit in Krotov's method and standard GRAPE.
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More generally, the control parameters could also be spectral coefficients (CRAB) or simple parameters for an analytic pulse shape (e.g., position, width, and amplitude of a Gaussian shape). All optimal control methods find optimized control fields by varying the control parameters.
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----
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##### Pulse
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(aka "control pulse") A control field discretized to a time grid, usually on the midpoints of the time grid, in a piecewise-constant approximation. Stored as a vector of floating point values. The parametrization of a control field as a "pulse" is implicit for Krotov's method and standard GRAPE. One might think of these methods to optimize the control fields *directly*, but a conceptually cleaner understanding is to think of the discretized "pulse" as a vector of control parameters for the time-continuous control field.
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(aka "control pulse") A control field discretized to a time grid, usually on the midpoints of the time grid, in a piecewise-constant approximation. Stored as a vector of floating point values. The parameterization of a control field as a "pulse" is implicit for Krotov's method and standard GRAPE. One might think of these methods to optimize the control fields *directly*, but a conceptually cleaner understanding is to think of the discretized "pulse" as a vector of control parameters for the time-continuous control field.
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----
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##### Pulse Parametrization
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##### Pulse Parameterization
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A special case of a [Control Amplitude)(@ref) where ``a(t) = a(ϵ(t))`` at every point in time. The purpose of this is to constrain the amplitude of the control amplitude ``a(t)``. See e.g. [`QuantumControl.PulseParametrizations.SquareParametrization`](@ref), where ``a(t) = ϵ^2(t)`` to ensure that ``a(t)`` is positive. Since Krotov's method inherently has no constraints on the optimized control fields, pulse parameterization is a method of imposing constraints on the amplitude in this context.
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A special case of a [Control Amplitude](@ref) where ``a(t) = a(ϵ(t))`` at every point in time. The purpose of this is to constrain the amplitude of the control amplitude ``a(t)``. See e.g. [`QuantumControl.PulseParameterizations.SquareParameterization`](@ref), where ``a(t) = ϵ^2(t)`` to ensure that ``a(t)`` is positive. Since Krotov's method inherently has no constraints on the optimized control fields, pulse parameterization is a method of imposing constraints on the amplitude in this context.
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----
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!!! note
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The above nomenclature does not consistently extend throughout the quantum control literature: the terms "control"/"control term"/"control Hamiltonian", and "control"/"control field"/"control function"/"control pulse"/"pulse" are generally somewhat ambiguous. In particular, the distinction between "control field" and "pulse" (as a parametrization of the control field in terms of amplitudes on a time grid) here is somewhat artifcial and borrowed from the [Krotov Python package](https://qucontrol.github.io/krotov). However, the terminology defined in this glossary is consistently applied within the `JuliaQuantumControl` organization, both in the documentation and in the names of members and methods.
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The above nomenclature does not consistently extend throughout the quantum control literature: the terms "control"/"control term"/"control Hamiltonian", and "control"/"control field"/"control function"/"control pulse"/"pulse" are generally somewhat ambiguous. In particular, the distinction between "control field" and "pulse" (as a parameterization of the control field in terms of amplitudes on a time grid) here is somewhat artifcial and borrowed from the [Krotov Python package](https://qucontrol.github.io/krotov). However, the terminology defined in this glossary is consistently applied within the `JuliaQuantumControl` organization, both in the documentation and in the names of members and methods.
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