Unitary Calculations

calculate_unitary_and_derivatives(problem::UnitaryRobustGRAPEProblem, x::Vector{<:Real})

Calculate the unitary evolution operator and its derivatives with respect to control parameters and error sources.

Arguments

• problem::UnitaryRobustGRAPEProblem: The robust GRAPE problem definition
• x::Vector{<:Real}: The optimization vector containing control parameters and additional parameters

Returns

A tuple with:

• U: Final unitary evolution
• U_dx: Derivatives with respect to control parameters
• U_dx_add: Derivatives with respect to additional parameters
• U_derr: Derivatives with respect to error sources
• U_derr_dx: Mixed derivatives (error and control parameters)
• U_derr_dx_add: Mixed derivatives (error and additional parameters)

calculate_interaction_error_operators(problem::UnitaryRobustGRAPEProblem, x::Vector{<:Real})

Calculate the interaction picture representation of error operators at each time step.

This function transforms error operators from the Schrödinger picture to the interaction picture, which is essential for analyzing how errors affect the quantum dynamics throughout the evolution. The interaction picture provides a way to separate the influence of the control Hamiltonian from the error terms.

Parameters

• problem::UnitaryRobustGRAPEProblem: The robust GRAPE problem definition
• x::Vector{<:Real}: The optimization vector containing control parameters and additional parameters

Returns

• A tensor of dimensions (ndim, ndim, ntimes, nerr) containing the interaction picture representation of each error operator at each time step.

Notes

• The interaction picture transformation uses the cumulative evolution operator
• Error operators are scaled by the small parameter ϵ used for numerical differentiation
• The returned tensor has dimensions permuted for convenient access to time-dependent error operators