update problem templates and bump PQO compat#225
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…instead of timesteps; refactor integrator functions for consistency
…ps; update system initialization parameters for consistency across tests.
… use N instead of T for consistency; update integrator functions accordingly.
…l problems - Changed control variable name from `a` to `u` across multiple problem templates: - `unitary_sampling_problem.jl` - `unitary_smooth_pulse_problem.jl` - `unitary_variational_problem.jl` - Updated associated bounds and regularization weights to reflect the new naming convention. - Enhanced trajectory initialization functions to support new control variable naming and added documentation for new methods. - Introduced new functions for generating initial unitary and control trajectories with detailed docstrings.
- Updated all manual pages and examples to use u, du, ddu naming - Changed .trajectory.a → .trajectory.u - Updated function parameters: a_bound → u_bound, da_bound → du_bound, etc. - Updated regularizers: R_a → R_u, R_da → R_du, R_dda → R_ddu - Updated math notation in index.md: a_t → u_t - Consistent with source code refactoring
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PiccoloQuantumObjects has updated a number of a its apis. The API that uses this inside of quantum collocation is primarily within problem templates.