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Optimization Algorithms

Ctrl-freeq provides access to multiple optimization algorithms through the algorithm configuration field. These algorithms are drawn from two distinct families, each offering complementary capabilities for the solution of quantum control problems.

Algorithm Families

The available algorithms are organized into two families. The first comprises gradient-based methods implemented via the pytorch-minimize library, which operates directly on PyTorch tensors and supports automatic differentiation for the computation of gradients and, where applicable, Hessians. The second family consists of wrapped Qiskit optimizers, identified by the qiskit- prefix, which include both gradient-based and derivative-free methods.

Built-in Algorithms

Algorithm Description
bfgs Broyden-Fletcher-Goldfarb-Shanno (quasi-Newton)
l-bfgs Limited-memory BFGS (lower memory usage)
cg Conjugate gradient
newton-cg Newton conjugate gradient
newton-exact Newton with exact Hessian
dogleg Dogleg trust-region
trust-ncg Trust-region Newton-CG
trust-krylov Trust-region with Krylov subspace
trust-exact Trust-region with exact Hessian

Qiskit Algorithms

The Qiskit optimizers are wrapped in ctrl_freeq/optimizers/qiskit_optimizers.py.

Algorithm Description
qiskit-cobyla Constrained Optimization BY Linear Approximation
qiskit-nelder-mead Nelder-Mead simplex (derivative-free)
qiskit-powell Powell's method (derivative-free)
qiskit-slsqp Sequential Least Squares Programming
qiskit-spsa Simultaneous Perturbation Stochastic Approximation
qiskit-adam Adam optimizer
qiskit-l-bfgs-b L-BFGS-B with bounds
qiskit-tnc Truncated Newton
qiskit-p-bfgs Parallel L-BFGS-B
qiskit-gsls Gaussian Smoothed Line Search

Note

The exact set of available Qiskit optimizers is determined by the get_supported_qiskit_optimizers() function and may vary with the installed version.

Choosing an Algorithm

The selection of an appropriate optimization algorithm depends on the characteristics of the problem at hand, the dimensionality of the parameter space, and the available computational resources.

For general-purpose applications, the BFGS or L-BFGS algorithms provide reliable quasi-Newton methods that are well-suited to the majority of pulse design problems; the latter is particularly advantageous when the parameter space is large, owing to its reduced memory requirements. For smooth, well-behaved cost landscapes, the Newton-CG method often exhibits faster convergence due to its use of curvature information.

In cases where derivative-free optimization is preferred or the problem involves constraints, COBYLA (qiskit-cobyla) offers a robust alternative that does not require gradient computation. For noisy or non-convex optimization landscapes, stochastic methods such as Adam (qiskit-adam) or SPSA (qiskit-spsa) may prove more effective, as they are designed to navigate irregular objective function surfaces.

When high numerical precision is required and the computational cost of exact Hessian evaluation is acceptable, the trust-exact or newton-exact algorithms should be considered, as they exploit full second-order information to achieve rapid convergence in the neighbourhood of a minimum.

Convergence Parameters

The following parameters control the termination criteria of the optimization:

Parameter Description Default
max_iter Maximum optimization iterations 1000
targ_fid Target penalized score (fidelity − penalty); stops when reached 0.999

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