Lyapunov quantum control provides a constructive mechanism for monotonically decreasing a target-dependent function, while generally leaving the transient dynamics of the associated quantum error unspecified. Here, we recast finite-dimensional state transfer as a Hamiltonian-induced error-channel assignment problem. For a selected fidelity or population error, the nominal error dynamics can be locally assigned when the corresponding input-explicit channel has a full-rank Hamiltonian-induced gain in a nonsingular region. Under this condition, the selected error can be shaped to follow a prescribed stable law, such as exponential decay with a chosen rate, thereby extending Lyapunov design from monotonic error reduction to explicit convergence shaping. We derive the local assignment condition, characterize the associated error-actuation singular set, and develop exact and regularized assignment laws for bounded controls and Hamiltonian perturbations. The error-control gain admits a direct quantum interpretation as the imaginary interference between the target amplitude and the control-induced transition amplitude. Numerical examples demonstrate tunable convergence, singular-set behavior, staged multilevel transfer, amplitude-constrained pump-Stokes transfer, and the validity regime of nominal assignment under mismatch. The resulting analysis provides explicit Hamiltonian actuation conditions, a transition-quadrature interpretation of the error gain, and a residual characterization of nonideal assignment.

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• Quantum control
• Quantum state transfer