Structured variational quantum control for spin-chain state transfer: Expressivity, trainability, and robustness

We propose a hybrid variational framework for quantum optimal control of high-fidelity state transfer in spin chains. The continuous-time control problem is reformulated as a trainable Trotterized quantum circuit, where drift dynamics are encoded by fixed two-qubit interaction blocks and control fields by parameterized on-site R Z rotations. This provides a physics-informed variational ansatz directly connecting the Hamiltonian model to hybrid quantum–classical optimization. We compare two control parameterizations: an expressive local scheme with site-wise trainable parameters and a compact global scheme with shared parameters per Trotter layer. Numerical experiments on XXZ spin chains show that both achieve near-unit fidelity for the main noiseless end-to-end transfer task. The reduced optimization dimension of the global parameterization provides favorable optimization behavior for several larger systems, while additional source–target experiments demonstrate that this advantage is task dependent and that local control can perform better for interior transfers. Studies under depolarizing and dephasing noise show that relative noise-induced degradation depends on system size, noise strength, and noise model, with no uniform robustness ordering. Additional analyses examine circuit depth, initialization sensitivity, empirical gradient statistics, interaction anisotropy, Trotter error, exact piecewise-constant control, and hardware execution. Overall, the results reveal a trade-off between control expressivity, optimization dimensionality, task structure, and noise sensitivity, providing a physically grounded framework for structured variational quantum control of distributed quantum systems.