Resource-bounded controllability benchmarking of open quantum systems
This paper develops a resource-bounded framework for evaluating practical controllability in open quantum systems using a trained graybox response model. Rather than treating controllability as a binary property of an idealised Hamiltonian model, the proposed approach evaluates the best-achievable process fidelity over a finite, hardware-realisable pulse family under explicit control constraints. The graybox model retains the known coherent dynamics while learning control-dependent open-system distortions from pulse-response data. The resulting surrogate predictions are used to reconstruct the implemented processes and compare them with Haar-random target gates. Practical controllability is then characterised through the distribution of best-achievable infidelities and an area-based summary metric. The framework is demonstrated for a driven qubit under closed-system, classical-noise, and combined quantum-plus-classical-noise dynamics, with pulse amplitude and inverse Gaussian width used as the control-resource coordinates. The results show how finite control resources and open-system noise jointly constrain the gate performance attainable by the chosen pulse family.