  A central challenge in quantum machine learning is the design and training of
parameterized quantum circuits (PQCs). Similar to deep learning, vanishing
gradients pose immense problems in the trainability of PQCs, which have been
shown to arise from a multitude of sources. One such cause are non-local loss
functions, that demand the measurement of a large subset of involved qubits. To
facilitate the parameter training for quantum applications using global loss
functions, we propose a Sequential Hamiltonian Assembly, which iteratively
approximates the loss function using local components. Aiming for a prove of
principle, we evaluate our approach using Graph Coloring problem with a
Varational Quantum Eigensolver (VQE). Simulation results show, that our
approach outperforms conventional parameter training by 29.99% and the
empirical state of the art, Layerwise Learning, by 5.12% in the mean accuracy.
This paves the way towards locality-aware learning techniques, allowing to
evade vanishing gradients for a large class of practically relevant problems.
