Improving Parameter Training for VQEs by Sequential Hamiltonian Assembly

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.