  Hybrid Quantum-Classical algorithms are a promising candidate for developing
uses for NISQ devices. In particular, Parametrised Quantum Circuits (PQCs)
paired with classical optimizers have been used as a basis for quantum
chemistry and quantum optimization problems. Training PQCs relies on methods to
overcome the fact that the gradients of PQCs vanish exponentially in the size
of the circuits used. Tensor network methods are being increasingly used as a
classical machine learning tool, as well as a tool for studying quantum
systems. We introduce a circuit pre-training method based on matrix product
state machine learning methods, and demonstrate that it accelerates training of
PQCs for both supervised learning, energy minimization, and combinatorial
optimization.
