Barren plateaus in quantum tensor network optimization

We analyze the barren plateau phenomenon in variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and multiscale entanglement renormalization ansatz (qMERA). consider as cost function expectation value a Hamiltonian that is sum local terms. For randomly chosen parameters we show variance gradient decreases exponentially with distance term from canonical centre network. Therefore, qubit count, for qMPS most variances decrease qTTN well qMERA they polynomially. also calculation these gradients more efficient on classical computer than computer.