Noise-induced barren plateaus in variational quantum algorithms due to non-unital and Hamiltonian control noise

Variational Quantum Algorithms (VQAs) are leading practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices. Despite their promise, VQAs suffer from the problem of vanishing gradients, also known as the barren plateau (BP) phenomenon. BP can arise from fundamentally different mechanisms, e.g., parameter initialization, the structure of the problem Hamiltonian, and noise. Noise-induced barren plateaus (NIBPs) have been shown to exist subject to unital CPTP maps. We generalize this result to non-unital CPTP noise via parameter shift rules and derive the validity of the rules in the presence of noise. We demonstrate the effects of noise on VQA training via simulations.