From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits

Optimisation via parameterised quantum circuits is the prevalent technique of near-term quantum algorithms. However, the omnipresent phenomenon of barren plateaus - parameter regions with vanishing gradients - sets a persistent hurdle that drastically diminishes its success in practice. In this work, we introduce an approach - based on non-unitary operations - that favours jumps out of a barren plateau into a fertile valley. These operations are constructed from conic extensions of parameterised unitary quantum circuits, relying on mid-circuit measurements and a small ancilla system. We further reduce the problem of finding optimal jump directions to a low-dimensional generalised eigenvalue problem. As a proof of concept we incorporate jumps within state-of-the-art implementations of the Quantum Approximate Optimisation Algorithm (QAOA). We demonstrate the extensions' effectiveness on QAOA through extensive simulations, showcasing robustness against barren plateaus and highly improved sampling probabilities of optimal solutions.