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Optimisation via parameterised quantum circuits is the prevalent technique ofnear-term quantum algorithms. However, the omnipresent phenomenon of barrenplateaus - parameter regions with vanishing gradients - sets a persistenthurdle that drastically diminishes its success in practice. In this work, weintroduce an approach - based on non-unitary operations - that favours jumpsout of a barren plateau into a fertile valley. These operations are constructedfrom conic extensions of parameterised unitary quantum circuits, relying onmid-circuit measurements and a small ancilla system. We further reduce theproblem of finding optimal jump directions to a low-dimensional generalisedeigenvalue problem. As a proof of concept we incorporate jumps withinstate-of-the-art implementations of the Quantum Approximate OptimisationAlgorithm (QAOA). We demonstrate the extensions' effectiveness on QAOA throughextensive simulations, showcasing robustness against barren plateaus and highlyimproved sampling probabilities of optimal solutions.

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