A note on equality-constrained continuous optimization within the quantum approximate optimization framework

Abstract The possibility of controlling the evolution of a quantum wavepacket to achieve optimization of a high-dimensional continuous function has been proposed and subsequently experimentally demonstrated in optical quantum hardware. In this short note we clarify how existing proposals for constrained continuous optimization are subject to instabilities which result from a Hamiltonian whose spectrum is unbounded in both directions. In addition we offer an alternative algorithm which is free from instabilities with potentially improved shot efficiency.