  Quadratically Constrained Quadratic Programs (QCQPs) are an important class
of optimization problems with diverse real-world applications. In this work, we
propose a variational quantum algorithm for general QCQPs. By encoding the
variables on the amplitude of a quantum state, the requirement of the qubit
number scales logarithmically with the dimension of the variables, which makes
our algorithm suitable for current quantum devices. Using the primal-dual
interior-point method in classical optimization, we can deal with general
quadratic constraints. Our numerical experiments on typical QCQP problems,
including Max-Cut and optimal power flow problems, demonstrate a better
performance of our hybrid algorithm over the classical counterparts.
