  Solving optimisation problems is a promising near-term application of quantum
computers. Quantum variational algorithms leverage quantum superposition and
entanglement to optimise over exponentially large solution spaces using an
alternating sequence of classically tunable unitaries. However, prior work has
primarily addressed discrete optimisation problems. In addition, these
algorithms have been designed generally under the assumption of an unstructured
solution space, which constrains their speedup to the theoretical limits for
the unstructured Grover's quantum search algorithm. In this paper, we show that
quantum variational algorithms can efficiently optimise continuous
multivariable functions by exploiting general structural properties of a
discretised continuous solution space with a convergence that exceeds the
limits of an unstructured quantum search. We introduce the Quantum
Multivariable Optimisation Algorithm (QMOA) and demonstrate its advantage over
pre-existing methods, particularly when optimising high-dimensional and
oscillatory functions.
