  Variational Quantum Algorithms have emerged as a leading paradigm for
near-term quantum computation. In such algorithms, a parameterized quantum
circuit is controlled via a classical optimization method that seeks to
minimize a problem-dependent cost function. Although such algorithms are
powerful in principle, the non-convexity of the associated cost landscapes and
the prevalence of local minima means that local optimization methods such as
gradient descent typically fail to reach good solutions. In this work we
suggest a method to improve gradient-based approaches to variational quantum
circuit optimization, which involves coupling the output of the quantum circuit
to a classical neural network. The effect of this neural network is to peturb
the cost landscape as a function of its parameters, so that local minima can be
escaped or avoided via a modification to the cost landscape itself. We present
two algorithms within this framework and numerically benchmark them on small
instances of the Max-Cut optimization problem. We show that the method is able
to reach deeper minima and lower cost values than standard gradient descent
based approaches. Moreover, our algorithms require essentially the same number
of quantum circuit evaluations per optimization step as the standard approach
since, unlike the gradient with respect to the circuit, the neural network
updates can be estimated in parallel via the backpropagation method. More
generally, our approach suggests that relaxing the cost landscape is a fruitful
path to improving near-term quantum computing algorithms.
