  The inherent noise and complexity of quantum communication networks leads to
challenges in designing quantum network protocols using classical methods. To
address this issue, we develop a variational quantum optimization framework
that simulates quantum networks on quantum hardware and optimizes the network
using differential programming techniques. We use our hybrid framework to
optimize nonlocality in noisy quantum networks. On the noisy IBM quantum
computers, we demonstrate our framework's ability to maximize quantum
nonlocality. On a classical simulator with a static noise model, we investigate
the noise robustness of quantum nonlocality with respect to unital and
nonunital channels. In both cases, we find that our optimization methods can
reproduce known results, while uncovering interesting phenomena. When unital
noise is present we find numerical evidence suggesting that maximally entangled
state preparations yield maximal nonlocality. When nonunital noise is present
we find that nonmaximally entangled states can yield maximal nonlocality. Thus,
we show that variational quantum optimization is a practical design tool for
quantum networks in the near-term. In the long-term, our variational quantum
optimization techniques show promise of scaling beyond classical approaches and
can be deployed on quantum network hardware to optimize quantum communication
protocols against their inherent noise.
