  Noise and decoherence are two major obstacles to the implementation of
large-scale quantum computing. Because of the no-cloning theorem, which says we
cannot make an exact copy of an arbitrary quantum state, simple redundancy will
not work in a quantum context, and unwanted interactions with the environment
can destroy coherence and thus the quantum nature of the computation. Because
of the parallel and distributed nature of classical neural networks, they have
long been successfully used to deal with incomplete or damaged data. In this
work, we show that our model of a quantum neural network (QNN) is similarly
robust to noise, and that, in addition, it is robust to decoherence. Moreover,
robustness to noise and decoherence is not only maintained but improved as the
size of the system is increased. Noise and decoherence may even be of advantage
in training, as it helps correct for overfitting. We demonstrate the robustness
using entanglement as a means for pattern storage in a qubit array. Our results
provide evidence that machine learning approaches can obviate otherwise
recalcitrant problems in quantum computing.
