Abstract
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.