Quantum Learning with Noise and Decoherence: A Robust Quantum Neural Network Noise and decoherence are two major obstacles to  :8,of largescale quantum computing. Because :8,of the  :16,which says we cannot make an exact copy :8,of an arbitrary quantum  :29,redundancy will not work in a quantum context, and unwanted  the :40,environment can destroy coherence and thus the quantum nature :8,of  Because :8,of the :52,parallel and distributed nature :8,of classical  :62,they  have long  :67,used to deal with incomplete or damaged data. In this   :78,show that our model :8,of a  :86,network (QNN) is similarly robust to noise, and that, in addition, it  to :99,decoherence. Moreover, robustness to noise and decoherence is  :109,maintained but improved as the size :8,of the system is increased. Noise  :122,may even be :8,of advantage in training, as it helps correct  :134,We demonstrate the robustness using entanglement as a means  :144,storage in a qubit array. Our results provide evidence that  :155,approaches can obviate otherwise recalcitrant problems in 

Supervised learning with a quantum classifier using multilevel systems We propose a quantum classifier, which can classify data under the supervised learning scheme using a quantum feature space. The input feature vectors are encoded in a single quNit (a Nlevel quantum system), as opposed to more commonly used entangled multiqubit systems. For training, we use the much used quantum variational algorithmxe2x80x94a hybrid quantumxe2x80x93classical algorithm, in which the forward part of the computation is performed on a quantum hardware, whereas the feedback part is carried out on a classical computer. We introduce xe2x80x9csingleshot trainingxe2x80x9d, where all input samples belonging to the same class are used to train the classifier simultaneously. This significantly speeds up the training procedure and provides an advantage over classical machine learning classifiers. We demonstrate successful classification of popular benchmark datasets with our quantum classifier and compare its performance with respect to classical machine learning classifiers. We also show that the number of training parameters in our classifier is significantly less than the classical classifiers.