COQHONET CONNECTING QUANTUM HOPFIELD NETWORKS

Classical Neural Networks (NNs) are architectures successfully employed in Machine Learning (ML) tasks, such as pattern recognition, analysis of big data, and digitalization. Currently, a full development of quantum technologies is considered the most promising improvement on classical ML. Motivated by this, various contributions are focusing on the emerging field of quantum NNs, regarded as the backbones of quantum ML. Though strategic to tackle digitalization challenges of Europe concerning e.g. secure information, a unifying framework for quantum NNs is still missing. This project aims at contributing to the general effort of defining the main features of quantum NNs, and further exploiting them for practical purposes. More concretely, it considers quantum generalizations of associative memory-type NNs, such as the prototypical example referred to as Hopfield NN. To start with, associative memories can perform relatively easy tasks such as pattern retrieval. However, they are employed in more complex architectures too, as it is the case of Hopfield NNs when embedded in Boltzmann Machines. State-of-the-art quantum associative memories exploit quantum spin NNs and bosonic platforms, describing them as Markovian, or memory-less, open quantum systems. Importantly, these setups are relevant for condensed matter and photonic implementations. Inserting these proposals in a more general theoretical frame can provide insights to answer timely questions, such as storing non-classical states, accounting for non-Markovian effects on the retrieval task, characterizing the storage capacity. The challenge of this proposal consists in unveiling the bridge between Markovian quantum Hopfield-type NNs, and the formalism of quantum maps. Fulfilling such a gap further enables to use associative memories for designing near-term quantum devices that are robust to detrimental effects of the environment, which generically cause deterioration of e.g. coherence and entanglement.