SAMOP 2023 – scientific programme
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QI: Fachverband Quanteninformation
QI 3: Quantum Machine Learning
QI 3.4: Talk
Monday, March 6, 2023, 12:00–12:15, B305
Optimal storage capacity of quantum Hopfield neural networks — •Lukas Bödeker1,2, Eliana Fiorelli1,2,3, and Markus Müller1,2 — 1Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, 52428 Jülich, Germany — 2Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany — 3Instituto de Fisica Interdisciplinar y Sistemas Complejos (IFISC), CSIC UIB Campus, Palma de Mallorca, E-07122, Spain
Quantum neural networks form one pillar of the emergent field of quantum machine learning. Here, quantum generalisations of classical networks realizing associative memories - capable of retrieving patterns, or memories, from corrupted initial states - have been proposed. It is a challenging open problem to analyze quantum associative memories with an extensive number of patterns, and to determine the maximal number of patterns the quantum networks can reliably store, i.e. their storage capacity. In this work, we propose and explore a general method for evaluating the maximal storage capacity of quantum neural network models. As an example, we apply our method to an open-system quantum associative memory formed of interacting spin-1/2 particles realizing coupled artificial neurons. The system undergoes a Markovian time evolution resulting from a dissipative retrieval dynamics that competes with a coherent quantum dynamics. We map out the non-equilibrium phase diagram and study the effect of temperature and Hamiltonian dynamics on the storage capacity. Our method opens an avenue for a systematic characterization of the storage capacity of quantum associative memories.